Baseball Musings: Probabilistic Model of Range, 2005

January 21, 2006

Probabilistic Model of Range, 2005

A number of readers inquired over the last two months if the Probabilistic Range number for 2005 were going to be published this off-season. I'm happy to say I've acquired the data and I'll be presenting tables this week, on teams, defenses behind pitchers, and individual pitchers.

Here's last year's explanation of the model, which I won't repeat here. The idea is to look not just at the balls turned into outs, but how difficult those balls were to turn into outs. Teams or fielders who turn difficult plays into outs do well. Teams or fielders who let easy balls drop for hits (or make errors) do poorly.

One of the hotly debated aspects of this model is how parks are included in the model. The biggest criticism is that home players have too much influence on the model. I'm going to present three tables for the teams that show how parks change the data.

One will be the model as described in the previous work.

One will be the model without parks in the model.

The third will be a combination of the two, 50% of each.

All models are built on data from four years, 2002-2005.

Probabilistic Model of Range, 2005. Model Includes Parks
Team	InPlay	Actual Outs	Predicted Outs	DER	Predicted DER	Difference
Astros	4204	2963	2854.17	0.705	0.679	0.02589
Indians	4385	3108	2995.26	0.709	0.683	0.02571
Phillies	4211	2962	2853.80	0.703	0.678	0.02570
Athletics	4286	3064	2954.86	0.715	0.689	0.02546
White Sox	4457	3175	3066.86	0.712	0.688	0.02426
Cardinals	4414	3101	3007.96	0.703	0.681	0.02108
Blue Jays	4511	3156	3063.16	0.700	0.679	0.02058
Braves	4559	3162	3073.91	0.694	0.674	0.01932
Twins	4545	3193	3107.42	0.703	0.684	0.01883
Angels	4383	3070	2998.12	0.700	0.684	0.01640
Giants	4520	3152	3080.03	0.697	0.681	0.01592
Orioles	4377	3032	2964.67	0.693	0.677	0.01538
Pirates	4467	3095	3032.44	0.693	0.679	0.01400
Diamondbacks	4571	3118	3059.45	0.682	0.669	0.01281
Red Sox	4575	3127	3068.95	0.683	0.671	0.01269
Devil Rays	4560	3112	3054.72	0.682	0.670	0.01256
Cubs	4117	2871	2819.97	0.697	0.685	0.01239
Mariners	4546	3184	3128.12	0.700	0.688	0.01229
Tigers	4527	3152	3097.51	0.696	0.684	0.01204
Brewers	4252	2960	2916.77	0.696	0.686	0.01017
Rangers	4697	3200	3158.10	0.681	0.672	0.00892
Dodgers	4392	3073	3036.02	0.700	0.691	0.00842
Mets	4424	3094	3058.20	0.699	0.691	0.00809
Rockies	4537	3043	3013.43	0.671	0.664	0.00652
Padres	4423	3051	3047.08	0.690	0.689	0.00089
Marlins	4367	2965	2965.42	0.679	0.679	-0.00010
Yankees	4483	3087	3092.01	0.689	0.690	-0.00112
Nationals	4538	3161	3166.79	0.697	0.698	-0.00128
Royals	4611	3068	3099.97	0.665	0.672	-0.00693
Reds	4650	3148	3182.99	0.677	0.685	-0.00753

Unlike 2004, this was a very good defensive year. Seven of the top eight teams in the list made the playoffs or were in contention as late as the last week of the season. Now for the teams with no park adjustment.

Probabilistic Model of Range, 2005. Model Does Not Include Parks
Team	InPlay	Actual Outs	Predicted Outs	DER	Predicted DER	Difference
Phillies	4211	2962	2812.44	0.703	0.668	0.03552
Athletics	4286	3064	2921.09	0.715	0.682	0.03334
Indians	4385	3108	2970.70	0.709	0.677	0.03131
Astros	4204	2963	2835.95	0.705	0.675	0.03022
Braves	4559	3162	3043.69	0.694	0.668	0.02595
White Sox	4457	3175	3061.04	0.712	0.687	0.02557
Cardinals	4414	3101	2992.97	0.703	0.678	0.02447
Blue Jays	4511	3156	3066.66	0.700	0.680	0.01981
Giants	4520	3152	3062.55	0.697	0.678	0.01979
Dodgers	4392	3073	2992.05	0.700	0.681	0.01843
Cubs	4117	2871	2799.86	0.697	0.680	0.01728
Nationals	4538	3161	3082.57	0.697	0.679	0.01728
Orioles	4377	3032	2960.89	0.693	0.676	0.01625
Diamondbacks	4571	3118	3051.28	0.682	0.668	0.01460
Angels	4383	3070	3007.42	0.700	0.686	0.01428
Twins	4545	3193	3130.04	0.703	0.689	0.01385
Pirates	4467	3095	3034.07	0.693	0.679	0.01364
Mariners	4546	3184	3124.61	0.700	0.687	0.01306
Tigers	4527	3152	3101.99	0.696	0.685	0.01105
Brewers	4252	2960	2913.06	0.696	0.685	0.01104
Mets	4424	3094	3051.37	0.699	0.690	0.00964
Devil Rays	4560	3112	3068.61	0.682	0.673	0.00951
Rangers	4697	3200	3165.60	0.681	0.674	0.00732
Red Sox	4575	3127	3104.20	0.683	0.679	0.00498
Padres	4423	3051	3039.75	0.690	0.687	0.00254
Rockies	4537	3043	3035.26	0.671	0.669	0.00171
Marlins	4367	2965	2958.27	0.679	0.677	0.00154
Reds	4650	3148	3155.28	0.677	0.679	-0.00157
Yankees	4483	3087	3135.64	0.689	0.699	-0.01085
Royals	4611	3068	3130.12	0.665	0.679	-0.01347

You can see the big drop in the Red Sox defense if you don't include the park in the calculation of team range. Lots of balls that would be outs other places hit the wall in Fenway. Without the adjustment, the Red Sox defense looks worse than it is.

Here's the smoothed model:

Probabilistic Model of Range, 2005. 50% Model With Parks, 50% Model Without Parks
Team	InPlay	Actual Outs	Predicted Outs	DER	Predicted DER	Difference
Phillies	4211	2962	2833.12	0.703	0.673	0.03061
Athletics	4286	3064	2937.98	0.715	0.685	0.02940
Indians	4385	3108	2982.98	0.709	0.680	0.02851
Astros	4204	2963	2845.06	0.705	0.677	0.02805
White Sox	4457	3175	3063.95	0.712	0.687	0.02492
Cardinals	4414	3101	3000.46	0.703	0.680	0.02278
Braves	4559	3162	3058.80	0.694	0.671	0.02264
Blue Jays	4511	3156	3064.91	0.700	0.679	0.02019
Giants	4520	3152	3071.29	0.697	0.679	0.01786
Twins	4545	3193	3118.73	0.703	0.686	0.01634
Orioles	4377	3032	2962.78	0.693	0.677	0.01581
Angels	4383	3070	3002.77	0.700	0.685	0.01534
Cubs	4117	2871	2809.92	0.697	0.683	0.01484
Pirates	4467	3095	3033.25	0.693	0.679	0.01382
Diamondbacks	4571	3118	3055.36	0.682	0.668	0.01370
Dodgers	4392	3073	3014.04	0.700	0.686	0.01343
Mariners	4546	3184	3126.36	0.700	0.688	0.01268
Tigers	4527	3152	3099.75	0.696	0.685	0.01154
Devil Rays	4560	3112	3061.67	0.682	0.671	0.01104
Brewers	4252	2960	2914.92	0.696	0.686	0.01060
Mets	4424	3094	3054.78	0.699	0.691	0.00886
Red Sox	4575	3127	3086.58	0.683	0.675	0.00884
Rangers	4697	3200	3161.85	0.681	0.673	0.00812
Nationals	4538	3161	3124.68	0.697	0.689	0.00800
Rockies	4537	3043	3024.35	0.671	0.667	0.00411
Padres	4423	3051	3043.42	0.690	0.688	0.00171
Marlins	4367	2965	2961.85	0.679	0.678	0.00072
Reds	4650	3148	3169.14	0.677	0.682	-0.00455
Yankees	4483	3087	3113.83	0.689	0.695	-0.00598
Royals	4611	3068	3115.04	0.665	0.676	-0.01020

I'm open as always to comments on which of these you think is best, or how any of them might be improved. The best suggestions I've heard, however, involve much more complicated programming. I like this simple model.

One thing is very clear, the Yankees, Royals and Reds did not help their pitching staffs in 2005, no matter how you look at the data.

A hat tip to Mitchel Lichtman, who used this idea first in UZR, but has gone on to private practice.

Posted by David Pinto at 08:28 PM | Probabilistic Model of Range | TrackBack (0)

Comments

I know this subject was brought up previous in the other PMR discussions, but looking at the Difference column, most teams are positive. What I'd like to see is some numbers metric of above/below average. That's one of the reasons why numbers like Rate and OPS+ are so easy to use. Just looking at the number tells you how the player did compared to average.

Posted by: sabernar at January 21, 2006 09:02 PM

With 25 of 30 teams in the basic model outperforming their predicted DER, and a 26th team being virtually identical to the model, it seems to me that there's either a problem in the model, or something in the BIP distribution changed between 2004 and 2005. The model should not be underpredicting DER for that many teams.

Posted by: Mike Emeigh at January 21, 2006 09:19 PM

I've re-done the numbers for my own use with a fudge factor. If anyone wants them, drop me an e-mail.

David

Oh, and David, this is great stuff! Keep it coming.

Posted by: David Gassko at January 21, 2006 09:23 PM

Mike, the model is based on four years of data. My guess is if I ran all four team seasons, you'd see an even number above and below 0.

Posted by: David Pinto at January 21, 2006 09:29 PM

David, interesting data. One question and observation. How do you interpret the DER? If the Phillies have a DER of .703, does that mean there's a 70 percent chance that a ball put in play will turn into an out? And I noticed that there's not a lot of variation in the data. It seems like all the team are in the .68 to .70 range. Is there any concrete way to describe how a team with a DER of .700 differs from a team with a DER of .680?

Posted by: steve at January 22, 2006 12:23 AM

Steve, your interpretation of DER is correct. These are fieldable balls in play, so out of the park home runs are removed from the equation.

It may help you get a handle on DER by thinking of it as 1.0-DER. That would be approximately batting average vs. the defense. So the difference between a .700 DER and a .680 DER is the difference between a .300 hitter and a .320 hitter.

Posted by: David Pinto at January 22, 2006 08:21 AM

David, you rock! Love this stuff.

Besides the Red Sox drop w/ no park variable, the Nationals rise is also quite drastic, from #12 to #27. That big stadium must let them catch many fly balls that would be HR's elsewhere.

Posted by: Jason at January 22, 2006 08:56 AM

Really great information.

Another way to think about what a .703 DER means is that the Phillies' fielders made 129 more outs than expected. That's about 100 runs (depending on distribution btwn IF and OF), or a reduction in team RA/G of 0.62. In fact, making the "difference" column in the table outs (or runs) rather than DER would probably be more helpful.

"Unlike 2004, this was a very good defensive year."
With about 130,000 BIP each year, I'm skeptical that there are really 'bad' or 'good' years. The THT site shows overall DER at .695 in 2004 and .695 in 2005. If that's right, it's hard to conclude this was a better fielding year. Or if DER was higher this year, I would look to factors like weather, park changes, strike zone changes, etc. before concluding the overall level of fielding changed.

Posted by: Guy at January 23, 2006 11:06 AM

David is taking the perspective, in his presentation and perhaps in his opinion, the following:

given that the "true mean" league-average is zero for the last 4 years, any deviation within those 4 years at the league-level is a true difference in skill.

There are a multitude of reasons why the "sample" mean is not zero for each of the last 4 years (within the 4-yr population). Change in personnel or quality of fielders is one, but that is probably way down the list. External factors, like the climate, or ball (or list your favorite) can be a cause.

It is much more beneficial, and probably more accurate, to list the annual "true mean" of each sample year as zero. It makes in-season comparisons much easier, and easier to grasp.

Year-to-year comparisons are probably more accurate as well (rather than making it seem like 80% of the fielders, improved, or whatever the number is).

That said, I love this!

Posted by: tangotiger at January 23, 2006 02:40 PM

There are two things being tracked: real DER and pred DER. Real DER changes very little -- approx .691 in 2004 and .694 in 2005 according to David's data. If 3 plays out of 1,000 makes '05 a "better fielding year," well OK (but the difference is w/in the MOE). But the predicted DER goes from .698 last year to .681 this year. That doesn't make sense to me. The distribution of 125,000 BIP can't possibly be that different.

Posted by: Guy at January 23, 2006 04:42 PM

Guy,

You raise an excellent point. I'll look into this. One problem is that if you look at the table from last year, there's a different underlying model, in that it's based on three years (2002-2004) of data. I don't know if that's enough to cause a difference, but I'm going to run 2004 against the four year model and see.

Posted by: David Pinto at January 23, 2006 04:53 PM

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