Probabilistic Model of Range

The road towards knowledge tends to be a pretty winding one.  

Take this Probabilistic Model of Range stuff, which I'd never heard of 'til Friday.  

What happened, was that the Fire Joe Morgan people, who always piss me off greatly for their snarky dogmatic approach, had written something that took issue with the idea of Justin Morneau as AL MVP.

Well, what's wrong with that? you may ask.  

Nothing, on the face of it; certainly Morneau is one of your least deserving MVP's in quite some time.  And even FJM's idea that maybe Derek Jeter should have won the thing--although I heartily disagree with it--is a lot more defensible than Morneau's having taken home the trophy.

But where I got all worked up was when this Junior avatar appealed to Jeter's defense to make his argument.

On top of all this, Jeter plays a premium defensive position, one that is difficult to fill, with adequate skill. Baseball Prospectus has him at 39 fielding runs above replacement, which is actually better than adequate.

And that's where I blew up.  Just because Baseball Prospectus cooked up some cockamamie number, this means Derek Jeter is a good defensive shortstop?  

Anyone who's seen Derek Jeter play short knows that he has microscopic range to go with merely average tools.  

And if Baseball Prospectus gives him an excellent FRAR score (the number was actually 30, not the 39 quoted, for what little it's worth), then that most likely means that the algortihm they're using to calculate the number is wrong.

So my point in this long missive I then wrote to FJM was this:  Feel free to use numbers all you want in discussing a player.  Employ all the tools at your disposal.  But please make sure that there is at least some relation between the real world and the numbers you so forcefully put forward as describing it.

People, and baseball fans especially, quote numbers all the time, but very few bother using their noggin to evaluate whether the numbers they're quoting make any kind of empirical sense.  So these purported pundits will tell you with a straight face that you're more likely to score from second with one out than from third, or that, again, Derek Jeter is an asset on defense.

So at this point I wrote fellow SBNation blogger Marc Normandin with my suspicions that FRAR might not be all it was cracked up to be, and he--as one of the most open-minded and least dogmatic stats guys you could ever want to meet--pointed me toward David Pinto's Probabilistic Model of Range.  For those who might be familiar, this is Pinto's extension of the old Ultimate Zone Rating system, and for those who are not, it's a method that in Pinto's words

calculate[s] the probability of a ball being turned into an out based on six parameters:

1. Direction of hit (a vector).
   
2. The type of hit (Fly, ground, line drive, bunt).
   
3. How hard the ball was hit (slow, medium, hard).
   
4. The park.
   
5. The handedness of the pitcher.
   
6. The handedness of the batter.

For each ball in play, the program sums the probability of that ball being turned into an out, and that gives us the expected outs. Dividing that by balls in play yields expected defensive efficiency rating (DER). That is compared to the team's actual DER. A good defensive team should have a better DER than it's expected DER.

A quick look showed that Pinto's system ranked Adam Everett number one in baseball in this differential he calculates between expected and actual outmaking rates.

That not only made me happy as an Astro fan, it jibed with my knowledge of the real world, so I decided to look further at numbers that Pinto has posted at his site over the last two weeks.

After the fold (Lord this is long, already!), you'll see the infield positions with the top three, the bottom three, Gold Glove Winners, and all Astros listed.

Just to emphasize, the key number, and the way the charts will be sorted, is "difference," the difference between the plays the model says the player SHOULD have made and the plays he DID make.

Probabilistic Model of Range, Third Basemen
Model is Based on 2006 Data Only, Min. 1000 Balls in Play
Uses Distance for Fly Balls

Rk		Player	In Play	Actual Outs	Predicted Outs	Outs/ Inplay	Predicted Outs/Inplay	Difference
1.		Joe Crede	3962	436	397.55	0.110	0.100	0.00971
2.		Freddy Sanchez	2527	285	265.88	0.113	0.105	0.00757
3.		Pedro Feliz	4278	420	391.93	0.098	0.092	0.00656
7.		Scott Rolen*	3788	390	371.79	0.103	0.098	0.00481
9.		Morgan Ensberg	2917	289	276.96	0.099	0.095	0.00413
15.		Eric Chavez*	3607	362	353.27	0.100	0.098	0.00242
34.		Aubrey Huff	2133	193	203.79	0.090	0.096	-0.00506
35.		Aaron Boone	2748	221	235.26	0.080	0.086	-0.00519
36.		Tony Batista	1354	114	124.03	0.084	0.092	-0.00741
37.		Rich Aurilia	1109	101	112.09	0.091	0.101	-0.01000
*Gold Glove Winner

In a post not too terribly long ago, I had talked about maybe giving not enough credit to Morgan as a much better than average third baseman just based on having stumbled across his range factor and zone rating from 2006. Interesting to see that this PMR stuff kind of validates that.

It also reinforces the idea that most of us have that Aubrey Huff just ain't much defensively at third base. Considering that if we resigned Huff, it'd basically mean we were hoping for a comeback year from Aubrey, AND that he's pretty clearly Morgan's defensive inferior, I say if you're gonna hope for a comeback year, you might as well hope it's Morgan who has it.

Probabilistic Model of Range, Shortstops
Model is Based on 2006 Data Only, Min. 1000 Balls in Play
Uses Distance for Fly Balls

Rk		Player	In Play	Actual Outs	Predicted Outs	Outs/ Inplay	Predicted Outs/Inplay	Difference
1.		Adam Everett	3801	500	464.88	0.132	0.122	0.00924
2.		Bill Hall	3311	404	375.73	0.122	0.113	0.00854
3.		Craig Counsell	2274	310	290.98	0.136	0.128	0.00836
7.		Ben Zobrist	1395	173	165.55	0.124	0.119	0.00534
13.		Omar Vizquel*	3974	441	430.32	0.111	0.108	0.00269
15.		Jack Wilson	3485	454	447.27	0.130	0.128	0.00193
33.		Derek Jeter*	4009	450	464.37	0.112	0.116	-0.00358
35.		Marco Scutaro	1773	207	218.44	0.117	0.123	-0.00645
36.		Felipe Lopez	4245	438	469.73	0.103	0.111	-0.00747
37.		Aaron Hill	1273	140	152.71	0.110	0.120	-0.00999
*Gold Glove Winner

Yes Adam's the man (and check out the early returns on Ben Zobrist!), but Jack Wilson at number fifteen gives me some pause. Wilson is to my mind clearly the second best shortstop in the National League. Shit, on days when Adam's feeling a little under the weather, he's probably the best. So I wonder at PRM's inability to capture that for us, although I'm more than willing to cite the low number for Jeter, because it matches my predispositions so well.

Probabilistic Model of Range, Second Basemen
Model is Based on 2006 Data Only, Min. 1000 Balls in Play
Uses Distance for Fly Balls

Rk		Player	In Play	Actual Outs	Predicted Outs	Outs/ Inplay	Predicted Outs/Inplay	Difference
1.		Tony Graffanino	1702	186	161.05	0.109	0.095	0.01466
2.		Neifi Perez	1374	166	152.40	0.121	0.111	0.00990
3.		Jamey Carroll	2806	396	372.04	0.141	0.133	0.00854
4.		Orlando Hudson*	4128	552	520.38	0.134	0.126	0.00766
6.		Mark Grudzielanek*	3595	367	344.87	0.102	0.096	0.00616
14.		Chris Burke	1012	128	124.23	0.126	0.123	0.00373
30.		Craig Biggio	3162	360	376.73	0.114	0.119	-0.00529
35.		Jorge Cantu	2859	283	311.98	0.099	0.109	-0.01014
36.		Ty Wigginton	1075	105	117.30	0.098	0.109	-0.01144
37.		Todd Walker	1279	128	147.72	0.100	0.115	-0.01542
*Gold Glove Winner

Burke over Biggio, no surprise, that's good, that computes.

Probabilistic Model of Range, First Basemen
Model is Based on 2006 Data Only, Min. 1000 Balls in Play
Uses Distance for Fly Balls

Rk		Player	In Play	Actual Outs	Predicted Outs	Outs/ Inplay	Predicted Outs/Inplay	Difference
1.		Kendry Morales	1338	124	110.53	0.093	0.083	0.01007
2.		Albert Pujols*	3864	306	267.43	0.079	0.069	0.00998
3.		Lance Niekro	1313	98	85.07	0.075	0.065	0.00984
22.		Lance Berkman	2722	198	194.25	0.073	0.071	0.00138
26.		Mark Teixeira*	4436	310	305.13	0.070	0.069	0.00110
30.		Mike Lamb	1488	98	98.33	0.066	0.066	-0.00022
44.		Conor Jackson	3295	231	254.95	0.070	0.077	-0.00727
45.		Sean Casey	2806	168	191.82	0.060	0.068	-0.00849
46.		Jason Giambi	1467	71	88.40	0.048	0.060	-0.01186
*Gold Glove Winner

Isn't Lance a better defensive first baseman than is shown here? And I HOPE that Mark Teixeira, your American League Gold Glove winner, does not play first at a level so close to that of Mike Lamb.

* * * I'll take a look at the outifeld spots later this week, but it is worth noting that I don't present this PMR stuff as any end-all/be-all for evaluating defense. But it does look intriguing, and perhaps you--like I--can find room to incorporate some of what it says into the way you approach the idea of major league defense.