Probabilistic Model of Range Archives

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