Tom Tango compares both UZR models with PMR at The Book Blog.

Dan Turkenkopf runs correlations of UZR and PMR and I find them surprisingly low, given the two systems use the same data.

Both PMR and UZR were calculated using the Baseball Info Solutions (BIS) data set this season. I wonder if David or MGL might be able to give some ideas as to where the differences might come from.

I don't know enough about the UZR calculations to speculate. I base my models mostly on visiting players in parks, however. UZR might use all the data. I also don't know if UZR, like +/-, doesn't penalize players for outs made by others. In PMR. If the right fielder catches a ball that the centerfielder might be able to catch, the centerfielder is penalized. In +/-, the centerfielder is not. Given the low correlation with centerfielders, I suspect that's the case.

The defensive charts for 2008 are now available here. These provide a nice visualization of the probabilistic model of range. Chase Utley's charts, for example, shows how well he does on ground balls toward first base.

Dan Turkenkopf takes the data from the PMR's look at defense behind the pitcher to see how many runs defense added to or removed from a pitcher's record per nine innings.

Billfer tries to explain the poor defense behind Nate Robertson and decides that batters were just very good at hitting balls in holes against the Tigers pitcher.

As we know, a pitcher's ERA can be influenced by the defense behind him. This posts explores which pitchers were helped or hurt by their defenses based on how well fielders turned balls in play into outs based on how difficult they were off the bat.

Team PMR, 2008, Defense Behind Pitchers, Visit Smooth Distance Model, 2008 data only

Pitcher	Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Chien-Ming Wang	NYY	306	215	200.92	0.703	0.657	107.01
Daisuke Matsuzaka	Bos	449	327	306.07	0.728	0.682	106.84
Jesse Litsch	Tor	569	407	382.14	0.715	0.672	106.51
Tim Wakefield	Bos	539	405	382.33	0.751	0.709	105.93
Ryan Rowland-Smith	Sea	366	262	249.06	0.716	0.680	105.20
Justin Duchscherer	Oak	409	308	292.97	0.753	0.716	105.13
CC Sabathia	Cle	334	228	217.23	0.683	0.650	104.96
Tim Hudson	Atl	435	317	302.69	0.729	0.696	104.73
Scott Kazmir	TB	378	277	264.57	0.733	0.700	104.70
Roy Oswalt	Hou	617	436	416.75	0.707	0.675	104.62
Jeremy Sowers	Cle	409	279	266.73	0.682	0.652	104.60
CC Sabathia	Mil	353	246	235.49	0.697	0.667	104.46
Armando Galarraga	Det	525	391	375.29	0.745	0.715	104.19
Greg Smith	Oak	578	423	406.63	0.732	0.704	104.03
John Lackey	LAA	469	329	316.59	0.701	0.675	103.92
Kyle Kendrick	Phi	560	380	365.69	0.679	0.653	103.91
Glen Perkins	Min	520	357	343.77	0.687	0.661	103.85
Ryan Dempster	ChC	572	406	391.16	0.710	0.684	103.80
Shaun Marcum	Tor	427	317	305.52	0.742	0.716	103.76
Paul Byrd	Cle	446	319	307.48	0.715	0.689	103.75
Brian Moehler	Hou	509	356	343.33	0.699	0.675	103.69
R.A. Dickey	Sea	374	263	253.88	0.703	0.679	103.59
Joe Saunders	LAA	623	445	429.72	0.714	0.690	103.56
Dustin McGowan	Tor	337	228	220.26	0.677	0.654	103.51
Adam Wainwright	StL	404	289	279.63	0.715	0.692	103.35
Josh Beckett	Bos	492	333	322.69	0.677	0.656	103.19
Jorge Campillo	Atl	490	347	336.39	0.708	0.687	103.16
Ben Sheets	Mil	589	417	404.45	0.708	0.687	103.10
John Lannan	Was	560	401	389.21	0.716	0.695	103.03
Zach Miner	Det	385	276	268.08	0.717	0.696	102.95
Kevin Slowey	Min	480	340	330.37	0.708	0.688	102.92
Vicente Padilla	Tex	524	356	345.93	0.679	0.660	102.91
Jake Peavy	SD	459	331	322.53	0.721	0.703	102.63
Jeremy Guthrie	Bal	587	428	417.45	0.729	0.711	102.53
Cole Hamels	Phi	635	464	453.13	0.731	0.714	102.40
David Bush	Mil	567	422	413.33	0.744	0.729	102.10
Paul Maholm	Pit	621	437	428.22	0.704	0.690	102.05
Jeff Francis	Col	469	321	314.83	0.684	0.671	101.96
John Danks	CWS	569	396	388.39	0.696	0.683	101.96
Scott Baker	Min	497	354	347.21	0.712	0.699	101.96
Roy Halladay	Tor	713	501	491.48	0.703	0.689	101.94
Matt Garza	TB	560	399	391.43	0.712	0.699	101.93
Micah Owings	Ari	312	220	215.84	0.705	0.692	101.93
Johan Santana	NYM	668	476	467.22	0.713	0.699	101.88
Scott Feldman	Tex	488	344	337.73	0.705	0.692	101.86
Oliver Perez	NYM	527	380	373.11	0.721	0.708	101.85
Derek Lowe	LAD	644	453	444.85	0.703	0.691	101.83
Scott Olsen	Fla	640	463	454.69	0.723	0.710	101.83
Felix Hernandez	Sea	577	391	384.12	0.678	0.666	101.79
Doug Davis	Ari	457	303	298.15	0.663	0.652	101.63
Edwin Jackson	TB	582	401	394.74	0.689	0.678	101.59
Dan Haren	Ari	610	421	414.60	0.690	0.680	101.54
Aaron Cook	Col	725	489	481.78	0.674	0.665	101.50
Kyle Lohse	StL	650	453	446.33	0.697	0.687	101.49
Jeff Suppan	Mil	589	407	401.18	0.691	0.681	101.45
Hiroki Kuroda	LAD	598	418	412.03	0.699	0.689	101.45
Dana Eveland	Oak	519	351	346.09	0.676	0.667	101.42
Jered Weaver	LAA	513	355	350.05	0.692	0.682	101.41
Todd Wellemeyer	StL	579	419	413.37	0.724	0.714	101.36
Carlos Zambrano	ChC	570	404	398.66	0.709	0.699	101.34
Jamie Moyer	Phi	625	437	431.36	0.699	0.690	101.31
Jon Garland	LAA	684	462	456.10	0.675	0.667	101.29
Braden Looper	StL	653	453	447.51	0.694	0.685	101.23
Miguel Batista	Sea	379	257	254.22	0.678	0.671	101.09
Jair Jurrjens	Atl	589	401	397.07	0.681	0.674	100.99
Matt Cain	SF	630	436	431.93	0.692	0.686	100.94
Kevin Correia	SF	382	248	245.75	0.649	0.643	100.91
Gavin Floyd	CWS	625	450	446.51	0.720	0.714	100.78
Javier Vazquez	CWS	598	405	401.92	0.677	0.672	100.77
Tim Lincecum	SF	562	385	382.12	0.685	0.680	100.75
Jason Marquis	ChC	554	390	387.25	0.704	0.699	100.71
Aaron Harang	Cin	552	379	376.37	0.687	0.682	100.70
Jose Contreras	CWS	402	280	278.09	0.697	0.692	100.69
Johnny Cueto	Cin	500	344	341.79	0.688	0.684	100.65
Joel Pineiro	StL	505	342	339.90	0.677	0.673	100.62
Brad Penny	LAD	311	212	211.06	0.682	0.679	100.45
Jon Lester	Bos	632	438	436.20	0.693	0.690	100.41
Boof Bonser	Min	382	249	248.24	0.652	0.650	100.31
Greg Maddux	SD	511	360	359.16	0.705	0.703	100.23
Aaron Laffey	Cle	316	217	216.67	0.687	0.686	100.15
Manny Parra	Mil	499	322	321.73	0.645	0.645	100.08
Gil Meche	KC	611	420	419.79	0.687	0.687	100.05
Mike Mussina	NYY	613	409	409.01	0.667	0.667	100.00
Jarrod Washburn	Sea	512	350	350.13	0.684	0.684	99.96
Chad Billingsley	LAD	556	370	370.36	0.665	0.666	99.90
Cliff Lee	Cle	670	462	462.50	0.690	0.690	99.89
Zack Greinke	KC	587	399	399.62	0.680	0.681	99.84
Ted Lilly	ChC	574	412	412.67	0.718	0.719	99.84
Tim Redding	Was	572	397	397.98	0.694	0.696	99.75
Wandy Rodriguez	Hou	393	266	266.71	0.677	0.679	99.74
Andy Sonnanstine	TB	632	432	433.24	0.684	0.686	99.71
Chris Sampson	Hou	383	267	267.83	0.697	0.699	99.69
Daniel Cabrera	Bal	594	409	410.64	0.689	0.691	99.60
Bronson Arroyo	Cin	605	408	409.76	0.674	0.677	99.57
Joe Blanton	Oak	440	303	304.31	0.689	0.692	99.57
Jason Bergmann	Was	445	310	311.45	0.697	0.700	99.53
Brandon Webb	Ari	671	458	460.45	0.683	0.686	99.47
Ervin Santana	LAA	605	422	424.34	0.698	0.701	99.45
Zach Duke	Pit	669	445	447.62	0.665	0.669	99.42
Kenny Rogers	Det	598	400	402.42	0.669	0.673	99.40
Ubaldo Jimenez	Col	572	395	397.49	0.691	0.695	99.37
Carlos Silva	Sea	564	365	367.36	0.647	0.651	99.36
Nate Robertson	Det	563	365	367.59	0.648	0.653	99.30
Jo-Jo Reyes	Atl	361	241	242.79	0.668	0.673	99.26
Clayton Kershaw	LAD	306	204	205.65	0.667	0.672	99.20
Ricky Nolasco	Fla	606	432	435.96	0.713	0.719	99.09
James Shields	TB	641	448	452.73	0.699	0.706	98.96
Justin Verlander	Det	598	415	419.47	0.694	0.701	98.93
Mike Pelfrey	NYM	652	446	450.98	0.684	0.692	98.89
Randy Johnson	Ari	531	359	363.22	0.676	0.684	98.84
Kyle Davies	KC	361	248	251.20	0.687	0.696	98.73
Edinson Volquez	Cin	511	350	354.63	0.685	0.694	98.69
Nick Blackburn	Min	658	445	451.38	0.676	0.686	98.59
John Maine	NYM	399	286	290.11	0.717	0.727	98.58
Pedro Martinez	NYM	337	225	228.38	0.668	0.678	98.52
A.J. Burnett	Tor	613	405	411.37	0.661	0.671	98.45
Jorge de la Rosa	Col	361	240	243.99	0.665	0.676	98.37
Mark Hendrickson	Fla	439	302	307.04	0.688	0.699	98.36
Brian Burres	Bal	460	309	314.46	0.672	0.684	98.26
Kevin Millwood	Tex	569	360	366.45	0.633	0.644	98.24
Brian Bannister	KC	603	408	415.51	0.677	0.689	98.19
Luke Hochevar	KC	430	291	297.11	0.677	0.691	97.94
Randy Wolf	SD	348	237	242.07	0.681	0.696	97.91
Brandon Backe	Hou	512	341	348.41	0.666	0.680	97.87
Barry Zito	SF	576	393	401.59	0.682	0.697	97.86
Cha Seung Baek	SD	353	238	243.40	0.674	0.690	97.78
Brett Myers	Phi	554	379	388.08	0.684	0.701	97.66
Mark Buehrle	CWS	699	466	477.66	0.667	0.683	97.56
Odalis Perez	Was	507	337	345.85	0.665	0.682	97.44
Andrew Miller	Fla	336	216	222.12	0.643	0.661	97.24
Tom Gorzelanny	Pit	332	225	231.65	0.678	0.698	97.13
Jonathan Sanchez	SF	442	297	306.08	0.672	0.692	97.03
Livan Hernandez	Min	525	339	349.78	0.646	0.666	96.92
Garrett Olson	Bal	451	295	304.47	0.654	0.675	96.89
Carlos Villanueva	Mil	320	220	228.02	0.688	0.713	96.48
Ian Snell	Pit	522	335	347.60	0.642	0.666	96.38
Andy Pettitte	NYY	641	420	439.26	0.655	0.685	95.62
Darrell Rasner	NYY	387	257	269.56	0.664	0.697	95.34
Adam Eaton	Phi	356	236	248.23	0.663	0.697	95.07
Fausto Carmona	Cle	405	273	288.06	0.674	0.711	94.77

Those are pretty impressive numbers for Daisuke Matsuzaka and Tim Wakefield. Not only were balls in play against them easy to field, the Red Sox did a great job of turning them into outs. For Yankees fans who are concerned about New York signing Andy Pettitte again, better defense would improve Andy's runs allowed a great deal. CC Sabathia certainly benefitted from good defense in both Cleveland and Milwaukee, so teams looking to sign him should be prepared to send their best fielders out behind the lefty.

Brian Bannister shows how important defense is to a low strikeout pitcher. His expected DER is low, and with the Royals doing a poor job fielding behind him, his actual DER was even lower. Bannister really needs to play for a team of defensive wizards.

The survey of the positions ends with the pitchers. First the teams:

Team Pitchers PMR, 2008, Visit Smooth Distance Model, 2008 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Blue Jays	4215	181	161.32	0.043	0.038	112.20
Tigers	4536	187	171.99	0.041	0.038	108.72
Padres	4419	217	202.55	0.049	0.046	107.13
Royals	4413	170	161.90	0.039	0.037	105.00
Mariners	4512	161	154.23	0.036	0.034	104.39
Twins	4607	190	183.22	0.041	0.040	103.70
Mets	4335	200	192.92	0.046	0.045	103.67
Nationals	4417	193	186.24	0.044	0.042	103.63
Dodgers	4265	217	209.44	0.051	0.049	103.61
Cubs	4156	179	174.74	0.043	0.042	102.44
Phillies	4396	198	193.35	0.045	0.044	102.40
Rockies	4535	204	201.22	0.045	0.044	101.38
Cardinals	4597	205	203.96	0.045	0.044	100.51
Braves	4383	213	211.93	0.049	0.048	100.51
Indians	4513	169	168.95	0.037	0.037	100.03
Astros	4292	159	160.96	0.037	0.038	98.78
Marlins	4338	162	164.14	0.037	0.038	98.70
Red Sox	4232	154	156.88	0.036	0.037	98.17
Diamondbacks	4224	193	196.62	0.046	0.047	98.16
Pirates	4683	211	215.78	0.045	0.046	97.78
White Sox	4409	190	194.51	0.043	0.044	97.68
Rangers	4667	178	184.54	0.038	0.040	96.46
Angels	4374	148	154.21	0.034	0.035	95.97
Reds	4299	174	181.34	0.040	0.042	95.95
Orioles	4540	152	158.73	0.033	0.035	95.76
Yankees	4349	186	194.41	0.043	0.045	95.67
Athletics	4285	142	149.52	0.033	0.035	94.97
Rays	4264	114	124.63	0.027	0.029	91.47
Giants	4232	142	156.07	0.034	0.037	90.98
Brewers	4354	183	205.85	0.042	0.047	88.90

The Blue Jays not only posted an excellent team ERA, but helped themselves defensively as well. The Brewers staff depended more on the fielders behind them. In looking at the individuals, experience appears to be a key to doing well:

Individual Pitchers PMR, 2008, Visit Smooth Distance Model, 2008 data only (500 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Jesse Litsch	569	39	24.20	0.069	0.043	161.16
Greg Maddux	649	59	39.59	0.091	0.061	149.04
Kenny Rogers	598	56	38.39	0.094	0.064	145.87
Livan Hernandez	674	31	22.40	0.046	0.033	138.39
Javier Vazquez	598	29	21.39	0.048	0.036	135.61
Felix Hernandez	577	32	24.02	0.055	0.042	133.25
Jeremy Guthrie	587	23	17.74	0.039	0.030	129.67
Jon Garland	684	31	24.42	0.045	0.036	126.92
Justin Verlander	598	23	18.21	0.038	0.030	126.33
Gil Meche	611	28	22.50	0.046	0.037	124.43
Kyle Kendrick	560	32	26.17	0.057	0.047	122.28
Zack Greinke	587	26	21.34	0.044	0.036	121.86
Bronson Arroyo	605	32	26.95	0.053	0.045	118.72
Cole Hamels	635	35	29.59	0.055	0.047	118.30
Joel Pineiro	505	28	23.71	0.055	0.047	118.07
Tim Wakefield	539	16	13.55	0.030	0.025	118.07
Tim Redding	572	22	18.86	0.038	0.033	116.64
Jason Marquis	554	35	30.06	0.063	0.054	116.42
Ryan Dempster	572	36	31.12	0.063	0.054	115.67
Joe Saunders	623	31	27.14	0.050	0.044	114.24
Glen Perkins	520	23	20.25	0.044	0.039	113.58
Vicente Padilla	524	20	17.70	0.038	0.034	113.02
Roy Oswalt	617	31	27.46	0.050	0.045	112.90
Brandon Webb	671	54	48.10	0.080	0.072	112.27
Aaron Cook	725	44	40.31	0.061	0.056	109.15
Jeff Suppan	589	28	25.91	0.048	0.044	108.06
Scott Olsen	640	20	18.55	0.031	0.029	107.84
Jair Jurrjens	589	37	34.69	0.063	0.059	106.66
Gavin Floyd	625	26	24.44	0.042	0.039	106.39
Zach Duke	669	37	35.21	0.055	0.053	105.09
Oliver Perez	527	17	16.28	0.032	0.031	104.42
Barry Zito	576	20	19.28	0.035	0.033	103.75
Paul Maholm	621	31	29.90	0.050	0.048	103.69
Matt Cain	630	27	26.14	0.043	0.041	103.30
Andy Sonnanstine	632	20	19.44	0.032	0.031	102.89
Hiroki Kuroda	598	39	37.92	0.065	0.063	102.84
Jon Lester	632	21	20.46	0.033	0.032	102.63
Kevin Millwood	569	25	24.56	0.044	0.043	101.80
Greg Smith	578	16	15.75	0.028	0.027	101.56
Brett Myers	554	23	22.85	0.042	0.041	100.64
Ted Lilly	574	15	15.03	0.026	0.026	99.79
Brian Bannister	603	30	30.11	0.050	0.050	99.63
Jamie Moyer	625	20	20.19	0.032	0.032	99.04
John Danks	569	24	24.25	0.042	0.043	98.97
Jarrod Washburn	512	20	20.39	0.039	0.040	98.07
Ubaldo Jimenez	572	35	35.69	0.061	0.062	98.06
Edinson Volquez	511	24	24.49	0.047	0.048	98.02
Mike Pelfrey	652	29	29.63	0.044	0.045	97.88
Kyle Lohse	650	30	30.67	0.046	0.047	97.81
CC Sabathia	687	27	27.67	0.039	0.040	97.59
Paul Byrd	608	17	17.52	0.028	0.029	97.04
Roy Halladay	713	31	32.28	0.043	0.045	96.03
Derek Lowe	644	39	40.83	0.061	0.063	95.52
Chad Billingsley	556	21	22.07	0.038	0.040	95.14
Joe Blanton	652	25	26.28	0.038	0.040	95.13
Odalis Perez	507	23	24.23	0.045	0.048	94.93
Dana Eveland	519	17	17.94	0.033	0.035	94.76
John Lannan	560	29	30.68	0.052	0.055	94.53
Armando Galarraga	525	13	14.04	0.025	0.027	92.57
Mike Mussina	613	28	30.47	0.046	0.050	91.88
Johan Santana	668	30	32.68	0.045	0.049	91.81
Ian Snell	522	21	23.11	0.040	0.044	90.85
Jered Weaver	513	10	11.02	0.019	0.021	90.71
Brandon Backe	512	16	18.01	0.031	0.035	88.85
Todd Wellemeyer	579	15	16.95	0.026	0.029	88.51
Carlos Zambrano	570	23	26.30	0.040	0.046	87.45
Nick Blackburn	658	24	27.47	0.036	0.042	87.36
Mark Buehrle	699	27	31.03	0.039	0.044	87.02
A.J. Burnett	613	24	27.68	0.039	0.045	86.70
James Shields	641	19	21.96	0.030	0.034	86.52
Carlos Silva	564	14	16.40	0.025	0.029	85.36
Dan Haren	610	24	28.16	0.039	0.046	85.21
Matt Garza	560	15	17.82	0.027	0.032	84.18
Edwin Jackson	582	12	14.35	0.021	0.025	83.61
Johnny Cueto	500	18	21.67	0.036	0.043	83.08
Ervin Santana	605	18	22.09	0.030	0.037	81.49
Ricky Nolasco	606	17	21.08	0.028	0.035	80.65
Nate Robertson	563	20	24.99	0.036	0.044	80.03
Randy Wolf	557	25	31.51	0.045	0.057	79.34
Tim Lincecum	562	17	21.44	0.030	0.038	79.28
Braden Looper	653	20	25.71	0.031	0.039	77.80
Brian Moehler	509	12	15.68	0.024	0.031	76.53
Aaron Harang	552	13	17.37	0.024	0.031	74.84
David Bush	567	18	24.87	0.032	0.044	72.37
Randy Johnson	531	12	16.86	0.023	0.032	71.17
Andy Pettitte	641	22	30.94	0.034	0.048	71.11
Cliff Lee	670	17	28.39	0.025	0.042	59.89
Daniel Cabrera	594	11	18.98	0.019	0.032	57.95
Ben Sheets	589	14	24.34	0.024	0.041	57.52

Jesse Litsch is young, but 2-4 are all veterans, and Maddux seems to come out near the top quite often. Mike Mussina, however, did not appear to deserve his gold glove. Remember to take this ranking with a grain of salt, since pitchers are not in the field that often compared to position players, and get many fewer chances to field balls. Luck is a much bigger factor in this group.

Dan Turkenkopf calculates runs allowed or saved for leftfielders based on their PMR stats.

Update: Here are the runs for first basemen as well.

Our survey of the positions continues with catchers. Catchers don't field very many balls, so take these rankings with a grain of salt. First, the teams:

Team Catchers PMR, 2008, Visit Smooth Distance Model, 2008 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Brewers	4354	71	63.52	0.016	0.015	111.78
Mets	4335	54	48.85	0.012	0.011	110.53
Astros	4292	41	37.24	0.010	0.009	110.11
Pirates	4683	53	48.61	0.011	0.010	109.03
Twins	4607	45	41.93	0.010	0.009	107.32
Yankees	4349	56	52.39	0.013	0.012	106.89
Rangers	4667	49	46.47	0.010	0.010	105.44
Rockies	4535	58	55.02	0.013	0.012	105.42
Orioles	4540	41	39.10	0.009	0.009	104.86
Phillies	4396	58	56.28	0.013	0.013	103.06
Braves	4383	63	61.73	0.014	0.014	102.07
Diamondbacks	4224	50	49.19	0.012	0.012	101.65
Nationals	4417	34	33.64	0.008	0.008	101.08
Padres	4419	64	63.44	0.014	0.014	100.88
Mariners	4512	42	42.22	0.009	0.009	99.47
Dodgers	4265	38	38.45	0.009	0.009	98.82
Blue Jays	4215	57	57.84	0.014	0.014	98.54
Angels	4374	44	44.74	0.010	0.010	98.35
Tigers	4536	58	59.27	0.013	0.013	97.86
White Sox	4409	39	39.88	0.009	0.009	97.80
Giants	4232	48	49.80	0.011	0.012	96.38
Rays	4264	50	51.91	0.012	0.012	96.32
Red Sox	4232	51	53.09	0.012	0.013	96.07
Royals	4413	49	51.24	0.011	0.012	95.62
Marlins	4338	58	60.75	0.013	0.014	95.47
Indians	4513	45	47.90	0.010	0.011	93.94
Cardinals	4597	47	50.66	0.010	0.011	92.78
Athletics	4285	28	31.42	0.007	0.007	89.12
Reds	4299	52	60.30	0.012	0.014	86.23
Cubs	4156	42	51.03	0.010	0.012	82.31

It looks like the Mets trade for Brian Schneider turned out to be a good one from a defensive standpoint. It also looks like rookie of the year Geovany Soto might have some things to learn behind the plate. Let's look at the individuals:

Individual Catchers PMR, 2008, Visit Smooth Distance Model, 2008 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Wil Nieves	1327	14	9.94	0.011	0.007	140.90
J.R. Towles	1252	8	6.01	0.006	0.005	133.04
Kevin Cash	1131	14	10.77	0.012	0.010	129.95
Ryan Doumit	2933	31	26.57	0.011	0.009	116.66
Carlos Ruiz	2517	42	36.54	0.017	0.015	114.95
Guillermo Quiroz	1176	8	7.01	0.007	0.006	114.11
Chris Iannetta	2633	35	30.83	0.013	0.012	113.52
Humberto Quintero	1321	15	13.41	0.011	0.010	111.87
Victor Martinez	1388	16	14.48	0.012	0.010	110.53
Jason Kendall	3988	67	60.93	0.017	0.015	109.97
Jason LaRue	1288	16	14.58	0.012	0.011	109.72
Joe Mauer	3805	41	37.60	0.011	0.010	109.03
Ramon Castro	1041	14	12.97	0.013	0.012	107.97
Gregg Zaun	1807	30	28.04	0.017	0.016	106.97
Dioner Navarro	2911	38	35.59	0.013	0.012	106.77
Ivan Rodriguez	2947	42	39.65	0.014	0.013	105.93
Brian Schneider	2575	30	28.52	0.012	0.011	105.19
Jeff Mathis	2351	33	31.46	0.014	0.013	104.90
Josh Bard	1253	21	20.28	0.017	0.016	103.56
Ramon Hernandez	3272	33	32.09	0.010	0.010	102.83
Miguel Montero	1191	15	14.77	0.013	0.012	101.53
Chris Snyder	2733	33	32.54	0.012	0.012	101.41
Brad Ausmus	1719	18	17.82	0.010	0.010	101.04
Gerald Laird	2419	24	23.76	0.010	0.010	101.00
Jarrod Saltalamacchia	1470	17	16.85	0.012	0.011	100.90
Jose Molina	2152	23	22.80	0.011	0.011	100.89
Brandon Inge	1541	21	21.16	0.014	0.014	99.24
A.J. Pierzynski	3428	31	31.53	0.009	0.009	98.31
Brian McCann	3470	49	50.81	0.014	0.015	96.44
Miguel Olivo	1509	19	19.85	0.013	0.013	95.70
John Buck	2902	30	31.39	0.010	0.011	95.57
Yorvit Torrealba	1819	21	22.19	0.012	0.012	94.65
Kurt Suzuki	3608	25	26.45	0.007	0.007	94.50
Matt Treanor	1561	23	24.36	0.015	0.016	94.43
Nick Hundley	1482	18	19.13	0.012	0.013	94.11
Bengie Molina	3272	36	39.00	0.011	0.012	92.31
Geovany Soto	3302	34	37.47	0.010	0.011	90.75
Rod Barajas	2262	24	26.60	0.011	0.012	90.24
Russell Martin	3655	31	34.63	0.008	0.009	89.52
Jason Varitek	3002	37	42.26	0.012	0.014	87.56
Jesus Flores	2116	13	15.03	0.006	0.007	86.52
David Ross	1238	17	19.69	0.014	0.016	86.35
Kenji Johjima	2617	20	23.53	0.008	0.009	85.01
Yadier Molina	3185	29	34.24	0.009	0.011	84.70
Mike Napoli	1931	10	12.08	0.005	0.006	82.77
Paul Bako	2272	20	24.25	0.009	0.011	82.48
Kelly Shoppach	2774	25	30.66	0.009	0.011	81.54
John Baker	1477	13	15.96	0.009	0.011	81.46
Chris Coste	1853	15	18.62	0.008	0.010	80.57
Shawn Riggans	1041	11	14.08	0.011	0.014	78.12

Here's another reason Joe Mauer gets my vote for AL MVP. He's not only a great offensive catcher, but he fields his position well also. For those teams interested in Jason Varitek, his ranking here is certainly another strike against him.

It's also interesting to note that Jarrod Saltalamacchia wasn't terrible behind the plate. I know there's much more to the position than the ability to field, but in this regard, Saltalamacchia shows a positive behind the plate.

The Probabilistic Model of Range survey continues with first basemen:

Team First Basemen PMR, 2008, Visit Smooth Distance Model, 2008 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Cardinals	4597	363	330.17	0.079	0.072	109.94
Rays	4264	337	309.47	0.079	0.073	108.90
Astros	4292	352	334.44	0.082	0.078	105.25
Angels	4374	348	332.57	0.080	0.076	104.64
Reds	4299	340	326.62	0.079	0.076	104.10
Orioles	4540	330	317.28	0.073	0.070	104.01
Braves	4383	309	301.26	0.070	0.069	102.57
Giants	4232	306	298.46	0.072	0.071	102.53
Mariners	4512	312	305.65	0.069	0.068	102.08
Padres	4419	314	308.13	0.071	0.070	101.90
Athletics	4285	287	282.84	0.067	0.066	101.47
Cubs	4156	339	334.40	0.082	0.080	101.38
Mets	4335	323	319.48	0.075	0.074	101.10
Pirates	4683	293	290.12	0.063	0.062	100.99
White Sox	4409	295	292.85	0.067	0.066	100.73
Red Sox	4232	300	298.07	0.071	0.070	100.65
Blue Jays	4215	346	345.24	0.082	0.082	100.22
Rangers	4667	292	292.72	0.063	0.063	99.75
Dodgers	4265	288	290.00	0.068	0.068	99.31
Rockies	4535	311	318.74	0.069	0.070	97.57
Phillies	4396	335	345.93	0.076	0.079	96.84
Tigers	4536	258	267.90	0.057	0.059	96.31
Brewers	4354	299	311.39	0.069	0.072	96.02
Royals	4413	270	282.47	0.061	0.064	95.58
Nationals	4417	279	292.73	0.063	0.066	95.31
Indians	4513	276	290.25	0.061	0.064	95.09
Yankees	4349	270	286.22	0.062	0.066	94.33
Marlins	4338	296	314.60	0.068	0.073	94.09
Diamondbacks	4224	292	311.45	0.069	0.074	93.76
Twins	4607	262	283.33	0.057	0.061	92.47

As you might expect from the ranking of the top two National League teams, Pujols and Berkman competed with the glove as well as the bat:

Individual First Basemen PMR, 2008, Visit Smooth Distance Model, 2008 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Albert Pujols	3833	310	275.70	0.081	0.072	112.44
Carlos Pena	3428	272	250.39	0.079	0.073	108.63
Rich Aurilia	1398	94	88.21	0.067	0.063	106.57
Lance Berkman	3899	329	309.21	0.084	0.079	106.40
Mark Teixeira	4009	322	302.91	0.080	0.076	106.30
Kevin Millar	3607	264	250.96	0.073	0.070	105.20
Joey Votto	3686	300	285.79	0.081	0.078	104.97
Todd Helton	2272	165	158.79	0.073	0.070	103.91
Casey Kotchman	3659	268	259.14	0.073	0.071	103.42
Paul Konerko	3069	214	207.95	0.070	0.068	102.91
Kevin Youkilis	2835	212	206.26	0.075	0.073	102.78
Adrian Gonzalez	4302	307	300.33	0.071	0.070	102.22
Derrek Lee	3848	322	315.59	0.084	0.082	102.03
Daric Barton	3322	211	207.92	0.064	0.063	101.48
Carlos Delgado	4088	306	305.60	0.075	0.075	100.13
Lyle Overbay	3919	330	329.98	0.084	0.084	100.01
James Loney	4023	267	267.57	0.066	0.067	99.79
Chris Davis	1295	81	81.23	0.063	0.063	99.72
Miguel Cairo	1223	84	84.91	0.069	0.069	98.93
Adam LaRoche	3647	224	226.60	0.061	0.062	98.85
Aaron Boone	1040	61	62.74	0.059	0.060	97.23
Richie Sexson	2103	133	137.24	0.063	0.065	96.91
Ryan Howard	4254	322	336.79	0.076	0.079	95.61
Nick Swisher	1340	81	84.91	0.060	0.063	95.40
Prince Fielder	4133	280	293.92	0.068	0.071	95.26
Chad Tracy	1496	110	115.89	0.074	0.077	94.92
Ross Gload	2727	163	171.75	0.060	0.063	94.91
John Bowker	1607	104	110.60	0.065	0.069	94.03
Miguel Cabrera	3772	220	234.22	0.058	0.062	93.93
Ryan Garko	3323	198	211.16	0.060	0.064	93.77
Conor Jackson	1696	109	117.40	0.064	0.069	92.85
Sean Casey	1042	65	70.15	0.062	0.067	92.65
Justin Morneau	4289	242	261.41	0.056	0.061	92.57
Jason Giambi	2795	164	177.51	0.059	0.064	92.39
Garrett Atkins	1638	101	110.77	0.062	0.068	91.18
Mike Jacobs	2860	175	194.95	0.061	0.068	89.77

Year after year Albert Pujols shows his defensive skill at first base. Lance Berkman is up there, also, making the MVP argument between the two that much closer. Mark Teixeira also offers an excellent glove to go along with his fine offense.

The most surprising ranking to me, however, is Justin Morneau. Justin is still young and shouldn't have lost a step. He's someone worth looking at in more detail. Of course, at the very bottom is Mike Jacobs, giving Royals fans another reason to dislike the trade.

Dan Turkenkopf list PMR Runs for rightfielders.

Dan Turkenkopf continues to translate PMR stats into runs, taking on third basemen this time.

The survery of range continues with leftfielders. The following table shows how the thirty teams fared at the position:

Team Leftfielders PMR, 2008, Visit Smooth Distance Model, 2008 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Royals	4413	368	353.21	0.083	0.080	104.19
Indians	4513	302	290.89	0.067	0.064	103.82
Rays	4264	344	331.81	0.081	0.078	103.67
Nationals	4417	350	339.72	0.079	0.077	103.03
Mets	4335	308	299.09	0.071	0.069	102.98
Diamondbacks	4224	306	298.79	0.072	0.071	102.41
Braves	4383	279	273.49	0.064	0.062	102.02
Brewers	4354	305	299.07	0.070	0.069	101.98
White Sox	4409	293	287.74	0.066	0.065	101.83
Rangers	4667	323	317.21	0.069	0.068	101.83
Orioles	4540	362	355.59	0.080	0.078	101.80
Athletics	4285	333	328.28	0.078	0.077	101.44
Astros	4292	282	278.71	0.066	0.065	101.18
Padres	4419	310	306.42	0.070	0.069	101.17
Cardinals	4597	312	308.84	0.068	0.067	101.02
Red Sox	4232	292	291.37	0.069	0.069	100.22
Dodgers	4265	286	285.62	0.067	0.067	100.13
Tigers	4536	356	355.77	0.078	0.078	100.06
Giants	4232	308	308.26	0.073	0.073	99.92
Yankees	4349	316	316.76	0.073	0.073	99.76
Angels	4374	285	286.29	0.065	0.065	99.55
Cubs	4156	302	304.23	0.073	0.073	99.27
Blue Jays	4215	270	272.75	0.064	0.065	98.99
Pirates	4683	293	299.34	0.063	0.064	97.88
Reds	4299	280	288.41	0.065	0.067	97.08
Rockies	4535	282	290.95	0.062	0.064	96.92
Marlins	4338	289	299.06	0.067	0.069	96.64
Mariners	4512	324	336.18	0.072	0.075	96.38
Twins	4607	306	327.83	0.066	0.071	93.34
Phillies	4396	260	279.09	0.059	0.063	93.16

As in rightfield, there doesn't seem to be a huge correlation between doing well in left and winning. The Royals displayed the best defense at the position, while the Phillies came out at the bottom of the pack.

The list of individuals in left shows that very few teams employ a regular at the position:

Individual Leftfielder PMR, 2008, Visit Smooth Distance Model, 2008 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Skip Schumaker	1085	85	73.79	0.078	0.068	115.20
David DeJesus	1522	136	121.91	0.089	0.080	111.56
Brandon Boggs	1818	131	118.10	0.072	0.065	110.92
Matt Joyce	1249	94	84.77	0.075	0.068	110.89
Ben Francisco	2021	150	138.34	0.074	0.068	108.43
Juan Pierre	1816	125	116.83	0.069	0.064	107.00
Willie Harris	1685	145	135.55	0.086	0.080	106.97
Carl Crawford	2715	231	217.97	0.085	0.080	105.98
Conor Jackson	1944	146	139.06	0.075	0.072	104.99
Gregor Blanco	1547	86	82.08	0.056	0.053	104.78
Jay Payton	1293	132	126.31	0.102	0.098	104.51
Luke Scott	2668	200	196.08	0.075	0.073	102.00
Johnny Damon	1998	155	152.00	0.078	0.076	101.97
Ryan Braun	3919	275	270.93	0.070	0.069	101.50
Wily Mo Pena	1260	99	97.68	0.079	0.078	101.35
Carlos Lee	2840	187	185.42	0.066	0.065	100.85
David Dellucci	1164	75	74.64	0.064	0.064	100.48
Adam Dunn	2942	210	209.06	0.071	0.071	100.45
Alfonso Soriano	2653	186	185.23	0.070	0.070	100.42
Fred Lewis	2622	178	177.57	0.068	0.068	100.24
Carlos Quentin	3465	228	228.42	0.066	0.066	99.81
Jack Cust	1753	129	129.74	0.074	0.074	99.43
Emil Brown	1229	89	89.70	0.072	0.073	99.21
Chase Headley	2159	156	157.62	0.072	0.073	98.97
Matt Holliday	3850	240	243.20	0.062	0.063	98.68
Manny Ramirez	2894	190	193.40	0.066	0.067	98.24
Adam Lind	1712	113	115.52	0.066	0.067	97.81
Xavier Nady	1212	87	89.04	0.072	0.073	97.71
Chris Duncan	1012	73	74.80	0.072	0.074	97.59
Raul Ibanez	4203	303	312.07	0.072	0.074	97.09
Garret Anderson	2113	144	148.53	0.068	0.070	96.95
Jose Guillen	1098	83	85.62	0.076	0.078	96.94
Luis Gonzalez	1547	105	109.32	0.068	0.071	96.05
David Murphy	1317	86	89.62	0.065	0.068	95.96
Josh Willingham	2551	166	173.80	0.065	0.068	95.51
Eric Byrnes	1209	76	80.12	0.063	0.066	94.86
Jason Bay	4215	254	268.19	0.060	0.064	94.71
Marcus Thames	1537	120	127.42	0.078	0.083	94.18
Delmon Young	4209	282	301.19	0.067	0.072	93.63
Pat Burrell	3646	202	223.39	0.055	0.061	90.42

Ryan Braun is the first player on the list on the field in left for over 3000 balls in play. Some of this was caused by injuries (Soriano, Matsui), but for the most part, managers mix and match at the position. The move to left was clearly the right one for Braun.

The other rankings of note belong to Manny Ramirez and Jason Bay. Manny actually did better than Jason in 2008. I'm going to need to break down the two by team to see how much the parks might have made a difference. Bay certainly looked better than Manny watching him play for the Red Sox.

All those late inning substitutions Charlie Manuel made for Pat Burrell looked proper, also. Pat ranks as the worst leftfielder in baseball in 2008, so it's no wonder Charlie wanted a better glove in left when the Phillies had the lead late.

The Probabilistic Model of Range reports continue with rightfielders. First, the team data:

Team Rightfielders PMR, 2008, Visit Smooth Distance Model, 2008 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Twins	4607	397	374.04	0.086	0.081	106.14
Blue Jays	4215	303	286.97	0.072	0.068	105.58
Giants	4232	392	372.99	0.093	0.088	105.10
Indians	4513	374	358.85	0.083	0.080	104.22
Padres	4419	339	329.60	0.077	0.075	102.85
Phillies	4396	318	310.41	0.072	0.071	102.45
Red Sox	4232	325	318.64	0.077	0.075	102.00
Braves	4383	313	307.02	0.071	0.070	101.95
Rangers	4667	382	375.27	0.082	0.080	101.79
Nationals	4417	353	346.81	0.080	0.079	101.78
Marlins	4338	345	340.25	0.080	0.078	101.40
Cubs	4156	333	329.14	0.080	0.079	101.17
Cardinals	4597	362	360.58	0.079	0.078	100.39
Diamondbacks	4224	269	268.33	0.064	0.064	100.25
Athletics	4285	377	376.50	0.088	0.088	100.13
Mariners	4512	309	310.73	0.068	0.069	99.44
Dodgers	4265	278	279.64	0.065	0.066	99.41
Brewers	4354	316	318.38	0.073	0.073	99.25
Pirates	4683	386	389.32	0.082	0.083	99.15
Royals	4413	334	336.94	0.076	0.076	99.13
Orioles	4540	338	341.58	0.074	0.075	98.95
Mets	4335	356	360.14	0.082	0.083	98.85
Astros	4292	357	365.06	0.083	0.085	97.79
Rays	4264	345	354.99	0.081	0.083	97.19
Reds	4299	327	338.05	0.076	0.079	96.73
Tigers	4536	301	311.48	0.066	0.069	96.64
White Sox	4409	296	308.31	0.067	0.070	96.01
Angels	4374	308	322.64	0.070	0.074	95.46
Yankees	4349	301	316.77	0.069	0.073	95.02
Rockies	4535	249	273.59	0.055	0.060	91.01

It seems rightfielder defense didn't have that much influence on playoff teams. Five of the eight post-season teams finished in the bottom half of the majors. Here's a look at the individuals:

Individual Rightfielder PMR, 2008, Visit Smooth Distance Model, 2008 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Alex Rios	2373	170	156.05	0.072	0.066	108.94
Denard Span	2099	192	176.27	0.091	0.084	108.92
Franklin Gutierrez	2400	224	207.25	0.093	0.086	108.08
Jayson Werth	1964	143	133.49	0.073	0.068	107.12
Randy Winn	3247	309	291.22	0.095	0.090	106.10
Matt Kemp	1391	97	91.48	0.070	0.066	106.04
Endy Chavez	1176	109	103.84	0.093	0.088	104.97
Austin Kearns	2268	187	179.28	0.082	0.079	104.30
Michael Cuddyer	1640	123	118.33	0.075	0.072	103.95
Justin Upton	2531	175	168.66	0.069	0.067	103.76
Kosuke Fukudome	3164	246	240.12	0.078	0.076	102.45
Jeff Francoeur	4016	284	278.05	0.071	0.069	102.14
David Murphy	1279	107	104.84	0.084	0.082	102.06
Ryan Sweeney	1462	136	133.41	0.093	0.091	101.94
Ichiro Suzuki	2491	176	172.83	0.071	0.069	101.83
Mark Teahen	2292	185	181.68	0.081	0.079	101.82
Brian Giles	3845	276	271.51	0.072	0.071	101.65
Jeremy Hermida	3310	266	263.10	0.080	0.079	101.10
J.D. Drew	2658	184	183.15	0.069	0.069	100.47
Gabe Gross	2225	186	185.51	0.084	0.083	100.26
Nick Markakis	4353	329	328.98	0.076	0.076	100.00
Corey Hart	4134	304	305.57	0.074	0.074	99.49
Brad Wilkerson	1428	95	95.58	0.067	0.067	99.39
Ryan Church	2158	180	181.26	0.083	0.084	99.31
Geoff Jenkins	1974	141	142.41	0.071	0.072	99.01
Elijah Dukes	1840	137	138.55	0.074	0.075	98.88
Shin-Soo Choo	1255	89	90.51	0.071	0.072	98.33
Hunter Pence	4112	341	349.04	0.083	0.085	97.70
Emil Brown	1264	112	114.89	0.089	0.091	97.49
Jay Bruce	1777	143	147.07	0.080	0.083	97.23
Jose Guillen	1673	121	124.68	0.072	0.075	97.05
Andre Ethier	2620	171	176.94	0.065	0.068	96.64
Ryan Ludwick	3037	232	240.07	0.076	0.079	96.64
Vladimir Guerrero	2541	180	186.37	0.071	0.073	96.58
Xavier Nady	2497	199	207.14	0.080	0.083	96.07
Magglio Ordonez	3588	220	229.25	0.061	0.064	95.96
Jermaine Dye	3981	266	277.60	0.067	0.070	95.82
Bobby Abreu	3933	271	284.58	0.069	0.072	95.23
Eric Hinske	1001	88	92.73	0.088	0.093	94.90
Ken Griffey Jr.	2257	157	166.16	0.070	0.074	94.48
Gary Matthews Jr.	1013	77	82.08	0.076	0.081	93.81
Brad Hawpe	3645	188	213.67	0.052	0.059	87.99

Denard Span not only improved the Twins leadoff slot, he also did a great job tracking down balls in rightfield. While I'm not surprised to see older players like Ken Griffey and Bobby Abreu near the bottom of the list, I didn't expect to see Gary Matthews, Jr. there.

Ichiro Suzuki also adds some interest. He came out near the top in center, but in the middle in right. It's a bit of a mystery why he does better in center than he does in right.

The Blue Jays and Cardinals made a challenge trade at the start of the season, swapping Scott Rolen and Troy Glaus. Defensively, at least, the Blue Jays came out on top. Here are the Probabilistic Model of Range team rankings for third base:

Team Third Basemen PMR, 2008, Visit Smooth Distance Model, 2008 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Blue Jays	4215	415	392.25	0.098	0.093	105.80
Mariners	4512	403	384.91	0.089	0.085	104.70
Red Sox	4232	440	423.21	0.104	0.100	103.97
Dodgers	4265	427	411.45	0.100	0.096	103.78
Angels	4374	391	377.04	0.089	0.086	103.70
Braves	4383	404	390.88	0.092	0.089	103.36
Rays	4264	420	406.66	0.098	0.095	103.28
Tigers	4536	471	458.72	0.104	0.101	102.68
Brewers	4354	396	387.21	0.091	0.089	102.27
White Sox	4409	463	455.46	0.105	0.103	101.66
Padres	4419	382	376.01	0.086	0.085	101.59
Astros	4292	408	402.20	0.095	0.094	101.44
Athletics	4285	385	380.25	0.090	0.089	101.25
Pirates	4683	445	442.19	0.095	0.094	100.64
Rockies	4535	412	410.31	0.091	0.090	100.41
Nationals	4417	416	415.43	0.094	0.094	100.14
Yankees	4349	379	378.81	0.087	0.087	100.05
Cubs	4156	341	342.34	0.082	0.082	99.61
Mets	4335	374	376.09	0.086	0.087	99.44
Indians	4513	419	423.48	0.093	0.094	98.94
Marlins	4338	370	375.82	0.085	0.087	98.45
Royals	4413	375	386.63	0.085	0.088	96.99
Phillies	4396	411	425.13	0.093	0.097	96.68
Rangers	4667	372	386.02	0.080	0.083	96.37
Diamondbacks	4224	350	363.76	0.083	0.086	96.22
Twins	4607	382	397.09	0.083	0.086	96.20
Cardinals	4597	416	432.51	0.090	0.094	96.18
Giants	4232	338	356.28	0.080	0.084	94.87
Reds	4299	337	356.45	0.078	0.083	94.54
Orioles	4540	421	446.86	0.093	0.098	94.21

I'm impressed that the Braves rank so high. Chipper Jones isn't known for his defense at third, but he played well this season.

Individual Third Baseman PMR, 2008, Visit Smooth Distance Model, 2008 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Chone Figgins	2787	249	230.03	0.089	0.083	108.25
Andy Marte	1849	185	173.47	0.100	0.094	106.64
Evan Longoria	3059	304	286.97	0.099	0.094	105.94
Ian Stewart	1651	160	151.25	0.097	0.092	105.78
Adrian Beltre	3804	338	321.08	0.089	0.084	105.27
Carlos Guillen	2396	246	233.91	0.103	0.098	105.17
Jack Hannahan	2882	267	254.14	0.093	0.088	105.06
Mike Lowell	2717	279	266.51	0.103	0.098	104.69
Geoff Blum	1773	179	171.00	0.101	0.096	104.68
Blake DeWitt	2152	233	223.28	0.108	0.104	104.35
Joe Crede	2492	251	242.47	0.101	0.097	103.52
Bill Hall	2709	238	229.92	0.088	0.085	103.51
Chipper Jones	2981	274	265.13	0.092	0.089	103.34
Scott Rolen	2935	274	267.64	0.093	0.091	102.37
Kevin Kouzmanoff	4179	368	361.20	0.088	0.086	101.88
Alex Rodriguez	3377	297	291.79	0.088	0.086	101.79
Jose Bautista	2478	243	240.95	0.098	0.097	100.85
Greg Dobbs	1000	92	91.52	0.092	0.092	100.53
Ryan Zimmerman	2786	275	273.75	0.099	0.098	100.46
David Wright	4234	367	365.59	0.087	0.086	100.39
Willy Aybar	1048	108	107.77	0.103	0.103	100.21
Andy LaRoche	1573	152	151.71	0.097	0.096	100.19
Juan Uribe	1424	156	157.08	0.110	0.110	99.31
Aramis Ramirez	3664	290	294.47	0.079	0.080	98.48
Edwin Encarnacion	3673	288	295.33	0.078	0.080	97.52
Mike Lamb	1508	117	120.22	0.078	0.080	97.32
Brian Buscher	1564	141	145.30	0.090	0.093	97.04
Jose Castillo	2560	214	220.73	0.084	0.086	96.95
Garrett Atkins	2528	221	228.04	0.087	0.090	96.91
Mark Reynolds	3759	304	315.66	0.081	0.084	96.31
Jorge Cantu	3264	271	281.48	0.083	0.086	96.28
Alex Gordon	3583	316	329.28	0.088	0.092	95.97
Pedro Feliz	2972	280	292.73	0.094	0.098	95.65
Casey Blake	3318	288	301.47	0.087	0.091	95.53
Ty Wigginton	2013	175	183.48	0.087	0.091	95.38
Troy Glaus	3908	351	368.31	0.090	0.094	95.30
Melvin Mora	3362	320	342.26	0.095	0.102	93.50
Ramon Vazquez	1712	138	149.87	0.081	0.088	92.08
Rich Aurilia	1271	93	106.18	0.073	0.084	87.59

Adrian Beltre comes through here as an interesting player. With the run up in salaries the last few seasons, his $12 million contract for 2009 is pretty good. It's the same amount Mike Lowell will make next season. The two are also very close in terms of win shares. If a team is looking to upgrade their defense at third base, Beltre is a great pickup. The Mariners may be looking to move his contract. If the surgery he underwent in September helps with his hitting, he could be a very good pickup.

Evan Longoria certainly was a big part of the Rays defensive improvement. Unexpected major leaguers Blake DeWitt and Jack Hannahan also provided much needed defense. In addition, Andy Marte hasn't hit but he did field the position well in limited playing time.

At the other end of the spectrum, Casey Blake appears to be as overrated defensively as offensively. Alex Gordon and Mark Reynolds look like they won't have long careers at the position, given their poor play at a young age.

Mike Emeigh took me up on my offer to watch the best and worst plays of a second baseman. I sent Mike the highest probability plays Dan Uggla didn't make, and the lowest probability plays Uggla did turn into outs. Here's his report:

Of Uggla's eight low-probability plays made, four of them were plays on which the Marlins had an infield shift on - three by Ryan Howard, one by Carlos Delgado - and in each case the ball was hit directly to where Uggla was playing; it's very likely that any 2B would have made those plays in that position, and I don't know thow much credit you want to give Uggla for being there. Two more plays - the 8/15 play against Alfonso Soriano and the 7/10 play against James Loney - also appear to be primarily due to positioning. On the former, Uggla was playing Soriano fairly far up the middle and had a good angle on his popup; on the latter, Uggla was pulled over fairly close to 1B. The other two plays were good, far-ranging plays - Uggla going far to his left to throw out Brian Schneider on 5/26, and ranging well to the left side of 2B in shallow center to grab a Mark Reynolds flare on 5/20 - although on the latter positioning also played a role, as Uggla was playing Reynolds up the middle and the CF was playing fairly deep. It was a good play, but one that a good CF or SS might have been able to make, also.

The six high-probability plays that Uggla should have made but didn't:

• 6/17: routing GB by Ichiro, just booted it
• 8/6: hard-hit "at 'em" GB by Jimmy Rollins, basically one of those you either catch or don't catch
• 5/30: GB by Pedro Feliz that took a bad hop as it got to Uggla; he barehanded it across his body, which threw off his timing
• 4/18: GB by Ryan Zimmerman toward the middle; Uggla made the play but didn't get enough on the throw, which Mike Jacobs should have scooped anyway
• 9/21: With Jamie Moyer on 1B, Jimmy Rollins hit a slow grounder to the right side. Uggla stopped to avoid a collision with Moyer, which made him have to hurry the play when he did get to the ball. Had he kept coming Moyer would likely have collided with him, which would have been interference on Moyer
• 7/28: Endy Chavez hit a GB which took a funky hop as it got to Uggla, who booted it

Mike brings up something I've discussed before. Range is probably a poor word for what we're studying here. Range isn't just the ability to move a long distance to field a ball. It also includes the ability to position yourself (or have someone position you) so you don't need to move very far. Uggla (and Utley) put themselves into position to field low probability balls without having too many high probability outs sneak through their vacated normal positions. Someday, we'll measure range directly.

The third position presented in this year's Probabilistic Model of Range study belongs to centerfielders. First, the overall team numbers:

Team Centerfielders PMR, 2008, Visit Smooth Distance Model, 2008 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Mets	4335	435	422.51	0.100	0.097	102.96
Rays	4264	451	438.07	0.106	0.103	102.95
Phillies	4396	389	378.54	0.088	0.086	102.76
Twins	4607	488	475.27	0.106	0.103	102.68
Athletics	4285	444	433.07	0.104	0.101	102.52
Reds	4299	413	404.02	0.096	0.094	102.22
Angels	4374	429	421.94	0.098	0.096	101.67
Brewers	4354	406	400.20	0.093	0.092	101.45
Astros	4292	427	420.91	0.099	0.098	101.45
Mariners	4512	435	429.86	0.096	0.095	101.19
Rockies	4535	405	400.30	0.089	0.088	101.17
Yankees	4349	407	402.92	0.094	0.093	101.01
Diamondbacks	4224	402	398.46	0.095	0.094	100.89
Dodgers	4265	377	374.62	0.088	0.088	100.64
Red Sox	4232	406	404.43	0.096	0.096	100.39
Marlins	4338	438	436.46	0.101	0.101	100.35
Braves	4383	360	361.20	0.082	0.082	99.67
Pirates	4683	433	434.85	0.092	0.093	99.58
Indians	4513	412	414.22	0.091	0.092	99.46
Orioles	4540	440	442.64	0.097	0.097	99.40
Padres	4419	453	456.46	0.103	0.103	99.24
Rangers	4667	451	456.50	0.097	0.098	98.79
Cubs	4156	391	396.42	0.094	0.095	98.63
Giants	4232	454	460.66	0.107	0.109	98.55
White Sox	4409	362	369.04	0.082	0.084	98.09
Blue Jays	4215	381	389.50	0.090	0.092	97.82
Tigers	4536	450	460.98	0.099	0.102	97.62
Nationals	4417	426	439.80	0.096	0.100	96.86
Royals	4413	417	436.29	0.094	0.099	95.58
Cardinals	4597	388	409.47	0.084	0.089	94.76

It was a good year for the Mets and the Rays. I find it interesting that the Rangers rank so low, as a number of people noted Josh Hamilton's defense this season. The next table will show where he ranks as an individual:

Individual Centerfielders PMR, 2008, Visit Smooth Distance Model, 2008 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Rajai Davis	1483	153	142.55	0.103	0.096	107.33
Ichiro Suzuki	1887	195	186.20	0.103	0.099	104.72
B.J. Upton	3642	378	362.20	0.104	0.099	104.36
Carlos Gonzalez	1585	176	169.00	0.111	0.107	104.14
Carlos Gomez	3988	437	422.56	0.110	0.106	103.42
Carlos Beltran	4171	418	407.47	0.100	0.098	102.58
Marlon Byrd	1372	149	145.28	0.109	0.106	102.56
Gregor Blanco	1495	128	124.87	0.086	0.084	102.51
Brian Anderson	1295	102	99.83	0.079	0.077	102.17
Willy Taveras	3124	282	276.52	0.090	0.089	101.98
Jacoby Ellsbury	1660	171	168.01	0.103	0.101	101.78
Torii Hunter	3587	350	344.29	0.098	0.096	101.66
Chris Young	4091	393	387.93	0.096	0.095	101.31
Andruw Jones	1481	133	131.63	0.090	0.089	101.04
Shane Victorino	3619	314	310.92	0.087	0.086	100.99
Michael Bourn	3051	291	289.00	0.095	0.095	100.69
Melky Cabrera	2919	272	270.56	0.093	0.093	100.53
Corey Patterson	2388	242	241.55	0.101	0.101	100.19
Alfredo Amezaga	1451	146	145.75	0.101	0.100	100.17
Grady Sizemore	4199	382	382.73	0.091	0.091	99.81
Adam Jones	3487	337	337.64	0.097	0.097	99.81
Matt Kemp	2425	209	209.73	0.086	0.086	99.65
Coco Crisp	2534	234	235.17	0.092	0.093	99.50
Jeremy Reed	1439	132	132.92	0.092	0.092	99.31
Cody Ross	2561	254	255.96	0.099	0.100	99.24
Aaron Rowand	3750	411	414.28	0.110	0.110	99.21
Mike Cameron	3174	293	295.47	0.092	0.093	99.16
Jim Edmonds	2420	242	244.43	0.100	0.101	99.00
Alex Rios	1531	156	158.34	0.102	0.103	98.52
Jody Gerut	1816	189	191.84	0.104	0.106	98.52
Mark Kotsay	2145	173	176.54	0.081	0.082	98.00
Reed Johnson	1618	144	147.07	0.089	0.091	97.91
Nate McLouth	4228	380	388.88	0.090	0.092	97.72
Scott Hairston	1152	114	116.69	0.099	0.101	97.69
Josh Hamilton	2977	268	274.44	0.090	0.092	97.65
Vernon Wells	2582	217	222.72	0.084	0.086	97.43
Joey Gathright	2242	197	202.50	0.088	0.090	97.28
Curtis Granderson	3740	366	379.16	0.098	0.101	96.53
Nick Swisher	1650	138	144.00	0.084	0.087	95.84
Lastings Milledge	3632	348	365.21	0.096	0.101	95.29
Rick Ankiel	2433	213	224.60	0.088	0.092	94.83
Skip Schumaker	1760	136	143.45	0.077	0.082	94.81
Ryan Sweeney	1053	95	102.85	0.090	0.098	92.37
David DeJesus	1524	151	163.83	0.099	0.108	92.17

It was a very good year to be a centerfielder named Carlos. B.J. Upton, however, gets the nod as the best everyday DF. Looking at individuals, it becomes apparent why the Cardinals rated so poorly at the position. Skip Shumaker and Rick Ankiel were equally below average.

As for Josh Hamilton, he ranks 35th out of 44 fielders in the study. He's going to be worth exploring in more detail, since I suspect people who watch him give him better marks.

Before I get to the centerfielders, a question arises sometimes that I'd like to address. I'm sometimes asked when a fielder does well, especially an outfielder on fly balls, what about ball hogs? So for outfielders, I'd like to take a look at where balls get hogged, and who does the hogging.

The first graph shows the percentage of plays made on each Probabilistic Model of Range vector, each vector representing about five degrees. Data is all outs made by major league outfielders in 2008. Leftfield is represented by low number vectors, rightfield by high number vectors. Straight-away centerfield is vector 36 (click for a larger image).

There are two things to notice from this graph. The first is that there are very few vectors in which ball hogging might occur. There are only six, in fact. Second, centerfielder hog more balls from leftfielder than they do from rightfielders. This makes some sense, since most hitters are right-handed, meaning centerfielders are going to be shaded toward left most of the time.

The other thing I want to point out is that balls are hogged in places where fewer outs get recorded (click for a larger image):

So, it's tough for an outfielder to get a huge boost by ball hogging. They don't stray that far into another's territory, and when they do there are fewer outs to be gathered in anyway.

This also gives us a tool to use to look at individual teams if a question of ball hogging comes up.

Beyond the Boxscore translates PMR for shortstops into runs.

The following table shows how team second basemen ranked according to the Probabilistic Model of Range:

Team Second Basemen PMR, 2008, Visit Smooth Distance Model, 2008 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Marlins	4338	527	500.98	0.121	0.115	105.19
Phillies	4396	528	504.35	0.120	0.115	104.69
Reds	4299	498	478.19	0.116	0.111	104.14
Diamondbacks	4224	561	539.98	0.133	0.128	103.89
Cubs	4156	500	487.52	0.120	0.117	102.56
Rockies	4535	564	552.06	0.124	0.122	102.16
Tigers	4536	505	495.02	0.111	0.109	102.02
Angels	4374	545	535.72	0.125	0.122	101.73
Indians	4513	554	545.22	0.123	0.121	101.61
Twins	4607	513	505.30	0.111	0.110	101.52
Athletics	4285	518	510.99	0.121	0.119	101.37
Blue Jays	4215	532	525.31	0.126	0.125	101.27
Brewers	4354	508	503.13	0.117	0.116	100.97
White Sox	4409	535	533.38	0.121	0.121	100.30
Orioles	4540	498	498.38	0.110	0.110	99.92
Cardinals	4597	517	517.91	0.112	0.113	99.82
Yankees	4349	556	557.46	0.128	0.128	99.74
Red Sox	4232	505	508.07	0.119	0.120	99.40
Astros	4292	464	467.09	0.108	0.109	99.34
Mariners	4512	602	608.69	0.133	0.135	98.90
Rangers	4667	539	546.88	0.115	0.117	98.56
Royals	4413	547	555.11	0.124	0.126	98.54
Nationals	4417	464	471.01	0.105	0.107	98.51
Braves	4383	526	534.13	0.120	0.122	98.48
Pirates	4683	466	478.32	0.100	0.102	97.43
Mets	4335	476	492.58	0.110	0.114	96.63
Giants	4232	417	432.81	0.099	0.102	96.35
Rays	4264	472	490.56	0.111	0.115	96.22
Padres	4419	475	499.74	0.107	0.113	95.05
Dodgers	4265	484	514.65	0.113	0.121	94.04

The Marlins number one at second base? That certainly flies in the face of Dan Uggla's performance in the All-Star Game. It's not that surprising, however, to see the Dodgers with the aging Jeff Kent coming in last. On to the individual players:

Individual Second Baseman PMR, 2008, Visit Smooth Distance Model, 2008 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Adam Kennedy	2036	247	226.55	0.121	0.111	109.03
Mike Fontenot	1448	175	160.82	0.121	0.111	108.82
Emilio Bonifacio	1008	100	93.17	0.099	0.092	107.33
Chase Utley	4231	513	485.09	0.121	0.115	105.75
Marco Scutaro	1077	144	136.95	0.134	0.127	105.15
Placido Polanco	3806	424	405.94	0.111	0.107	104.45
Dan Uggla	3841	465	445.31	0.121	0.116	104.42
Howie Kendrick	2341	308	295.94	0.132	0.126	104.07
Joe Inglett	1554	205	197.44	0.132	0.127	103.83
Asdrubal Cabrera	2446	316	304.98	0.129	0.125	103.61
Juan Uribe	1112	138	133.57	0.124	0.120	103.32
Brandon Phillips	3704	429	416.27	0.116	0.112	103.06
Clint Barmes	1519	183	177.61	0.120	0.117	103.03
Mark Ellis	3006	373	365.23	0.124	0.122	102.13
Alexi Casilla	2611	288	282.01	0.110	0.108	102.12
Orlando Hudson	2668	346	339.70	0.130	0.127	101.86
Kaz Matsui	2485	267	265.25	0.107	0.107	100.66
Rickie Weeks	3150	355	353.07	0.113	0.112	100.55
Dustin Pedroia	4003	479	477.12	0.120	0.119	100.39
Brian Roberts	4195	471	469.83	0.112	0.112	100.25
Robinson Cano	4152	531	530.64	0.128	0.128	100.07
Sean Rodriguez	1229	149	148.91	0.121	0.121	100.06
Mark Loretta	1110	129	128.96	0.116	0.116	100.03
Jose Lopez	3861	531	533.54	0.138	0.138	99.52
Alexei Ramirez	3081	371	373.04	0.120	0.121	99.45
Luis Castillo	2054	219	220.31	0.107	0.107	99.41
Mark Grudzielanek	2175	280	282.08	0.129	0.130	99.26
Tadahito Iguchi	1962	217	218.94	0.111	0.112	99.12
Jamey Carroll	1800	206	207.94	0.114	0.116	99.07
Ian Kinsler	3462	413	417.34	0.119	0.121	98.96
Kelly Johnson	3631	441	448.84	0.121	0.124	98.25
Mark DeRosa	1930	232	236.45	0.120	0.123	98.12
Freddy Sanchez	3688	368	378.01	0.100	0.102	97.35
Eugenio Velez	1355	128	133.20	0.094	0.098	96.09
Jeff Baker	1174	139	144.85	0.118	0.123	95.96
Felipe Lopez	2435	266	279.15	0.109	0.115	95.29
Aaron Hill	1375	164	172.51	0.119	0.125	95.07
Akinori Iwamura	3916	435	457.88	0.111	0.117	95.00
Aaron Miles	1551	171	182.78	0.110	0.118	93.55
Alberto Callaspo	1128	128	137.62	0.113	0.122	93.01
Ray Durham	2160	212	228.31	0.098	0.106	92.86
Edgar Gonzalez	1701	191	205.90	0.112	0.121	92.76
Brendan Harris	1016	101	109.08	0.099	0.107	92.59
Damion Easley	1607	170	186.57	0.106	0.116	91.12
Jeff Kent	2630	290	318.37	0.110	0.121	91.09

One thing I need to look at more closely is why Dan Uggla does so well. In the previous post on shortstops, a couple of commenters wanted more proof that this system actually works. I was a bit suprised by Akinori Iwamura rating so low, so I thought I would look at his poorest plays to see if they made sense. Of his four worst plays, all with a probablility of .889 or higher of being turned, two were errors hit right at him. One was a grounder to his right when he was playing too far left (poor positioning) and one was just bad judgement on a double play ball.

To compare, I looked at Utley's best play, since he was the best regular at the position. All three of his best plays were balls to the right of first base that got by Howard off the bats of left handers. In each case, Utley ranged into the outfield to field the ball and throw out the batter at first, twice I believe to the pitcher covering. He made those plays because Howard couldn't, but he was positioned so well he was in the right place to cover for Ryan.

The other thing I noticed is that toughest plays Utley made were much tougher than the best plays Iwamura executed. At the other end, easiest balls in play that Iwamura failed to turn into outs were much easier than Utley's worse plays.

If anyone would like to review video on MLB.com for a particular player, I'll be happy to send you the dates and innings of their best and worst plays.

In case you want to check my work, Iwamura's worst plays were on 9/7, 3rd inning, 8/20, 9th inning, 4/25, 9th inning, 7/30, 5th inning. Utley's best plays were on 7/23, 1st inning, 7/1, 1st inning and 8/3, 3rd inning.

Dan Turkenkopf at Beyond the Boxscore is translating PMR into runs so I don't need to. Thanks, Dan.

The first position to examine is the most important of the fielders working behind the pitcher, the shortstop. As a reference, the first table looks at the position on a team-wide basis:

Team Shortstop PMR, 2008, Visit Smooth Distance Model, 2008 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Brewers	4354	551	526.00	0.127	0.121	104.75
Giants	4232	492	469.81	0.116	0.111	104.72
Marlins	4338	517	501.00	0.119	0.115	103.19
Angels	4374	524	510.64	0.120	0.117	102.62
Cardinals	4597	580	566.37	0.126	0.123	102.41
Red Sox	4232	480	472.55	0.113	0.112	101.58
Phillies	4396	557	551.85	0.127	0.126	100.93
Braves	4383	566	561.40	0.129	0.128	100.82
Diamondbacks	4224	469	465.74	0.111	0.110	100.70
Cubs	4156	498	495.33	0.120	0.119	100.54
Astros	4292	500	497.32	0.116	0.116	100.54
Athletics	4285	477	474.54	0.111	0.111	100.52
Rangers	4667	538	536.31	0.115	0.115	100.31
Dodgers	4265	546	544.65	0.128	0.128	100.25
Indians	4513	542	540.73	0.120	0.120	100.23
White Sox	4409	548	546.97	0.124	0.124	100.19
Royals	4413	508	507.30	0.115	0.115	100.14
Rays	4264	490	490.56	0.115	0.115	99.89
Orioles	4540	537	539.06	0.118	0.119	99.62
Rockies	4535	587	589.61	0.129	0.130	99.56
Pirates	4683	577	580.37	0.123	0.124	99.42
Blue Jays	4215	476	479.71	0.113	0.114	99.23
Twins	4607	578	584.70	0.125	0.127	98.85
Yankees	4349	491	499.00	0.113	0.115	98.40
Nationals	4417	526	538.02	0.119	0.122	97.76
Mariners	4512	480	493.64	0.106	0.109	97.24
Padres	4419	520	536.39	0.118	0.121	96.94
Reds	4299	468	485.83	0.109	0.113	96.33
Tigers	4536	519	544.40	0.114	0.120	95.33
Mets	4335	498	524.64	0.115	0.121	94.92

Notice the Mets are last. While recent articles mention Jeter as the worst fielder in the majors, in 2008 he wasn't the worst shortstop in New York:

Individual Shortstop PMR, 2008, Visit Smooth Distance Model, 2008 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Marco Scutaro	1352	173	157.04	0.128	0.116	110.16
Omar Vizquel	1863	210	193.60	0.113	0.104	108.47
Mike Aviles	2277	271	252.42	0.119	0.111	107.36
Maicer Izturis	1307	151	144.80	0.116	0.111	104.28
Jed Lowrie	1142	123	118.01	0.108	0.103	104.23
J.J. Hardy	3804	477	460.72	0.125	0.121	103.53
Erick Aybar	2437	305	295.72	0.125	0.121	103.14
Alex Cora	1137	140	135.75	0.123	0.119	103.13
Cesar Izturis	3136	408	396.19	0.130	0.126	102.98
Jack Wilson	2231	285	276.88	0.128	0.124	102.93
Bobby Crosby	3740	423	411.71	0.113	0.110	102.74
Jason Bartlett	3208	380	372.71	0.118	0.116	101.96
Hanley Ramirez	3986	472	462.98	0.118	0.116	101.95
Juan Castro	1331	153	150.32	0.115	0.113	101.78
Jimmy Rollins	3537	451	443.43	0.128	0.125	101.71
Luis Rodriguez	1191	143	140.93	0.120	0.118	101.47
Yunel Escobar	3344	440	434.04	0.132	0.130	101.37
Nick Punto	1646	227	224.05	0.138	0.136	101.32
Orlando Cabrera	4218	527	521.06	0.125	0.124	101.14
Adam Everett	1183	156	154.33	0.132	0.130	101.08
Miguel Tejada	4062	472	469.63	0.116	0.116	100.50
Jhonny Peralta	3963	469	467.52	0.118	0.118	100.32
Michael Young	4165	489	487.98	0.117	0.117	100.21
Ryan Theriot	3615	425	424.27	0.118	0.117	100.17
Julio Lugo	1947	216	217.95	0.111	0.112	99.11
Angel Berroa	1730	225	227.09	0.130	0.131	99.08
Derek Jeter	3815	429	433.24	0.112	0.114	99.02
Stephen Drew	3820	422	429.34	0.110	0.112	98.29
Cristian Guzman	3640	441	449.15	0.121	0.123	98.19
John McDonald	1387	150	154.82	0.108	0.112	96.89
Yuniesky Betancourt	4173	446	460.45	0.107	0.110	96.86
Troy Tulowitzki	2730	354	365.56	0.130	0.134	96.84
Edgar Renteria	3696	428	449.40	0.116	0.122	95.24
Jose Reyes	4196	480	504.15	0.114	0.120	95.21
Khalil Greene	2841	327	345.54	0.115	0.122	94.64
Tony F Pena	1808	199	211.52	0.110	0.117	94.08
Brendan Harris	1480	159	170.68	0.107	0.115	93.16
Jeff Keppinger	2636	274	296.50	0.104	0.112	92.41
David Eckstein	1445	149	163.53	0.103	0.113	91.11

Jose Reyes converted 24 fewer balls into outs than expected while Jeter was just down four. It was actually one of Derek's better years.

Omar Vizquel remains impressive at an advanced age. He didn't play a whole season, so he didn't get a chance to wear down, but if any team is looking for a great late inning defensive replacement, Omar is it.

Mike Aviles came up as a great find for the Royals in terms of his batting, but he also performed well with the glove.

Troy Tulowitzki went from first to almost worst in 2008. His injuries seemed to limit his range.

Jimmy Rollins won the Gold Glove today, but J.J. Hardy deserved it based on this data.

Feel free to comment and criticize.

Baseball Info Solutions sent me their fielding data, and that means it's time to start presenting the 2008 Probabilistic Model of Range. If you're new to this, you can find explanations in this archive. Basically, for each fieldable (non inside the park home runs) ball put in play, six parameters are used to determine how difficult it was to field the ball. A probability of turning the ball into an out is calculated, and those probabilities are summed. That gives us expected batted balls turned into outs. We turn that into a predicted DER (defensive efficiency record), compare that to the actual DER and calculate a ranking.

The model is based primarily on visiting player data, smoothed, using distance on fly balls and a hard hit indicator on ground balls. Only 2008 data was used to construct the model.

Note that a team can post a poor DER during the season, but do well in this model if the balls put into play were extremely difficult to field. This helps the Braves rank second.

Probabilistic Model of Range, 2007 Data, Teams, Visit Smooth Distance Model, Ranked by Difference

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Index
Blue Jays	4215	2961	2896.74	0.702	0.687	102.22
Braves	4383	3033	2977.44	0.692	0.679	101.87
Rays	4264	3023	2979.66	0.709	0.699	101.45
Athletics	4285	2991	2950.73	0.698	0.689	101.36
Red Sox	4232	2953	2913.30	0.698	0.688	101.36
Astros	4292	2990	2952.74	0.697	0.688	101.26
Angels	4374	3022	2985.77	0.691	0.683	101.21
Brewers	4354	3036	3000.17	0.697	0.689	101.19
Cardinals	4597	3190	3163.77	0.694	0.688	100.83
Dodgers	4265	2941	2919.81	0.690	0.685	100.73
Cubs	4156	2925	2906.58	0.704	0.699	100.63
Twins	4607	3161	3144.82	0.686	0.683	100.51
Mariners	4512	3068	3053.72	0.680	0.677	100.47
Indians	4513	3093	3082.17	0.685	0.683	100.35
White Sox	4409	3021	3013.27	0.685	0.683	100.26
Marlins	4338	3002	2994.74	0.692	0.690	100.24
Diamondbacks	4224	2892	2886.85	0.685	0.683	100.18
Giants	4232	2897	2898.76	0.685	0.685	99.94
Tigers	4536	3105	3109.78	0.685	0.686	99.85
Phillies	4396	3054	3062.15	0.695	0.697	99.73
Mets	4335	3024	3033.17	0.698	0.700	99.70
Rangers	4667	3124	3136.62	0.669	0.672	99.60
Padres	4419	3074	3088.40	0.696	0.699	99.53
Pirates	4683	3157	3175.46	0.674	0.678	99.42
Rockies	4535	3072	3090.76	0.677	0.682	99.39
Nationals	4417	3041	3060.09	0.688	0.693	99.38
Orioles	4540	3119	3139.36	0.687	0.691	99.35
Yankees	4349	2962	2984.01	0.681	0.686	99.26
Reds	4299	2889	2921.00	0.672	0.679	98.90
Royals	4413	3038	3076.09	0.688	0.697	98.76

The Rays turned in the best combination of good pitching and good defense. Their .699 predicted DER was second to the Mets. Unlike the Mets, however, the Rays fielded more balls than expected, giving the best DER, but only the third best Index. The Blue Jays turned in a tremendous defensive season, a big reason their pitching staff did so well in ERA in 2008.

The bottom of this chart is very interesting. From the Padres down, teams 23-30 all turned out to be very poor teams with the exception of the Yankees. Defense didn't necessarily help a team win, as the Phillies were pretty middle of the road, but it certainly seemed to indicate a pretty bad team.

Note that last season, the Devil Rays were at the very bottom of the list. They improved both their predicted DER and their ability to turn batted balls into outs. That was enough to lower their runs allowed from 944 to 671 and make them American League champions.

Gideon Gil attended the AAAS symposia yesterday and gave both SAFE and PMR a nice writeup.

On Saturday morning I'll make a presentation at the American Association for the Advancement of Science (AAAS) meeting on the Probabilistic Model of Range. The symposia is called New Techniques in the Evaluation and Prediction of Baseball Performance and meets in the Hynes Convention Center, Second Level, Room 202 at 8:30 AM. Alan Schwarz and Shane Jensen will also present.

The 2007 Defensive Charts are up. These provide a visualization of the Probabilistic Model of Range data based on position and batted ball type. Enjoy!

One criticism leveled at the Probabilistic Model of Range this year is that due to building the models based on the visiting team fielders, teams with good offenses get a bonus defensively. The example given is the Yankees, but there are other high offense teams ranked high in terms of PMR.

The idea is that since the Yankees hit well, their opponents DER must by definition be low. A ball put in play by the Yankees must have a lower probability of being turned into an out. This causes the model to underestimate the fielding ability of opponents, and over estimate the fielding ability of the Yankees. If the model contained one parameter, ballpark, then this would be absolutely true. However, there are six parameters, including a vector indicating the direction of the ball. I propose that the Yankees hit better than their opponents not because a random ball in play has a higher probability of falling for a hit, but because the Yankees do a better job of hitting balls where they are tough to field.

The following table shows the number of ground balls hit by the Yankees and their opponents by vector:

Vector	Yankees	Opponents	Predicted DER
25	4	4	0.000
26	12	14	0.000
27	37	26	0.766
28	118	57	0.898
29	175	118	0.706
30	193	156	0.671
31	148	119	0.844
32	111	82	0.934
33	164	136	0.868
34	114	105	0.585
35	100	74	0.535
36	117	124	0.624
37	101	108	0.617
38	116	150	0.838
39	119	131	0.865
40	163	139	0.764
41	165	174	0.550
42	110	130	0.688
43	61	55	0.847
44	35	40	0.572
45	7	13	0.010
46	5	5	0.000

As you can see, the low probability vectors are 29-30, the shortstop hole, 34-37, up the middle, 41-42, the second base hole, and 44, right down the first base line. I'm not looking at the foul vectors where a ball is always a hit. Breaking these down:

Ground balls	Yankees	Opponents
In Holes	1110	1029
At Fielders	882	895

So the Yankees hit more grounders where they are less likely to be fielded, and fewer grounders where they are more likely to be fielded than their opponents. Later I want to look at how the Yankees field home and road. If they field much better at home, then the objection still my have some validity.

To complete the survery of range, here are how pitchers rank. First the teams:

Team Pitchers PMR, 2007, Visit Smooth Distance Model, 2007 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Astros	4530	205	183.71	0.045	0.041	111.59
Padres	4476	243	228.50	0.054	0.051	106.35
Rockies	4599	218	206.59	0.047	0.045	105.52
Indians	4548	181	171.92	0.040	0.038	105.28
Mets	4362	173	164.61	0.040	0.038	105.09
White Sox	4545	196	186.52	0.043	0.041	105.08
Yankees	4511	181	172.92	0.040	0.038	104.67
Tigers	4486	167	159.73	0.037	0.036	104.55
Red Sox	4226	149	142.79	0.035	0.034	104.35
Mariners	4535	174	167.33	0.038	0.037	103.99
Blue Jays	4349	200	194.00	0.046	0.045	103.09
Phillies	4505	193	187.33	0.043	0.042	103.02
Pirates	4608	204	200.82	0.044	0.044	101.58
Cubs	4177	166	163.95	0.040	0.039	101.25
Rangers	4518	197	195.59	0.044	0.043	100.72
Braves	4404	206	204.60	0.047	0.046	100.69
Devil Rays	4378	148	147.07	0.034	0.034	100.63
Twins	4384	150	152.30	0.034	0.035	98.49
Orioles	4403	160	162.54	0.036	0.037	98.44
Nationals	4591	167	170.78	0.036	0.037	97.78
Marlins	4491	178	182.52	0.040	0.041	97.52
Angels	4325	143	146.86	0.033	0.034	97.37
Giants	4467	159	163.87	0.036	0.037	97.03
Diamondbacks	4351	207	213.40	0.048	0.049	97.00
Cardinals	4587	158	166.21	0.034	0.036	95.06
Athletics	4499	165	174.70	0.037	0.039	94.45
Brewers	4392	179	192.64	0.041	0.044	92.92
Dodgers	4310	189	205.96	0.044	0.048	91.76
Reds	4533	162	180.13	0.036	0.040	89.93
Royals	4528	151	179.20	0.033	0.040	84.27

The Padres not only induce the most predicted outs back to the pitcher, they exceed those outs by a great deal. Maddux is one reason:

Individual Pitcher PMR, 2007, Visit Smooth Distance Model, 2007 data only (400 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Chris Sampson	414	24	15.23	0.058	0.037	157.55
Matt Cain	571	26	19.79	0.046	0.035	131.37
Chad Durbin	417	15	11.48	0.036	0.028	130.65
Shaun Marcum	456	27	20.71	0.059	0.045	130.37
Steve Trachsel	549	35	26.89	0.064	0.049	130.17
Mike Mussina	512	27	20.84	0.053	0.041	129.54
Woody Williams	632	36	27.90	0.057	0.044	129.04
Aaron Cook	572	37	28.69	0.065	0.050	128.98
Miguel Batista	615	26	20.17	0.042	0.033	128.92
Jon Garland	705	34	26.84	0.048	0.038	126.66
Kelvim Escobar	572	17	13.58	0.030	0.024	125.21
Wandy Rodriguez	536	21	16.87	0.039	0.031	124.46
Greg Maddux	681	53	42.87	0.078	0.063	123.64
Ervin Santana	457	13	10.59	0.028	0.023	122.72
Jake Peavy	571	30	24.58	0.053	0.043	122.03
Brandon Webb	692	53	43.55	0.077	0.063	121.69
Mike Bacsik	414	15	12.35	0.036	0.030	121.42
Tim Wakefield	600	24	19.83	0.040	0.033	121.05
Carlos Zambrano	610	30	25.00	0.049	0.041	119.98
Javier Vazquez	583	28	23.46	0.048	0.040	119.34
Adam Eaton	525	22	18.49	0.042	0.035	119.00
Nate Robertson	573	27	22.77	0.047	0.040	118.56
John Danks	427	15	12.83	0.035	0.030	116.94
James Shields	615	26	22.26	0.042	0.036	116.80
Justin Verlander	577	17	14.69	0.029	0.025	115.76
Chien-Ming Wang	643	34	29.61	0.053	0.046	114.84
Carlos Silva	699	27	23.54	0.039	0.034	114.70
John Smoltz	586	30	26.16	0.051	0.045	114.69
Dustin McGowan	484	31	27.18	0.064	0.056	114.04
Justin Germano	426	21	18.42	0.049	0.043	114.04
Ted Lilly	586	24	21.09	0.041	0.036	113.81
Dontrelle Willis	667	39	34.32	0.058	0.051	113.64
Kyle Davies	432	16	14.08	0.037	0.033	113.60
Sergio Mitre	522	29	25.58	0.056	0.049	113.35
Daisuke Matsuzaka	555	24	21.21	0.043	0.038	113.18
Joe Blanton	750	28	25.10	0.037	0.033	111.54
Jake Westbrook	481	27	24.51	0.056	0.051	110.17
Andy Sonnanstine	408	14	12.81	0.034	0.031	109.28
Matt Chico	548	16	14.77	0.029	0.027	108.33
Jamie Moyer	633	30	27.83	0.047	0.044	107.81
Johan Santana	555	24	22.27	0.043	0.040	107.75
Tom Glavine	674	27	25.15	0.040	0.037	107.37
C.C. Sabathia	701	24	22.47	0.034	0.032	106.80
Brett Tomko	415	16	14.99	0.039	0.036	106.77
Jarrod Washburn	627	20	18.81	0.032	0.030	106.33
Noah Lowry	502	23	21.69	0.046	0.043	106.02
Jeremy Guthrie	527	21	19.85	0.040	0.038	105.81
Chris Capuano	456	28	26.47	0.061	0.058	105.77
Fausto Carmona	654	36	34.14	0.055	0.052	105.43
Roy Halladay	722	36	34.31	0.050	0.048	104.94
Mark Buehrle	648	33	31.47	0.051	0.049	104.86
Bronson Arroyo	661	27	25.79	0.041	0.039	104.71
David Bush	594	24	23.12	0.040	0.039	103.80
Kyle Kendrick	401	20	19.29	0.050	0.048	103.69
David Wells	545	20	19.32	0.037	0.035	103.52
Erik Bedard	431	17	16.46	0.039	0.038	103.29
Jeff Suppan	708	34	32.99	0.048	0.047	103.05
Barry Zito	608	21	20.40	0.035	0.034	102.94
Jason Marquis	626	25	24.34	0.040	0.039	102.70
Jeff Francis	662	30	29.40	0.045	0.044	102.04
Kameron Loe	464	28	27.74	0.060	0.060	100.93
Livan Hernandez	704	38	37.71	0.054	0.054	100.78
Paul Maholm	583	30	29.99	0.051	0.051	100.02
Matt Morris	693	28	28.14	0.040	0.041	99.50
Kip Wells	522	20	20.10	0.038	0.039	99.48
Ian Snell	606	20	20.14	0.033	0.033	99.33
Odalis Perez	494	18	18.33	0.036	0.037	98.20
John Maine	527	17	17.37	0.032	0.033	97.86
Cole Hamels	495	23	23.78	0.046	0.048	96.70
Chad Gaudin	603	21	21.76	0.035	0.036	96.51
A.J. Burnett	414	15	15.67	0.036	0.038	95.73
Mike Maroth	417	17	17.85	0.041	0.043	95.22
Tim Hudson	722	41	43.25	0.057	0.060	94.81
Felix Hernandez	567	26	27.45	0.046	0.048	94.73
Jered Weaver	514	18	19.04	0.035	0.037	94.51
Brian Bannister	540	20	21.19	0.037	0.039	94.40
Oliver Perez	483	11	11.65	0.023	0.024	94.40
Micah Owings	461	22	23.32	0.048	0.051	94.34
Kyle Lohse	615	22	23.48	0.036	0.038	93.71
Jeff Weaver	511	10	10.72	0.020	0.021	93.32
Chuck James	484	15	16.10	0.031	0.033	93.18
Tom Gorzelanny	642	24	25.76	0.037	0.040	93.18
Roy Oswalt	675	36	38.80	0.053	0.057	92.79
Adam Wainwright	654	28	30.29	0.043	0.046	92.44
Jose Contreras	647	22	23.80	0.034	0.037	92.43
Scott Kazmir	534	16	17.46	0.030	0.033	91.64
Lenny DiNardo	430	15	16.48	0.035	0.038	91.04
Derek Lowe	604	27	29.69	0.045	0.049	90.95
Andy Pettitte	690	26	28.59	0.038	0.041	90.93
Paul Byrd	686	21	23.15	0.031	0.034	90.72
Aaron Harang	642	23	25.44	0.036	0.040	90.42
Doug Davis	597	32	36.17	0.054	0.061	88.47
Scott Olsen	578	21	23.75	0.036	0.041	88.41
Josh Fogg	556	21	23.79	0.038	0.043	88.26
Scott Baker	454	13	14.84	0.029	0.033	87.58
Rich Hill	527	21	23.98	0.040	0.046	87.57
Brad Penny	643	25	28.93	0.039	0.045	86.41
Kevin Millwood	571	16	18.75	0.028	0.033	85.32
John Lackey	668	24	28.71	0.036	0.043	83.60
Braden Looper	581	19	23.06	0.033	0.040	82.41
Chad Billingsley	400	17	20.94	0.043	0.052	81.18
Josh Beckett	566	11	13.68	0.019	0.024	80.41
Vicente Padilla	407	12	15.11	0.029	0.037	79.44
Chris Young	448	11	14.27	0.025	0.032	77.08
Claudio Vargas	419	14	18.20	0.033	0.043	76.91
Edwin Jackson	516	12	15.91	0.023	0.031	75.43
Jeremy Bonderman	533	14	18.78	0.026	0.035	74.53
Boof Bonser	539	14	18.92	0.026	0.035	74.00
Jorge de la Rosa	431	11	15.32	0.026	0.036	71.79
Gil Meche	663	20	28.05	0.030	0.042	71.31
Julian Tavarez	455	11	15.86	0.024	0.035	69.38
Brad Thompson	451	10	14.58	0.022	0.032	68.61
Matt Belisle	570	15	22.66	0.026	0.040	66.18
Dan Haren	661	17	26.01	0.026	0.039	65.36
Daniel Cabrera	608	13	20.82	0.021	0.034	62.44
Ben Sheets	431	11	19.19	0.026	0.045	57.31
Curt Schilling	485	7	12.87	0.014	0.027	54.40

Peavy is also very good, however. Looking at Schilling's low ranking should give his opponents a clue as to his weakness next season. Bunting for hits against Curt might be a very good idea.

Fielding by catchers isn't the most important aspect of the job, and the number of outs attributed to the postion are few. But for completeness, here are the tables for the position. First, teams:

Team Catchers PMR, 2007, Visit Smooth Distance Model, 2007 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Cardinals	4587	57	47.59	0.012	0.010	119.76
Braves	4404	64	55.33	0.015	0.013	115.67
Rockies	4599	76	66.39	0.017	0.014	114.48
Yankees	4511	66	59.51	0.015	0.013	110.90
Dodgers	4310	68	62.43	0.016	0.014	108.91
Angels	4325	39	35.96	0.009	0.008	108.47
Marlins	4491	57	53.73	0.013	0.012	106.09
Nationals	4591	60	57.21	0.013	0.012	104.87
Astros	4530	58	55.59	0.013	0.012	104.33
Tigers	4486	50	47.96	0.011	0.011	104.25
White Sox	4545	50	49.10	0.011	0.011	101.82
Giants	4467	58	57.06	0.013	0.013	101.64
Cubs	4177	51	50.42	0.012	0.012	101.15
Reds	4533	74	73.68	0.016	0.016	100.44
Blue Jays	4349	50	49.79	0.011	0.011	100.42
Royals	4528	46	45.90	0.010	0.010	100.22
Rangers	4518	48	48.05	0.011	0.011	99.90
Red Sox	4226	49	49.56	0.012	0.012	98.88
Devil Rays	4378	41	41.89	0.009	0.010	97.88
Indians	4548	36	37.23	0.008	0.008	96.70
Diamondbacks	4351	50	51.94	0.011	0.012	96.26
Padres	4476	59	61.48	0.013	0.014	95.97
Orioles	4403	37	38.96	0.008	0.009	94.97
Mariners	4535	42	44.86	0.009	0.010	93.63
Pirates	4608	51	54.75	0.011	0.012	93.15
Phillies	4505	56	60.25	0.012	0.013	92.95
Twins	4384	30	32.50	0.007	0.007	92.32
Athletics	4499	37	41.10	0.008	0.009	90.03
Mets	4362	50	56.67	0.011	0.013	88.22
Brewers	4392	51	59.91	0.012	0.014	85.13

The Mets are Brewers, who just completed a trade at the position, came out at the bottom team wise. New York might have been better off with Torrealba, at least fielding wise.

Individual Catcher PMR, 2007, Visit Smooth Distance Model, 2007 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Yadier Molina	2719	32	26.82	0.012	0.010	119.33
Brian McCann	3433	52	43.65	0.015	0.013	119.14
Yorvit Torrealba	2863	54	45.73	0.019	0.016	118.07
Miguel Olivo	3131	44	37.90	0.014	0.012	116.11
Jorge Posada	3484	50	43.52	0.014	0.012	114.90
Eric Munson	1012	17	15.02	0.017	0.015	113.21
Jeff Mathis	1421	21	18.96	0.015	0.013	110.78
Jose Molina	1431	16	14.52	0.011	0.010	110.18
Kelly Shoppach	1365	14	12.72	0.010	0.009	110.07
Gerald Laird	3118	37	33.82	0.012	0.011	109.40
Russell Martin	3687	60	55.76	0.016	0.015	107.60
Gregg Zaun	2559	32	29.91	0.013	0.012	106.98
Brad Ausmus	2728	33	31.07	0.012	0.011	106.22
Chris Iannetta	1613	20	18.83	0.012	0.012	106.20
Toby Hall	1002	10	9.45	0.010	0.009	105.82
Gary Bennett	1223	15	14.18	0.012	0.012	105.75
Jesus Flores	1258	21	19.87	0.017	0.016	105.69
Ivan Rodriguez	3216	41	38.98	0.013	0.012	105.19
John Buck	2879	30	28.52	0.010	0.010	105.18
Brian Schneider	3333	39	37.34	0.012	0.011	104.43
Mike Napoli	1814	12	11.53	0.007	0.006	104.09
Miguel Montero	1629	20	19.57	0.012	0.012	102.20
Javier Valentin	1494	20	19.72	0.013	0.013	101.42
Bengie Molina	3389	42	41.51	0.012	0.012	101.17
Mike Rabelo	1270	9	8.99	0.007	0.007	100.16
Dave Ross	2603	46	46.32	0.018	0.018	99.32
A.J. Pierzynski	3270	37	37.40	0.011	0.011	98.92
Ronny Paulino	3423	40	40.81	0.012	0.012	98.02
Michael Barrett	2291	33	33.76	0.014	0.015	97.74
Ramon Hernandez	2617	24	24.82	0.009	0.009	96.71
Josh Bard	2761	38	39.31	0.014	0.014	96.67
Mike Redmond	1461	11	11.42	0.008	0.008	96.30
Kurt Suzuki	1696	14	14.61	0.008	0.009	95.82
Paul Lo Duca	2922	33	34.63	0.011	0.012	95.29
Dioner Navarro	2901	25	26.29	0.009	0.009	95.09
Jason LaRue	1537	16	16.89	0.010	0.011	94.72
Jason Kendall	3448	31	32.85	0.009	0.010	94.37
Carlos Ruiz	2802	44	46.89	0.016	0.017	93.83
Jason Varitek	3061	33	35.49	0.011	0.012	92.99
Chris Snyder	2611	26	28.37	0.010	0.011	91.64
Johnny Estrada	2922	36	39.51	0.012	0.014	91.12
Kenji Johjima	3548	32	35.22	0.009	0.010	90.85
Rob Bowen	1268	11	12.14	0.009	0.010	90.59
Jarrod Saltalamacchia	1201	11	12.25	0.009	0.010	89.78
Victor Martinez	3183	22	24.51	0.007	0.008	89.76
Joe Mauer	2331	16	18.22	0.007	0.008	87.83
Paul Bako	1290	8	9.42	0.006	0.007	84.90
Matt Treanor	1317	13	15.83	0.010	0.012	82.12
Jason Phillips	1025	7	8.88	0.007	0.009	78.82
Damian Miller	1367	13	17.73	0.010	0.013	73.30

Two of the old men, Posada and Ivan Rodriguez, are still cat like behind the plate.

Here's a look at the range of first basemen. First, the team table. The Yankees at least did a good job of improving their defense at the position:

Team First Basemen PMR, 2007, Visit Smooth Distance Model, 2007 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Cardinals	4587	366	329.22	0.080	0.072	111.17
Yankees	4511	314	285.78	0.070	0.063	109.87
Giants	4467	325	304.72	0.073	0.068	106.66
Royals	4528	315	296.64	0.070	0.066	106.19
Padres	4476	311	295.59	0.069	0.066	105.21
Cubs	4177	283	269.44	0.068	0.065	105.03
Braves	4404	320	306.86	0.073	0.070	104.28
Angels	4325	308	296.32	0.071	0.069	103.94
Pirates	4608	315	304.66	0.068	0.066	103.39
Rockies	4599	336	326.21	0.073	0.071	103.00
Astros	4530	335	328.42	0.074	0.072	102.00
Red Sox	4226	323	321.65	0.076	0.076	100.42
Brewers	4392	294	293.80	0.067	0.067	100.07
Diamondbacks	4351	292	292.06	0.067	0.067	99.98
Devil Rays	4378	316	317.18	0.072	0.072	99.63
Blue Jays	4349	337	339.17	0.077	0.078	99.36
Orioles	4403	273	277.29	0.062	0.063	98.45
Athletics	4499	303	310.84	0.067	0.069	97.48
Dodgers	4310	285	293.60	0.066	0.068	97.07
Mariners	4535	297	308.37	0.065	0.068	96.31
Mets	4362	285	296.03	0.065	0.068	96.27
White Sox	4545	309	321.66	0.068	0.071	96.06
Indians	4548	295	307.96	0.065	0.068	95.79
Tigers	4486	296	310.16	0.066	0.069	95.44
Rangers	4518	283	297.18	0.063	0.066	95.23
Phillies	4505	302	317.82	0.067	0.071	95.02
Marlins	4491	291	307.52	0.065	0.068	94.63
Twins	4384	311	337.63	0.071	0.077	92.11
Reds	4533	263	290.87	0.058	0.064	90.42
Nationals	4591	270	299.99	0.059	0.065	90.00

It looks like the Nationals missed Nick Johnson's glove at first base. It's even more evident in the individual listing:

Individual First Basemen PMR, 2007, Visit Smooth Distance Model, 2007 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Doug Mientkiewicz	1427	109	92.24	0.076	0.065	118.17
Rich Aurilia	1115	70	59.31	0.063	0.053	118.02
Andy Phillips	1325	93	80.91	0.070	0.061	114.95
Albert Pujols	4220	349	308.82	0.083	0.073	113.01
Ryan Shealy	1336	88	78.66	0.066	0.059	111.87
Derrek Lee	3691	254	239.65	0.069	0.065	105.99
Casey Kotchman	3085	225	214.03	0.073	0.069	105.12
Adrian Gonzalez	4401	307	292.23	0.070	0.066	105.06
Tony Clark	1345	98	93.58	0.073	0.070	104.72
Scott Thorman	1859	126	120.75	0.068	0.065	104.35
Todd Helton	4170	306	293.61	0.073	0.070	104.22
Ryan Klesko	2504	190	183.08	0.076	0.073	103.78
Ben Broussard	1057	72	69.60	0.068	0.066	103.45
James Loney	2355	168	162.45	0.071	0.069	103.42
Ross Gload	2169	153	148.21	0.071	0.068	103.23
Carlos Pena	3708	277	268.41	0.075	0.072	103.20
Adam LaRoche	4141	283	274.52	0.068	0.066	103.09
Nick Swisher	1075	91	88.68	0.085	0.082	102.61
Kevin Youkilis	3208	253	249.42	0.079	0.078	101.44
Matt Stairs	1024	86	85.07	0.084	0.083	101.10
Lance Berkman	3315	229	229.22	0.069	0.069	99.91
Lyle Overbay	2887	221	221.32	0.077	0.077	99.86
Prince Fielder	4073	266	271.21	0.065	0.067	98.08
Conor Jackson	2647	173	176.80	0.065	0.067	97.85
Mark Teixeira	3404	240	246.41	0.071	0.072	97.40
Carlos Delgado	3649	244	251.39	0.067	0.069	97.06
Kevin Millar	2666	171	176.83	0.064	0.066	96.70
Robert Fick	1221	80	82.79	0.066	0.068	96.64
Aubrey Huff	1295	67	69.45	0.052	0.054	96.47
Ryan Howard	3871	263	274.29	0.068	0.071	95.88
Paul Konerko	3864	256	267.48	0.066	0.069	95.71
Richie Sexson	3137	201	210.24	0.064	0.067	95.61
Aaron Boone	1219	85	89.73	0.070	0.074	94.72
Brad Wilkerson	1444	82	86.94	0.057	0.060	94.32
Ryan Garko	3271	209	223.33	0.064	0.068	93.58
Sean Casey	3100	198	211.63	0.064	0.068	93.56
Dan Johnson	2679	166	177.43	0.062	0.066	93.56
Justin Morneau	3872	281	302.07	0.073	0.078	93.02
Mike Jacobs	2821	170	183.72	0.060	0.065	92.53
Jeff Conine	1595	86	94.78	0.054	0.059	90.74
Scott Hatteberg	2457	144	160.66	0.059	0.065	89.63
Nomar Garciaparra	1678	106	118.73	0.063	0.071	89.28
Dmitri Young	2808	162	184.81	0.058	0.066	87.66

Once again, Albert Pujols comes out on top among every day first basemen. If the Yankees had kept Miguel Cairo off first, they might have finished first as a team. Not only did Nomar not hit like a first baseman, he didn't even field well.

Correction: Cairo, not Cabrera.

Here's something the Orioles excelled at during 2007, fielding by leftfielders:

Team Leftfielders PMR, 2007, Visit Smooth Distance Model, 2007 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Orioles	4403	362	343.61	0.082	0.078	105.35
Indians	4548	339	325.23	0.075	0.072	104.23
Braves	4404	316	306.69	0.072	0.070	103.04
Rangers	4518	337	327.32	0.075	0.072	102.96
Nationals	4591	352	341.94	0.077	0.074	102.94
Yankees	4511	334	324.93	0.074	0.072	102.79
Brewers	4392	322	314.81	0.073	0.072	102.28
Mets	4362	324	317.91	0.074	0.073	101.91
Padres	4476	310	305.07	0.069	0.068	101.62
Royals	4528	373	367.39	0.082	0.081	101.53
Devil Rays	4378	339	334.26	0.077	0.076	101.42
Cubs	4177	341	337.65	0.082	0.081	100.99
Diamondbacks	4351	349	345.83	0.080	0.079	100.92
Blue Jays	4349	294	292.63	0.068	0.067	100.47
Dodgers	4310	288	287.78	0.067	0.067	100.08
Angels	4325	340	341.60	0.079	0.079	99.53
Giants	4467	314	317.61	0.070	0.071	98.86
Tigers	4486	327	331.60	0.073	0.074	98.61
Marlins	4491	274	278.60	0.061	0.062	98.35
Astros	4530	285	290.69	0.063	0.064	98.04
Athletics	4499	337	344.34	0.075	0.077	97.87
White Sox	4545	318	325.73	0.070	0.072	97.63
Pirates	4608	303	310.81	0.066	0.067	97.49
Rockies	4599	317	326.69	0.069	0.071	97.03
Reds	4533	326	336.27	0.072	0.074	96.95
Twins	4384	334	345.60	0.076	0.079	96.64
Phillies	4505	282	295.91	0.063	0.066	95.30
Red Sox	4226	284	299.24	0.067	0.071	94.91
Cardinals	4587	320	346.16	0.070	0.075	92.44
Mariners	4535	288	315.31	0.064	0.070	91.34

Among individuals, Matt Diaz had a career year with the glove as well as the bat.

Individual Leftfielder PMR, 2007, Visit Smooth Distance Model, 2007 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Matt Diaz	2064	155	142.05	0.075	0.069	109.11
Jose Cruz	1099	89	82.33	0.081	0.075	108.10
Joey Gathright	1595	154	142.69	0.097	0.089	107.93
Jay Payton	2776	231	214.85	0.083	0.077	107.52
David Dellucci	1210	97	91.32	0.080	0.075	106.22
Scott Hairston	1689	115	108.48	0.068	0.064	106.01
Wily Mo Pena	1126	68	64.97	0.060	0.058	104.66
Ryan Church	2304	196	188.59	0.085	0.082	103.93
Geoff Jenkins	2985	243	234.55	0.081	0.079	103.60
Carl Crawford	3623	286	276.65	0.079	0.076	103.38
Hideki Matsui	3091	214	207.16	0.069	0.067	103.30
Adam Lind	1969	137	132.73	0.070	0.067	103.22
Jason Michaels	1567	117	113.59	0.075	0.072	103.00
Reggie Willits	1557	151	146.83	0.097	0.094	102.84
Reed Johnson	1518	108	105.47	0.071	0.069	102.40
Emil Brown	1909	155	153.22	0.081	0.080	101.16
Eric Byrnes	2924	239	236.90	0.082	0.081	100.89
Alfonso Soriano	3074	245	243.79	0.080	0.079	100.50
Rob Mackowiak	1468	98	97.52	0.067	0.066	100.49
Kenny Lofton	1189	82	82.28	0.069	0.069	99.66
Willie Harris	1873	138	139.21	0.074	0.074	99.13
Ryan Ludwick	1011	86	86.83	0.085	0.086	99.04
Frank Catalanotto	1540	98	99.82	0.064	0.065	98.18
Jason Bay	3974	266	271.62	0.067	0.068	97.93
Luis Gonzalez	3008	192	196.31	0.064	0.065	97.81
Matt Holliday	4331	296	303.68	0.068	0.070	97.47
Carlos Lee	4244	261	268.68	0.061	0.063	97.14
Moises Alou	2105	138	142.80	0.066	0.068	96.64
Shannon Stewart	3606	277	287.12	0.077	0.080	96.47
Kevin Mench	1139	55	57.41	0.048	0.050	95.81
Craig Monroe	2512	166	174.76	0.066	0.070	94.99
Garret Anderson	2169	143	150.84	0.066	0.070	94.81
Scott Podsednik	1421	108	114.15	0.076	0.080	94.61
Josh Willingham	3653	211	223.26	0.058	0.061	94.51
Adam Dunn	3691	245	259.98	0.066	0.070	94.24
Terrmel Sledge	1192	77	82.16	0.065	0.069	93.72
Barry Bonds	2588	162	173.93	0.063	0.067	93.14
Jason Kubel	2153	159	172.31	0.074	0.080	92.27
Raul Ibanez	3559	224	243.95	0.063	0.069	91.82
Manny Ramirez	2925	182	198.85	0.062	0.068	91.53
Chris Duncan	2437	158	175.74	0.065	0.072	89.90
Pat Burrell	3176	176	198.31	0.055	0.062	88.75

There's no real surprises at the bottom of the list. Bonds, however, fell off quite a bit. He was average in 2006, but well below average in 2007. You can also see that there are few regular leftfielders. Only twelve players on the list were on the field at that position for at least 3000 balls in play.

The following table presents probabilistic model of range data for team rightfielders:

Team Rightfielders PMR, 2007, Visit Smooth Distance Model, 2007 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Phillies	4505	363	328.75	0.081	0.073	110.42
Rangers	4518	341	317.30	0.075	0.070	107.47
Yankees	4511	341	328.36	0.076	0.073	103.85
Royals	4528	410	397.12	0.091	0.088	103.24
Nationals	4591	392	381.19	0.085	0.083	102.84
Indians	4548	313	304.41	0.069	0.067	102.82
Marlins	4491	379	368.66	0.084	0.082	102.81
Astros	4530	360	354.55	0.079	0.078	101.54
Brewers	4392	393	387.42	0.089	0.088	101.44
Diamondbacks	4351	336	331.82	0.077	0.076	101.26
Athletics	4499	330	327.02	0.073	0.073	100.91
Blue Jays	4349	281	278.50	0.065	0.064	100.90
Cubs	4177	303	301.51	0.073	0.072	100.50
Angels	4325	311	310.00	0.072	0.072	100.32
Padres	4476	331	331.59	0.074	0.074	99.82
Twins	4384	306	307.17	0.070	0.070	99.62
Tigers	4486	318	319.88	0.071	0.071	99.41
Red Sox	4226	287	289.46	0.068	0.068	99.15
Mets	4362	340	343.80	0.078	0.079	98.89
Orioles	4403	314	317.86	0.071	0.072	98.79
Braves	4404	331	336.45	0.075	0.076	98.38
Devil Rays	4378	309	314.27	0.071	0.072	98.32
Reds	4533	377	384.09	0.083	0.085	98.15
Pirates	4608	312	319.06	0.068	0.069	97.79
Cardinals	4587	316	323.36	0.069	0.070	97.72
White Sox	4545	345	354.49	0.076	0.078	97.32
Dodgers	4310	317	326.76	0.074	0.076	97.01
Giants	4467	338	349.14	0.076	0.078	96.81
Mariners	4535	305	323.57	0.067	0.071	94.26
Rockies	4599	296	316.91	0.064	0.069	93.40

As shown below, Jayson Werth and Shane Victorino made quite the dynamic duo in rightfield for the Phillies. My uncle Anthony will not be happy with this list, however. He's a Yankees season ticket holder and he loves to tell me how much Bobby Abreu is afraid of the wall. It looks like he's still getting to lots of balls.

Individual Rightfielder PMR, 2007, Visit Smooth Distance Model, 2007 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Jayson Werth	1389	109	95.35	0.078	0.069	114.32
Shane Victorino	2837	229	210.62	0.081	0.074	108.72
Nick Swisher	1289	109	101.65	0.085	0.079	107.23
Carlos Quentin	1718	138	129.11	0.080	0.075	106.89
Franklin Gutierrez	1757	136	128.55	0.077	0.073	105.79
Nelson Cruz	1922	148	141.26	0.077	0.073	104.77
Luke Scott	2560	198	190.34	0.077	0.074	104.02
Bobby Abreu	4148	313	302.45	0.075	0.073	103.49
Corey Hart	2641	253	246.33	0.096	0.093	102.71
Austin Kearns	4356	375	366.16	0.086	0.084	102.41
Mark Teahen	3663	318	311.33	0.087	0.085	102.14
Alex Rios	3730	243	240.17	0.065	0.064	101.18
Travis Buck	1561	110	109.03	0.070	0.070	100.89
Jeremy Hermida	3035	247	245.88	0.081	0.081	100.46
Randy Winn	2686	209	208.12	0.078	0.077	100.42
Delmon Young	3463	252	251.16	0.073	0.073	100.33
Trot Nixon	2140	129	129.17	0.060	0.060	99.86
Michael Cuddyer	3749	256	256.95	0.068	0.069	99.63
Nick Markakis	4279	303	306.74	0.071	0.072	98.78
Magglio Ordonez	3835	261	264.54	0.068	0.069	98.66
Jeff Francoeur	4356	328	333.45	0.075	0.077	98.37
Jermaine Dye	3682	284	289.80	0.077	0.079	98.00
Shawn Green	2771	203	207.55	0.073	0.075	97.81
Vladimir Guerrero	2819	208	213.12	0.074	0.076	97.60
Matt Kemp	1851	129	132.50	0.070	0.072	97.36
Brian Giles	3199	216	223.54	0.068	0.070	96.63
J.D. Drew	3128	212	219.98	0.068	0.070	96.37
Ken Griffey Jr.	3649	291	302.61	0.080	0.083	96.16
Andre Ethier	2315	177	184.39	0.076	0.080	95.99
Xavier Nady	2390	162	168.97	0.068	0.071	95.88
Jose Guillen	4063	268	284.73	0.066	0.070	94.13
Juan Encarnacion	1983	125	132.90	0.063	0.067	94.06
Jack Cust	1205	79	84.93	0.066	0.070	93.01
Brad Hawpe	3851	247	267.07	0.064	0.069	92.48
Cliff Floyd	1185	69	78.30	0.058	0.066	88.12

Mark Teahen did a much better job of adjusting to rightfield than Ken Griffey, Jr. Of course, Junior is old and slow, and with all the injuries might be better off as a DH in AL at this point.

The Washington Nationals and Ryan Zimmerman lead the way at third base.

Team Third Basemen PMR, 2007, Visit Smooth Distance Model, 2007 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Nationals	4591	448	403.22	0.098	0.088	111.11
Cubs	4177	433	400.61	0.104	0.096	108.09
Giants	4467	434	404.44	0.097	0.091	107.31
Mets	4362	415	390.52	0.095	0.090	106.27
Red Sox	4226	377	356.44	0.089	0.084	105.77
Tigers	4486	446	426.09	0.099	0.095	104.67
Yankees	4511	370	354.08	0.082	0.078	104.50
Orioles	4403	423	406.97	0.096	0.092	103.94
Mariners	4535	423	407.60	0.093	0.090	103.78
Angels	4325	341	329.04	0.079	0.076	103.64
Cardinals	4587	468	459.66	0.102	0.100	101.81
Rangers	4518	385	378.51	0.085	0.084	101.72
Blue Jays	4349	376	371.58	0.086	0.085	101.19
Dodgers	4310	380	376.79	0.088	0.087	100.85
Braves	4404	364	364.35	0.083	0.083	99.90
Brewers	4392	369	371.77	0.084	0.085	99.26
Athletics	4499	399	405.18	0.089	0.090	98.47
Padres	4476	376	382.21	0.084	0.085	98.37
Astros	4530	401	409.30	0.089	0.090	97.97
Phillies	4505	433	442.07	0.096	0.098	97.95
Reds	4533	398	406.34	0.088	0.090	97.95
Royals	4528	378	387.55	0.083	0.086	97.54
Devil Rays	4378	361	370.39	0.082	0.085	97.46
White Sox	4545	426	438.55	0.094	0.096	97.14
Twins	4384	393	405.89	0.090	0.093	96.82
Pirates	4608	450	470.32	0.098	0.102	95.68
Indians	4548	400	421.84	0.088	0.093	94.82
Diamondbacks	4351	344	363.60	0.079	0.084	94.61
Marlins	4491	359	395.76	0.080	0.088	90.71
Rockies	4599	349	393.86	0.076	0.086	88.61

Given that David Wright scores better than Alex Rodriguez, if the Mets sign A-Rod, they should move him to first.

Individual Third Base PMR, 2007, Visit Smooth Distance Model, 2007 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Ryan Zimmerman	4528	443	398.27	0.098	0.088	111.23
Joe Crede	1184	125	113.00	0.106	0.095	110.62
Pedro Feliz	3718	373	341.20	0.100	0.092	109.32
Aramis Ramirez	3208	329	308.47	0.103	0.096	106.65
David Wright	4260	403	378.91	0.095	0.089	106.36
Mike Lowell	3890	342	321.90	0.088	0.083	106.24
Melvin Mora	3225	318	301.25	0.099	0.093	105.56
Maicer Izturis	1320	101	95.97	0.077	0.073	105.24
Brandon Inge	4062	400	380.28	0.098	0.094	105.18
Adrian Beltre	4036	379	362.12	0.094	0.090	104.66
Alex Rodriguez	4158	342	330.85	0.082	0.080	103.37
Scott Rolen	2983	296	287.61	0.099	0.096	102.92
Troy Glaus	2803	241	234.49	0.086	0.084	102.78
Ramon Vazquez	1671	152	148.03	0.091	0.089	102.68
Chone Figgins	2561	198	192.85	0.077	0.075	102.67
Hank Blalock	1082	83	80.94	0.077	0.075	102.55
Morgan Ensberg	1778	165	162.23	0.093	0.091	101.71
Travis Metcalf	1376	114	113.26	0.083	0.082	100.65
Chipper Jones	3231	278	277.24	0.086	0.086	100.27
Nomar Garciaparra	1103	87	86.81	0.079	0.079	100.21
Eric Chavez	2379	218	218.17	0.092	0.092	99.92
Akinori Iwamura	3174	260	261.21	0.082	0.082	99.54
Abraham Nunez	1792	205	206.06	0.114	0.115	99.49
Alex Gordon	3609	318	321.97	0.088	0.089	98.77
Edwin Encarnacion	3620	308	314.99	0.085	0.087	97.78
Chad Tracy	1152	96	98.41	0.083	0.085	97.55
Wilson Betemit	1235	94	96.37	0.076	0.078	97.54
Nick Punto	2518	239	245.24	0.095	0.097	97.46
Jack Hannahan	1122	93	96.13	0.083	0.086	96.74
Wes Helms	1394	116	120.21	0.083	0.086	96.50
Greg Dobbs	1309	111	115.27	0.085	0.088	96.29
Kevin Kouzmanoff	3415	279	292.44	0.082	0.086	95.40
Ty Wigginton	1995	186	195.65	0.093	0.098	95.07
Mike Lamb	1320	108	113.69	0.082	0.086	95.00
Mark Reynolds	2542	196	208.42	0.077	0.082	94.04
Jose Bautista	3413	317	338.96	0.093	0.099	93.52
Casey Blake	3743	325	351.27	0.087	0.094	92.52
Josh Fields	2234	200	217.44	0.090	0.097	91.98
Miguel Cabrera	4055	330	361.80	0.081	0.089	91.21
Ryan Braun	2886	211	239.01	0.073	0.083	88.28
Garrett Atkins	4136	305	352.46	0.074	0.085	86.53

The bottom three on the list pretty much define all-hit and no-field.

Here are the PMR numbers for second basemen. First the team stats.

Team Second Basemen PMR, 2007, Visit Smooth Distance Model, 2007 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Reds	4533	517	470.97	0.114	0.104	109.77
Phillies	4505	507	486.30	0.113	0.108	104.26
Yankees	4511	551	528.65	0.122	0.117	104.23
Diamondbacks	4351	536	514.78	0.123	0.118	104.12
Rangers	4518	561	541.66	0.124	0.120	103.57
Twins	4384	508	491.17	0.116	0.112	103.43
Athletics	4499	610	592.38	0.136	0.132	102.97
Blue Jays	4349	589	574.80	0.135	0.132	102.47
Tigers	4486	505	494.43	0.113	0.110	102.14
Royals	4528	453	444.63	0.100	0.098	101.88
Red Sox	4226	524	515.37	0.124	0.122	101.67
Rockies	4599	558	548.82	0.121	0.119	101.67
Angels	4325	505	497.11	0.117	0.115	101.59
Mariners	4535	554	546.62	0.122	0.121	101.35
Nationals	4591	491	485.03	0.107	0.106	101.23
Indians	4548	564	557.26	0.124	0.123	101.21
Orioles	4403	534	528.33	0.121	0.120	101.07
White Sox	4545	467	466.32	0.103	0.103	100.15
Mets	4362	493	494.92	0.113	0.113	99.61
Cubs	4177	471	476.31	0.113	0.114	98.88
Brewers	4392	447	456.43	0.102	0.104	97.93
Braves	4404	521	533.24	0.118	0.121	97.70
Pirates	4608	428	440.07	0.093	0.096	97.26
Devil Rays	4378	493	507.26	0.113	0.116	97.19
Dodgers	4310	480	494.92	0.111	0.115	96.99
Cardinals	4587	509	525.15	0.111	0.114	96.92
Padres	4476	556	575.50	0.124	0.129	96.61
Marlins	4491	463	487.55	0.103	0.109	94.96
Giants	4467	450	478.37	0.101	0.107	94.07
Astros	4530	461	495.20	0.102	0.109	93.09

Looking at the teams at the bottom of the list, old second basemen are a detriment to defense. Not only did Biggio at second not help the Astros offensively, it hurt them defensively as well. Now for the individual players.

Individual Second Base PMR, 2007, Visit Smooth Distance Model, 2007 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Brandon Phillips	4288	488	442.09	0.114	0.103	110.38
Chase Utley	3571	410	386.97	0.115	0.108	105.95
Jose Valentin	1123	154	145.56	0.137	0.130	105.80
Orlando Hudson	3552	435	412.20	0.122	0.116	105.53
Esteban German	1248	117	111.06	0.094	0.089	105.35
Ian Kinsler	3581	459	438.84	0.128	0.123	104.59
Ronnie Belliard	3168	337	322.49	0.106	0.102	104.50
Robinson Cano	4380	532	509.76	0.121	0.116	104.36
Josh Barfield	3237	396	381.63	0.122	0.118	103.76
Mark Ellis	4119	561	540.88	0.136	0.131	103.72
Kaz Matsui	2634	335	323.55	0.127	0.123	103.54
Aaron Hill	4230	576	558.01	0.136	0.132	103.22
B.J. Upton	1305	174	168.87	0.133	0.129	103.04
Placido Polanco	3724	420	409.07	0.113	0.110	102.67
Jose Lopez	3899	486	475.59	0.125	0.122	102.19
Mike Fontenot	1343	152	148.82	0.113	0.111	102.14
Howie Kendrick	2222	276	270.90	0.124	0.122	101.88
Alexi Casilla	1262	144	141.60	0.114	0.112	101.70
Mark Grudzielanek	3021	312	307.78	0.103	0.102	101.37
Luis Castillo	3569	370	365.52	0.104	0.102	101.23
Tadahito Iguchi	3285	359	354.84	0.109	0.108	101.17
Geoff Blum	1481	178	176.84	0.120	0.119	100.65
Brian Roberts	4068	487	487.37	0.120	0.120	99.92
Dustin Pedroia	3365	417	417.32	0.124	0.124	99.92
Kevin Frandsen	1044	111	112.56	0.106	0.108	98.61
Danny Richar	1554	152	154.45	0.098	0.099	98.42
Jamey Carroll	1396	165	168.34	0.118	0.121	98.02
Adam Kennedy	2060	250	256.18	0.121	0.124	97.59
Freddy Sanchez	4064	378	387.80	0.093	0.095	97.47
Kelly Johnson	3474	412	423.58	0.119	0.122	97.27
Felipe Lopez	1208	129	134.76	0.107	0.112	95.72
Jeff Kent	3237	355	372.41	0.110	0.115	95.33
Mark DeRosa	2056	223	234.54	0.108	0.114	95.08
Marcus Giles	2883	364	383.01	0.126	0.133	95.04
Aaron Miles	1834	183	194.00	0.100	0.106	94.33
Dan Uggla	4310	438	466.30	0.102	0.108	93.93
Rickie Weeks	3003	301	320.45	0.100	0.107	93.93
Ray Durham	3183	320	343.81	0.101	0.108	93.08
Craig Biggio	2878	283	308.32	0.098	0.107	91.79
Brendan Harris	1206	110	124.59	0.091	0.103	88.29

Rickie Weeks and Dan Uggla need to be at the top of their offensive games to stay at this important defensive position.

Correction: Fixed caption on first table.

Here are the team rankings for centerfielders:

Team Centerfielder PMR, 2007, Visit Smooth Distance Model, 2007 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Mariners	4535	452	423.84	0.100	0.093	106.64
Red Sox	4226	481	452.99	0.114	0.107	106.18
Tigers	4486	468	445.78	0.104	0.099	104.98
Cubs	4177	414	400.21	0.099	0.096	103.45
Mets	4362	464	449.88	0.106	0.103	103.14
Braves	4404	431	421.41	0.098	0.096	102.28
Dodgers	4310	379	371.16	0.088	0.086	102.11
Rockies	4599	414	407.81	0.090	0.089	101.52
Padres	4476	409	404.18	0.091	0.090	101.19
Cardinals	4587	417	412.78	0.091	0.090	101.02
Reds	4533	455	451.03	0.100	0.100	100.88
Giants	4467	438	437.08	0.098	0.098	100.21
Nationals	4591	486	485.40	0.106	0.106	100.12
Royals	4528	424	425.45	0.094	0.094	99.66
Yankees	4511	468	470.38	0.104	0.104	99.49
Phillies	4505	418	421.10	0.093	0.093	99.26
Twins	4384	415	418.19	0.095	0.095	99.24
White Sox	4545	415	418.55	0.091	0.092	99.15
Angels	4325	441	445.14	0.102	0.103	99.07
Marlins	4491	453	458.41	0.101	0.102	98.82
Astros	4530	433	439.56	0.096	0.097	98.51
Blue Jays	4349	366	372.05	0.084	0.086	98.37
Pirates	4608	448	456.67	0.097	0.099	98.10
Diamondbacks	4351	406	414.42	0.093	0.095	97.97
Indians	4548	413	422.64	0.091	0.093	97.72
Rangers	4518	388	399.38	0.086	0.088	97.15
Athletics	4499	398	410.38	0.088	0.091	96.98
Orioles	4403	409	423.66	0.093	0.096	96.54
Devil Rays	4378	419	444.79	0.096	0.102	94.20
Brewers	4392	410	437.27	0.093	0.100	93.76

The Mariners come out on top of the Red Sox overall, but Boston has the better individual fielder:

Individual Centerfielder PMR, 2007, Visit Smooth Distance Model, 2007 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Coco Crisp	3560	408	377.29	0.115	0.106	108.14
Ichiro Suzuki	4233	424	394.49	0.100	0.093	107.48
Felix Pie	1169	120	112.75	0.103	0.096	106.43
Curtis Granderson	3995	424	402.22	0.106	0.101	105.42
Jacque Jones	1911	195	187.25	0.102	0.098	104.14
Darin Erstad	1117	105	101.18	0.094	0.091	103.77
Willy Taveras	2274	212	204.80	0.093	0.090	103.52
So Taguchi	1190	118	114.17	0.099	0.096	103.35
Ryan Church	1024	118	114.35	0.115	0.112	103.19
Andruw Jones	4080	396	385.38	0.097	0.094	102.76
Juan Pierre	4215	366	356.47	0.087	0.085	102.67
Josh Hamilton	1702	168	163.71	0.099	0.096	102.62
Carlos Beltran	3733	389	380.89	0.104	0.102	102.13
Johnny Damon	1211	121	118.84	0.100	0.098	101.82
Gary Matthews Jr.	3462	362	356.66	0.105	0.103	101.50
Mike Cameron	4016	365	360.75	0.091	0.090	101.18
Nook Logan	2398	248	245.18	0.103	0.102	101.15
Norris Hopper	1280	133	132.11	0.104	0.103	100.67
Dave Roberts	2334	224	222.68	0.096	0.095	100.59
Torii Hunter	4034	389	389.12	0.096	0.096	99.97
David DeJesus	4256	400	400.98	0.094	0.094	99.76
Alfredo Amezaga	2005	208	208.88	0.104	0.104	99.58
Jim Edmonds	2688	244	245.68	0.091	0.091	99.32
Aaron Rowand	4243	392	394.89	0.092	0.093	99.27
Hunter Pence	2636	260	261.99	0.099	0.099	99.24
Chris Duffy	1693	172	174.17	0.102	0.103	98.75
Melky Cabrera	3297	347	351.54	0.105	0.107	98.71
Rajai Davis	1162	124	125.75	0.107	0.108	98.60
Ryan Freel	1419	136	138.16	0.096	0.097	98.44
Vernon Wells	3813	321	326.31	0.084	0.086	98.37
Grady Sizemore	4383	399	407.44	0.091	0.093	97.93
Jerry Owens	2294	208	212.80	0.091	0.093	97.75
Chris Young	3824	354	364.20	0.093	0.095	97.20
B.J. Upton	2014	204	210.16	0.101	0.104	97.07
Mark Kotsay	1492	141	145.40	0.095	0.097	96.98
Nick Swisher	1515	139	144.94	0.092	0.096	95.90
Marlon Byrd	1541	114	119.68	0.074	0.078	95.25
Nate McLouth	1583	142	150.82	0.090	0.095	94.15
Kenny Lofton	2219	188	199.69	0.085	0.090	94.15
Corey Patterson	3225	281	298.69	0.087	0.093	94.08
Bill Hall	3159	295	314.62	0.093	0.100	93.76
Elijah Dukes	1010	82	92.28	0.081	0.091	88.86

Note to that the shift of Bill Hall to center worked neither offensively nor defensively. Andruw Jones may not be as good as he once was, but he can still go get the ball.

A number of people are suggesting new ways to construct the models, but before I try those methods I'd like to present the model used last year for the nine fielding positions, starting with shortstops. I am including something new, however, the full team at the position.

Team Shortstop PMR, 2007, Visit Smooth Distance Model, 2007 data only

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Rockies	4599	657	602.67	0.143	0.131	109.01
Twins	4384	556	523.57	0.127	0.119	106.19
Dodgers	4310	556	526.50	0.129	0.122	105.60
Royals	4528	543	514.33	0.120	0.114	105.57
Blue Jays	4349	567	544.69	0.130	0.125	104.09
Phillies	4505	531	516.45	0.118	0.115	102.82
Indians	4548	571	558.76	0.126	0.123	102.19
Pirates	4608	588	575.51	0.128	0.125	102.17
Red Sox	4226	500	492.12	0.118	0.116	101.60
Giants	4467	592	584.51	0.133	0.131	101.28
Diamondbacks	4351	493	488.99	0.113	0.112	100.82
Brewers	4392	501	497.76	0.114	0.113	100.65
Angels	4325	502	498.77	0.116	0.115	100.65
Marlins	4491	508	506.53	0.113	0.113	100.29
Mariners	4535	515	514.50	0.114	0.113	100.10
Orioles	4403	505	506.89	0.115	0.115	99.63
Astros	4530	561	563.85	0.124	0.124	99.49
Braves	4404	516	520.04	0.117	0.118	99.22
Cardinals	4587	539	544.84	0.118	0.119	98.93
Reds	4533	496	502.70	0.109	0.111	98.67
Athletics	4499	531	538.40	0.118	0.120	98.62
Padres	4476	536	544.49	0.120	0.122	98.44
Mets	4362	506	518.72	0.116	0.119	97.55
Cubs	4177	481	495.42	0.115	0.119	97.09
White Sox	4545	563	580.23	0.124	0.128	97.03
Tigers	4486	517	536.95	0.115	0.120	96.28
Rangers	4518	531	556.38	0.118	0.123	95.44
Devil Rays	4378	441	466.20	0.101	0.106	94.59
Nationals	4591	532	566.26	0.116	0.123	93.95
Yankees	4511	478	516.85	0.106	0.115	92.48

The above table will give you an idea of how the regular shortstop fit in the team context. You might imagine that Troy Tulowitzki was very good and Derek Jeter very bad:

Individual Shortstop PMR, 2007, Visit Smooth Distance Model, 2007 data only (1000 balls in play)

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Troy Tulowitzki	4294	615	564.54	0.143	0.131	108.94
Tony F Pena	4010	480	449.44	0.120	0.112	106.80
Rafael Furcal	3574	473	445.28	0.132	0.125	106.23
John McDonald	2389	311	294.27	0.130	0.123	105.69
Jason Bartlett	3631	466	443.58	0.128	0.122	105.05
Jimmy Rollins	4447	528	511.62	0.119	0.115	103.20
Jack Wilson	3657	470	457.15	0.129	0.125	102.81
Yunel Escobar	1116	135	131.47	0.121	0.118	102.69
Jhonny Peralta	4206	512	502.37	0.122	0.119	101.92
Omar Vizquel	3739	504	497.76	0.135	0.133	101.25
Julio Lugo	3592	431	426.14	0.120	0.119	101.14
Adam Everett	1631	217	214.61	0.133	0.132	101.12
Orlando Cabrera	3997	462	456.91	0.116	0.114	101.11
Alex Gonzalez	2728	306	306.06	0.112	0.112	99.98
J.J. Hardy	3873	442	442.35	0.114	0.114	99.92
Cesar Izturis	1904	216	216.36	0.113	0.114	99.83
Bobby Crosby	2524	313	313.77	0.124	0.124	99.75
Stephen Drew	3877	434	435.25	0.112	0.112	99.71
Hanley Ramirez	4054	460	462.96	0.113	0.114	99.36
Ryan Theriot	2494	301	303.06	0.121	0.122	99.32
Khalil Greene	4206	504	507.64	0.120	0.121	99.28
Mark Loretta	1537	177	178.28	0.115	0.116	99.28
Yuniesky Betancourt	4103	464	467.60	0.113	0.114	99.23
Edgar Renteria	3067	361	365.13	0.118	0.119	98.87
Eric Bruntlett	1075	131	132.81	0.122	0.124	98.63
Royce Clayton	1538	200	202.77	0.130	0.132	98.63
Marco Scutaro	1064	122	124.14	0.115	0.117	98.28
Juan Uribe	4113	513	524.43	0.125	0.128	97.82
Jose Reyes	4295	500	511.97	0.116	0.119	97.66
David Eckstein	3002	349	357.57	0.116	0.119	97.60
Miguel Tejada	3317	363	373.46	0.109	0.113	97.20
Jeff Keppinger	1209	130	135.67	0.108	0.112	95.82
Carlos Guillen	3361	389	408.05	0.116	0.121	95.33
Felipe Lopez	2949	359	377.76	0.122	0.128	95.03
Michael Young	4083	476	504.85	0.117	0.124	94.29
Josh Wilson	1340	141	151.37	0.105	0.113	93.15
Brendan Harris	2336	234	253.12	0.100	0.108	92.45
Derek Jeter	4117	421	461.63	0.102	0.112	91.20
Cristian Guzman	1189	117	130.96	0.098	0.110	89.34

Troy really blew the competition away in terms of PMR, and Tony Pena did his best to make up for his poor hitting. And while New York enjoys two fine offensive shortstops, neither exactly sparkles with the glove. You can also see why the Tigers are moving Carlos Guillen to first. Michael Young may not be far behind him.

One thing PMR can measure is the luck of pitchers by looking at the predicted DER and actual DER behind them. The following table rates pitchers with at least 300 balls in play against them:

Probabilistic Model of Range, Defense Behind Pitchers, 2007. Visit Smoothed Distance Model. 2007 Data Only

Pitcher	Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Chien-Ming Wang	NYY	643	448	414.94	0.697	0.645	107.97
Jeremy Guthrie	Bal	527	375	356.60	0.712	0.677	105.16
Dustin McGowan	Tor	484	346	330.21	0.715	0.682	104.78
Sean Marshall	ChC	330	231	221.12	0.700	0.670	104.47
Roger Clemens	NYY	307	215	205.94	0.700	0.671	104.40
Brian Bannister	KC	540	393	376.52	0.728	0.697	104.38
Jarrod Washburn	Sea	627	440	422.32	0.702	0.674	104.19
Mike Bacsik	Was	414	291	279.42	0.703	0.675	104.14
Tom Glavine	NYM	674	474	455.80	0.703	0.676	103.99
Jason Hirsh	Col	340	252	242.53	0.741	0.713	103.91
Ted Lilly	ChC	586	427	411.59	0.729	0.702	103.74
Braden Looper	StL	581	416	401.23	0.716	0.691	103.68
Chris Sampson	Hou	414	292	281.66	0.705	0.680	103.67
Cole Hamels	Phi	495	348	336.00	0.703	0.679	103.57
Brad Penny	LAD	643	450	435.62	0.700	0.677	103.30
Dontrelle Willis	Fla	667	442	428.96	0.663	0.643	103.04
Yovani Gallardo	Mil	318	216	209.67	0.679	0.659	103.02
Jesse Litsch	Tor	371	259	251.51	0.698	0.678	102.98
Jason Bergmann	Was	332	248	241.02	0.747	0.726	102.90
Anthony Reyes	StL	332	236	229.52	0.711	0.691	102.82
Curt Schilling	Bos	485	338	328.75	0.697	0.678	102.82
Chuck James	Atl	484	352	342.43	0.727	0.707	102.80
Nate Robertson	Det	573	389	378.44	0.679	0.660	102.79
Aaron Cook	Col	572	401	390.44	0.701	0.683	102.70
Tim Lincecum	SF	389	277	269.87	0.712	0.694	102.64
Jon Garland	CWS	705	493	480.70	0.699	0.682	102.56
Steve Trachsel	Bal	491	351	342.47	0.715	0.697	102.49
Daisuke Matsuzaka	Bos	555	384	375.16	0.692	0.676	102.36
Noah Lowry	SF	502	349	340.97	0.695	0.679	102.35
Tim Hudson	Atl	722	504	492.65	0.698	0.682	102.30
C.C. Sabathia	Cle	701	476	465.40	0.679	0.664	102.28
Chad Durbin	Det	417	304	297.37	0.729	0.713	102.23
Carlos Zambrano	ChC	610	439	429.45	0.720	0.704	102.22
Micah Owings	Ari	461	332	324.88	0.720	0.705	102.19
James Shields	TB	615	435	425.93	0.707	0.693	102.13
Erik Bedard	Bal	431	306	299.70	0.710	0.695	102.10
Jake Westbrook	Cle	481	329	322.43	0.684	0.670	102.04
John Lackey	LAA	668	459	450.14	0.687	0.674	101.97
Oliver Perez	NYM	483	341	334.57	0.706	0.693	101.92
Justin Verlander	Det	577	407	399.34	0.705	0.692	101.92
Barry Zito	SF	608	441	432.73	0.725	0.712	101.91
Roy Halladay	Tor	722	497	488.79	0.688	0.677	101.68
Jason Marquis	ChC	626	440	432.86	0.703	0.691	101.65
Zack Greinke	KC	350	239	235.18	0.683	0.672	101.63
Buddy Carlyle	Atl	335	229	225.46	0.684	0.673	101.57
A.J. Burnett	Tor	414	301	296.47	0.727	0.716	101.53
Johan Santana	Min	555	394	388.14	0.710	0.699	101.51
Jake Peavy	SD	571	409	403.20	0.716	0.706	101.44
Kyle Kendrick	Phi	401	284	280.03	0.708	0.698	101.42
Greg Maddux	SD	681	466	459.63	0.684	0.675	101.39
Tim Wakefield	Bos	600	425	419.24	0.708	0.699	101.37
Fausto Carmona	Cle	654	463	456.92	0.708	0.699	101.33
Kelvim Escobar	LAA	572	387	382.00	0.677	0.668	101.31
Joe Blanton	Oak	750	520	513.28	0.693	0.684	101.31
Rich Hill	ChC	527	378	373.19	0.717	0.708	101.29
Odalis Perez	KC	494	325	320.93	0.658	0.650	101.27
Matt Morris	SF	473	315	311.16	0.666	0.658	101.23
Carlos Silva	Min	699	485	479.14	0.694	0.685	101.22
Adam Eaton	Phi	525	356	351.83	0.678	0.670	101.19
Felix Hernandez	Sea	567	372	367.73	0.656	0.649	101.16
Wandy Rodriguez	Hou	536	366	361.86	0.683	0.675	101.14
Vicente Padilla	Tex	407	270	266.96	0.663	0.656	101.14
Aaron Harang	Cin	642	451	446.11	0.702	0.695	101.10
Livan Hernandez	Ari	704	488	482.76	0.693	0.686	101.08
Orlando Hernandez	NYM	388	299	295.82	0.771	0.762	101.08
Jamie Moyer	Phi	633	432	427.41	0.682	0.675	101.08
Ian Snell	Pit	606	413	408.93	0.682	0.675	101.00
Andy Pettitte	NYY	690	457	452.68	0.662	0.656	100.96
Tom Gorzelanny	Pit	642	439	435.75	0.684	0.679	100.75
Matt Albers	Hou	362	247	245.52	0.682	0.678	100.60
Lenny DiNardo	Oak	430	302	300.28	0.702	0.698	100.57
John Danks	CWS	427	289	287.39	0.677	0.673	100.56
Mark Hendrickson	LAD	395	262	260.58	0.663	0.660	100.55
Jorge Sosa	NYM	361	256	254.94	0.709	0.706	100.42
Brandon Webb	Ari	692	480	478.35	0.694	0.691	100.34
Carlos Villanueva	Mil	318	229	228.36	0.720	0.718	100.28
John Maine	NYM	527	377	376.07	0.715	0.714	100.25
Justin Germano	SD	426	302	301.31	0.709	0.707	100.23
Chad Billingsley	LAD	400	279	278.70	0.697	0.697	100.11
Ben Sheets	Mil	431	307	306.74	0.712	0.712	100.09
Roy Oswalt	Hou	675	456	456.10	0.676	0.676	99.98
Jered Weaver	LAA	514	348	348.13	0.677	0.677	99.96
Mike Mussina	NYY	512	335	335.31	0.654	0.655	99.91
Josh Beckett	Bos	566	385	385.40	0.680	0.681	99.90
Matt Chico	Was	548	380	380.44	0.693	0.694	99.88
Matt Belisle	Cin	570	378	378.52	0.663	0.664	99.86
Shaun Marcum	Tor	456	329	329.69	0.721	0.723	99.79
Jeff Weaver	Sea	511	340	340.84	0.665	0.667	99.75
Derek Lowe	LAD	604	412	413.67	0.682	0.685	99.60
Kameron Loe	Tex	464	305	306.28	0.657	0.660	99.58
Joe Saunders	LAA	358	235	236.04	0.656	0.659	99.56
Brad Thompson	StL	451	307	308.45	0.681	0.684	99.53
Josh Fogg	Col	556	381	383.08	0.685	0.689	99.46
Horacio Ramirez	Sea	361	231	232.31	0.640	0.644	99.44
Jeff Francis	Col	662	447	449.57	0.675	0.679	99.43
Miguel Batista	Sea	615	415	417.51	0.675	0.679	99.40
Paul Byrd	Cle	686	465	467.91	0.678	0.682	99.38
Gil Meche	KC	663	459	462.21	0.692	0.697	99.31
Claudio Vargas	Mil	419	281	283.02	0.671	0.675	99.29
Mark Buehrle	CWS	648	455	458.82	0.702	0.708	99.17
Boof Bonser	Min	539	359	362.02	0.666	0.672	99.17
Javier Vazquez	CWS	583	409	412.68	0.702	0.708	99.11
Edwin Jackson	TB	516	333	336.02	0.645	0.651	99.10
Bartolo Colon	LAA	328	205	206.87	0.625	0.631	99.09
Tony Armas Jr.	Pit	305	208	209.93	0.682	0.688	99.08
Jorge de la Rosa	KC	431	285	287.91	0.661	0.668	98.99
Jason Jennings	Hou	319	214	216.25	0.671	0.678	98.96
Edgar Gonzalez	Ari	324	228	230.41	0.704	0.711	98.96
Chris Young	SD	448	336	339.55	0.750	0.758	98.96
Julian Tavarez	Bos	455	307	310.39	0.675	0.682	98.91
Woody Williams	Hou	632	443	448.01	0.701	0.709	98.88
Daniel Cabrera	Bal	608	415	419.74	0.683	0.690	98.87
Bronson Arroyo	Cin	661	449	454.60	0.679	0.688	98.77
Kyle Lohse	Cin	426	293	296.71	0.688	0.697	98.75
Cliff Lee	Cle	317	216	218.74	0.681	0.690	98.75
Paul Maholm	Pit	583	391	396.00	0.671	0.679	98.74
Chad Gaudin	Oak	603	413	418.34	0.685	0.694	98.72
Ervin Santana	LAA	457	302	306.05	0.661	0.670	98.68
Doug Davis	Ari	597	400	405.62	0.670	0.679	98.61
Sergio Mitre	Fla	522	343	347.92	0.657	0.667	98.59
Adam Wainwright	StL	654	441	447.57	0.674	0.684	98.53
Byung-Hyun Kim	Fla	316	212	215.40	0.671	0.682	98.42
Ramon Ortiz	Min	324	217	220.56	0.670	0.681	98.39
Kevin Correia	SF	306	217	220.82	0.709	0.722	98.27
Kevin Millwood	Tex	571	364	370.63	0.637	0.649	98.21
Jeremy Bonderman	Det	533	354	360.70	0.664	0.677	98.14
Scott Baker	Min	454	302	308.06	0.665	0.679	98.03
Dan Haren	Oak	661	457	466.27	0.691	0.705	98.01
Randy Wolf	LAD	309	205	209.32	0.663	0.677	97.93
Jeff Suppan	Mil	708	472	482.96	0.667	0.682	97.73
Josh Towers	Tor	347	229	234.38	0.660	0.675	97.71
Matt Cain	SF	571	409	419.20	0.716	0.734	97.57
John Smoltz	Atl	586	400	410.60	0.683	0.701	97.42
Brandon McCarthy	Tex	340	232	238.54	0.682	0.702	97.26
Taylor Buchholz	Col	305	207	212.87	0.679	0.698	97.24
Andy Sonnanstine	TB	408	272	280.02	0.667	0.686	97.13
Brian Burres	Bal	378	249	256.88	0.659	0.680	96.93
Brett Tomko	LAD	339	219	226.04	0.646	0.667	96.89
Joe Kennedy	Oak	346	242	250.10	0.699	0.723	96.76
Scott Kazmir	TB	534	346	358.19	0.648	0.671	96.60
Chris Capuano	Mil	456	297	307.78	0.651	0.675	96.50
Robinson Tejeda	Tex	302	204	212.16	0.675	0.703	96.16
David Wells	SD	416	271	282.44	0.651	0.679	95.95
David Bush	Mil	594	395	412.87	0.665	0.695	95.67
Zach Duke	Pit	399	246	258.54	0.617	0.648	95.15
Jose Contreras	CWS	647	420	441.74	0.649	0.683	95.08
Kip Wells	StL	522	342	360.50	0.655	0.691	94.87
Scott Olsen	Fla	578	366	387.16	0.633	0.670	94.53

Chien-Ming Wang comes out on top by far, not surprising given the Yankees overall defensive rating. What bothers me about Wang, however, is the low level of his predicted DER. You would think that someone who gets a lot of ground balls would be somewhat higher. The following chart breaks down Wang by ball in play type:

CM Wang by Batted Ball Type, 2007

Batted Ball Type	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Fly	112	101	98.85	0.902	0.883	102.18
Liner	92	29	16.14	0.315	0.175	179.66
Grounder	377	291	269.40	0.772	0.715	108.02
Bunt Grounder	6	4	4.20	0.667	0.700	95.24
Bunt Fly	1	1	1.00	1.000	1.000	100.00
Fliner (Fly)	29	13	14.12	0.448	0.487	92.09
Fliner (Liner)	26	9	11.23	0.346	0.432	80.12

Notice that the defense behind Wang caught a lot more line drives than predicted. Line drives tend to fall for hits, so by adding thirteen extra outs with liners, the Yankees really helped Wang. So Chien-Ming got a bit lucky that way. The grounders, however, is where the defense really shined. They picked up about twenty one more outs than expected on ground balls. How did they do that? The Yankees made a lot of plays on low probability vectors:

Wang Ground Balls by Vector, 2007

Vector	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
28	8	6	7.02	0.750	0.877	85.52
29	17	13	12.05	0.765	0.709	107.90
30	29	21	17.57	0.724	0.606	119.49
31	28	27	24.76	0.964	0.884	109.04
32	19	18	18.43	0.947	0.970	97.66
33	32	29	26.75	0.906	0.836	108.40
34	17	12	9.48	0.706	0.558	126.59
35	11	9	7.38	0.818	0.671	121.97
36	23	14	13.01	0.609	0.566	107.58
37	22	12	13.66	0.545	0.621	87.82
38	27	24	23.07	0.889	0.854	104.04
39	31	30	25.58	0.968	0.825	117.26
40	22	19	17.41	0.864	0.792	109.11
41	34	24	17.12	0.706	0.504	140.19
42	27	17	19.83	0.630	0.734	85.73
43	11	9	9.71	0.818	0.883	92.67
44	10	5	4.56	0.500	0.456	109.71

The vectors go from a low of 28 at the third base line to a high of 44 at the first base line. By looking at the Predicted DER column, you can see where the holes are in the infield. Vector 30 represents the hole between third and short, vectors 34-37 the area around second base where ground balls go into centerfield, and vector 41, the hole between first and second. Note that Wang does well in the holes, as if the defense were shifted a bit toward first base. Both the line drive and ground ball data make me wonder if someone was doing a very good job of positioning the Yankees fielders. I don't know who was in charge of that, but in the case of Wang, they did a very good job.

That brings up a point I haven't made in a while. Range is probably a poor word for the ability measured here. Range implies that the fielder can move a long way to get a ball. But sometimes anticipating where the ball gets hit is just as important. So the ability to move and the ability to position are two factors in what the model means by range.

On the other end of the spectrum, Matt Cain not only received no run support, he didn't get much defensive support either. And the defense behind Kazmir was just ridiculous. Here's a pitcher who keeps balls in play to a minimum, and his defense can't turn the few hit to them into outs.

I'll start on individual positions tomorrow.

Baseball Info Solutions sent me their final stats for 2007 over the weekend. That means it's time to start presenting the 2007 Probabilistic Model or Range. If you're new to this, you can find explanations in this archive. Basically, for each fieldable (non inside the park home runs) ball put in play, six parameters are used to determine how difficult it was to field the ball. A probability of turning the ball into an out is calculated, and those probabilities are summed. That gives us expected batted balls turned into outs. We turn that into a predicted DER (defensive efficiency record), compare that to the actual DER and calculate a ranking.

The model is based primarily on visiting player data, smoothed, distance on fly balls. Only 2007 data was used to construct the model.

Note that a team can post a poor DER during the season, but do well in this model if the balls put into play were extremely difficult to field. In fact, the team ranked first in 2007 is a bit of a surprise for that very reason.

Probabilistic Model of Range, 2007 Data, Teams, Visit Smooth Distance Model, Ranked by Difference

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Difference
Yankees	4511	3103	3041.46	0.688	0.674	0.01364
Red Sox	4226	2974	2919.61	0.704	0.691	0.01287
Cubs	4177	2943	2895.51	0.705	0.693	0.01137
Blue Jays	4349	3060	3017.22	0.704	0.694	0.00984
Royals	4528	3093	3058.20	0.683	0.675	0.00768
Angels	4325	2930	2900.79	0.677	0.671	0.00675
Phillies	4505	3085	3056.00	0.685	0.678	0.00644
Rockies	4599	3221	3195.95	0.700	0.695	0.00545
Tigers	4486	3094	3072.58	0.690	0.685	0.00477
Braves	4404	3069	3048.96	0.697	0.692	0.00455
Mets	4362	3050	3033.08	0.699	0.695	0.00388
Giants	4467	3108	3096.80	0.696	0.693	0.00251
Orioles	4403	3017	3006.12	0.685	0.683	0.00247
Rangers	4518	3071	3061.36	0.680	0.678	0.00213
Nationals	4591	3198	3191.04	0.697	0.695	0.00152
Indians	4548	3112	3107.26	0.684	0.683	0.00104
Padres	4476	3131	3128.60	0.700	0.699	0.00054
Mariners	4535	3050	3051.99	0.673	0.673	-0.00044
Diamondbacks	4351	3013	3016.84	0.692	0.693	-0.00088
Dodgers	4310	2942	2945.91	0.683	0.684	-0.00091
Cardinals	4587	3150	3154.99	0.687	0.688	-0.00109
Twins	4384	3003	3014.01	0.685	0.688	-0.00251
Astros	4530	3099	3120.86	0.684	0.689	-0.00483
Reds	4533	3068	3096.08	0.677	0.683	-0.00619
Pirates	4608	3099	3132.67	0.673	0.680	-0.00731
Athletics	4499	3110	3144.35	0.691	0.699	-0.00763
Brewers	4392	2966	3011.82	0.675	0.686	-0.01043
White Sox	4545	3089	3141.16	0.680	0.691	-0.01148
Marlins	4491	2962	3039.28	0.660	0.677	-0.01721
Devil Rays	4378	2867	2943.31	0.655	0.672	-0.01743

That's right, the Yankees are number one. Without running the individual numbers, I'm guessing that a full season of Melky Cabrera and keeping Giambi off first really helped. The Red Sox defense turned a higher percentage of their balls in play into outs, but they also were given easier balls to field in general.

I wondered why the Tampa Bay pitching staff did so poorly with the high number of strikeouts they collected, and the reason is clear in these numbers. The Devil Rays defense was horrible. In fact, the state of Florida just can't play defense, with the Marlins ranking 29th in the majors.

For the second year in a row, the Kansas City Royals look a lot better than their posted DER. If they ever get a good set of pitchers on that team, they're going to post a low ERA.

For those of you who prefer a ranking by ratio of DER/Predicted DER, here's the table with that data.

Probabilistic Model of Range, 2007 Data, Teams, Visit Smooth Distance Model, Ranked by Difference

Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Ratio
Yankees	4511	3103	3041.46	0.688	0.674	102.02
Red Sox	4226	2974	2919.61	0.704	0.691	101.86
Cubs	4177	2943	2895.51	0.705	0.693	101.64
Blue Jays	4349	3060	3017.22	0.704	0.694	101.42
Royals	4528	3093	3058.20	0.683	0.675	101.14
Angels	4325	2930	2900.79	0.677	0.671	101.01
Phillies	4505	3085	3056.00	0.685	0.678	100.95
Rockies	4599	3221	3195.95	0.700	0.695	100.78
Tigers	4486	3094	3072.58	0.690	0.685	100.70
Braves	4404	3069	3048.96	0.697	0.692	100.66
Mets	4362	3050	3033.08	0.699	0.695	100.56
Orioles	4403	3017	3006.12	0.685	0.683	100.36
Giants	4467	3108	3096.80	0.696	0.693	100.36
Rangers	4518	3071	3061.36	0.680	0.678	100.31
Nationals	4591	3198	3191.04	0.697	0.695	100.22
Indians	4548	3112	3107.26	0.684	0.683	100.15
Padres	4476	3131	3128.60	0.700	0.699	100.08
Mariners	4535	3050	3051.99	0.673	0.673	99.93
Diamondbacks	4351	3013	3016.84	0.692	0.693	99.87
Dodgers	4310	2942	2945.91	0.683	0.684	99.87
Cardinals	4587	3150	3154.99	0.687	0.688	99.84
Twins	4384	3003	3014.01	0.685	0.688	99.63
Astros	4530	3099	3120.86	0.684	0.689	99.30
Reds	4533	3068	3096.08	0.677	0.683	99.09
Pirates	4608	3099	3132.67	0.673	0.680	98.93
Athletics	4499	3110	3144.35	0.691	0.699	98.91
Brewers	4392	2966	3011.82	0.675	0.686	98.48
White Sox	4545	3089	3141.16	0.680	0.691	98.34
Marlins	4491	2962	3039.28	0.660	0.677	97.46
Devil Rays	4378	2867	2943.31	0.655	0.672	97.41

A few days ago I introduced the idea of a probabilistic model of Ground into Double Plays (GDP). The probabilistic model of range just measures the ability to turn a ball into an out. For infielders, however, they're often asked to turn a ground ball into more than one out. The idea is to take a very specific situation; ground ball hit, man on first, less than two out and build a model that measures both plays made and GDP turned. With that model, we can ask which fielders perform well in that situation.

In building this model, I left parks out of the parameters. Basically, I thought the sample size would be too small if I left the parks in. This probably hurts the three teams that play of artifical turf.

Let's start by looking at the ability of shortstops to start a double play. The following table looks at three indexes for each fielder. The Plays Made (PM) index measures Plays Made / Predicted Plays Made. This measures the fielder's ability to turn a ball into an out. The GDP index does the same for ground double plays. Does the fielder start the expected number of double plays? And finally, an outs index that looks at the total number of outs accured to the fielder on these balls in play. It could be a fielder is making up for a lack of range by being really good at starting GDPs, or vice versa. Remember, this says nothing about the pivot man or the receiver at first base. In this context, we're only looking at the fielder who starts the play.

Probabilistic Model of GDPs, Ground Balls, Man on First, Less than Two Out, Shortstops Starting GDP (2006 Data Used to Build Model)

Player	Ground Balls In Play	Actual Plays Made	Predicted Plays Made	PM Index	Actual GDP	Predicted GDP	GDP Index	Actual Outs	Predicted Outs	Outs Index
Craig Counsell	183	40	32.14	124.44	32	21.23	150.72	72	53.38	134.89
Khalil Greene	219	53	45.27	117.08	31	28.68	108.07	84	73.95	113.59
Stephen Drew	121	26	23.68	109.82	17	14.29	118.92	43	37.97	113.25
Clint Barmes	283	56	53.75	104.18	42	33.03	127.16	98	86.78	112.92
Juan Uribe	274	58	50.75	114.29	34	31.85	106.75	92	82.60	111.38
Hanley Ramirez	352	71	67.58	105.05	49	43.18	113.48	120	110.76	108.34
Miguel Tejada	342	76	72.84	104.33	52	45.35	114.66	128	118.20	108.30
David Eckstein	298	61	56.74	107.50	38	34.92	108.81	99	91.67	108.00
Jack Wilson	290	64	62.47	102.45	46	39.39	116.77	110	101.86	107.99
Rafael Furcal	396	92	85.54	107.55	58	55.24	104.99	150	140.78	106.55
Bill Hall	228	55	50.83	108.21	33	32.90	100.30	88	83.73	105.10
Bobby Crosby	237	44	42.12	104.47	29	27.37	105.94	73	69.49	105.05
Alex Gonzalez	244	50	51.18	97.69	38	33.41	113.74	88	84.59	104.03
Jimmy Rollins	333	70	69.50	100.72	48	44.05	108.97	118	113.54	103.92
Carlos Guillen	303	65	64.24	101.18	45	41.63	108.10	110	105.87	103.90
Adam Everett	309	66	63.51	103.91	41	40.15	102.11	107	103.67	103.22
Ronny Cedeno	240	49	46.28	105.87	28	29.54	94.79	77	75.82	101.55
Michael Young	410	88	86.89	101.28	54	55.41	97.46	142	142.30	99.79
Jason A Bartlett	214	50	47.40	105.49	28	31.86	87.90	78	79.25	98.42
Jose Reyes	304	67	66.70	100.45	40	43.66	91.62	107	110.36	96.96
Omar Vizquel	297	64	65.48	97.73	42	44.00	95.45	106	109.49	96.82
John McDonald	170	25	26.52	94.26	18	17.91	100.50	43	44.43	96.77
Orlando Cabrera	319	58	60.40	96.03	38	39.02	97.38	96	99.42	96.56
Felipe Lopez	319	67	64.47	103.93	34	40.58	83.78	101	105.05	96.15
Angel Berroa	337	69	72.29	95.44	46	47.91	96.02	115	120.20	95.67
Jhonny Peralta	357	82	84.45	97.10	50	55.63	89.88	132	140.08	94.23
Alex Cora	127	30	32.94	91.07	21	22.16	94.76	51	55.10	92.56
Marco Scutaro	146	34	37.58	90.47	24	25.22	95.15	58	62.81	92.35
Edgar Renteria	347	63	67.67	93.10	39	43.19	90.30	102	110.86	92.01
Yuniesky Betancourt	350	60	66.40	90.36	43	46.02	93.44	103	112.42	91.62
Julio Lugo	182	32	35.29	90.68	21	23.66	88.74	53	58.95	89.90
Ben T Zobrist	131	25	28.09	89.00	17	18.93	89.82	42	47.02	89.33
Juan Castro	146	23	25.18	91.33	13	15.27	85.11	36	40.46	88.98
Derek Jeter	336	63	70.96	88.79	40	45.81	87.32	103	116.77	88.21
Royce Clayton	234	43	47.02	91.44	20	29.67	67.40	63	76.70	82.14
Aaron W Hill	108	16	20.33	78.70	7	12.82	54.62	23	33.14	69.39

Notice how few chances fielders get to turn GDPs. On the best teams, they get a little over two chances a game. Secondly, Arizona does a good job of picking out shortstops, as Counsell and Drew are near the top of the list. And if you don't like Derek Jeter, here's another area where you can pick on him.

The other thing that strikes me about the list is that shortstops who are good at making plays are also the ones good at starting double plays. Ronny Cedeno is unusual in that he's good at getting an out, but didn't do well starting DPs. Could it be that Todd Walker was just a poor pivot man? I hope further research using these models will help answer that question.

Something that's been on my mind is using ideas from the Proabilistic Model of Range on a very specific issue, double plays. The idea is to look at a particular set of balls in play, ground balls with a man on first and less than two outs, and see what fielders do well. What might make this very interesting, however, is that we can not only look at who starts the double play, but who is the pivot man, and who finishes the job. I'm imagining we can look at shortstop/second baseman combinations and see if the probabilities go up or down with a change in personnel, or with who is fielding vs. who is pivoting.

As always, your thoughts are welcome. Here's a couple of tables to start us off. The first shows how often each of the infield positions starts a double play.

Probability of a Fielding Position Starting a GDP, Groundballs Only, Man on First, Less Than Two Out, 2006

Position	GDP	Total	Pct
1	274	11076	0.025
2	4	11076	0.00036
3	234	11076	0.021
4	1099	11076	0.099
5	802	11076	0.072
6	1484	11076	0.134

Pretty much what you'd expect, although I'm impressed that third basemen start as many as they do. This next chart divides the infield into eighteen pie slices, five degrees wide. Zero represents the third base line, 17 the first base line. The probability given is the probability of a ball being turned into a double play on that vector.

Probability of a GDP on a Ball Hit on the Vector, Groundballs Only, Man on First, Less Than Two Out, 2006

Vector	GDP	Total	Probability
0	17	177	0.096
1	112	334	0.335
2	369	869	0.425
3	243	987	0.246
4	213	803	0.265
5	370	711	0.520
6	533	842	0.633
7	335	626	0.535
8	119	452	0.263
9	264	643	0.411
10	212	464	0.457
11	394	660	0.597
12	331	647	0.512
13	129	636	0.203
14	52	765	0.068
15	109	761	0.143
16	85	414	0.205
17	10	102	0.098

You can see from this that second baseman cheat more toward the bag than shortstops. Vector 8 represents the five degrees to the shortstop side of the bag. Vector 9 represents the five degrees to the second base side of the bag. As you can see, a lot more GDP's are started on the second base side. That makes sense, of course, as there are more right-handed hitters, and against a righty, a shortstop can't cheat as much. And while the lines are great places to hit the ball to avoid a double play, the absolute best place is the hole between second and first. I guess there is something to the idea of hitting behind the runner!

Baseball Musings is holding a pledge drive in March. If research like this interests you, I hope you'll consider a donation.

Speaking to a reporter this afternoon about the Probabilistic Model of Range (PMR), I realized I never published the chart of how pitchers were helped or hurt by their defense in 2006. So without further ado:

Probabilistic Model of Range, Fielders Behind Pitchers, 2006. Smoothed Visit Model with Distance for Fly Balls

Pitcher	Team	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Difference
Kris Benson	Bal	595	425	402.81	0.714	0.677	0.03730
Chris Young	SD	468	357	339.63	0.763	0.726	0.03712
Ervin R Santana	LAA	603	435	412.64	0.721	0.684	0.03708
Roy Halladay	Tor	686	491	466.71	0.716	0.680	0.03540
Kevin Millwood	Tex	670	458	434.82	0.684	0.649	0.03460
Joel Pineiro	Sea	569	378	361.55	0.664	0.635	0.02891
Kenny Rogers	Det	656	472	454.00	0.720	0.692	0.02743
Chris Carpenter	StL	638	455	437.61	0.713	0.686	0.02726