PMR and Carlos Guillen

David Pinto at Baseball Musings has started posting his Probabilistic Model of Range (PMR) tables for 2006. PMR may be the most sophisticated freely available fielding statistic you can find on the internet. It is based on detailed play by play data collected by Baseball Info Solutions.

Here is how it works: The difficulty of turning a ball in play into an out is determine by several parameters: location of ball, how hard the ball is hit (soft, medium, hard), type of ball hit (e.g. ground ball, fly ball, line drive), handedness of batter and pitcher and ballpark. The expectation that a particular ball in play is turned into an out is determined by aggregation of this data for all games played in 2006.

Pinto then determined, for each fielder, how may balls were in play when he was on the field, how many he should have been expected to turn into outs and how many he actually turned into outs. The idea is that good fielders will record more outs than expected and poor fielders will record fewer outs than expected. David Pinto, himself, explains the whole PMR system in more detail on YouTube.

For example, 3808 balls were in play when Carlos Guillen was on the field. Based on all the parameters and data for all fielders, it was determined that Guillen should have turned approximatelly 455 balls into outs. In actuality, he turned 465 balls into outs. So he made 10 more plays than would be expected by the typical shortstop.

The other stats you'll see on Table 1 below are DER or Defensive Efficiency Ratio which is the proportion of balls in play turned into outs (465/3808 = .122), predicted or expected DER (455.45/3808) and the difference between actual and expected DER (.00251 in this example). The players are ranked on the difference.

Among 30 Major League shortstops with 2,000 or more balls in play in 2006, Guillen ranked 12th. Your first reaction might be: "but he made so many throwing errors so that negates his range". However, PMR takes care of that because he does not get credit for making a play if he throws the ball away. Instead, he gets penalized as he should.

The best shortstops according to PMR were Adam Everett (who made 35 more plays than expected), Billy Hall (+28) and Yuniesky Betancourt (+27). Two interesting names near the bottom of the list were Derek Jeter (who made 14 fewer plays than expected) and Miguel Tejada (-12). This will anger Jeter fans no doubt but it's not the first time he has found himself near the bottom of a statistical fielding list.

Table 1: PMR for Shortstops in 2006

Player	In Play	Actual Outs	Predicted Outs	DER	Predicted DER	Difference
Adam Everett	3801	500	464.88	0.132	0.122	0.00924
Bill Hall	3311	404	375.73	0.122	0.113	0.00854
Craig Counsell	2274	310	290.98	0.136	0.128	0.00836
Yuniesky Betancourt	4225	501	474.18	0.119	0.112	0.00635
Jason A Bartlett	2570	348	333.97	0.135	0.130	0.00546
Julio Lugo	2103	253	241.59	0.120	0.115	0.00542
Ben T Zobrist	1395	173	165.55	0.124	0.119	0.00534
Khalil Greene	3007	352	335.93	0.117	0.112	0.00534
Clint Barmes	3411	404	386.61	0.118	0.113	0.00510
Juan Castro	1743	205	197.03	0.118	0.113	0.00457
Jhonny Peralta	4086	533	516.35	0.130	0.126	0.00408
Rafael Furcal	4257	538	525.08	0.126	0.123	0.00304
Omar Vizquel	3974	441	430.32	0.111	0.108	0.00269
Carlos Guillen	3808	465	455.45	0.122	0.120	0.00251
Jack Wilson	3485	454	447.27	0.130	0.128	0.00193
Juan Uribe	3553	429	424.28	0.121	0.119	0.00133
John McDonald	2024	237	235.34	0.117	0.116	0.00082
Bobby Crosby	2595	307	304.87	0.118	0.117	0.00082
Alex Gonzalez	2991	350	347.62	0.117	0.116	0.00080
David Eckstein	3222	385	383.63	0.119	0.119	0.00043
Orlando Cabrera	3903	433	432.08	0.111	0.111	0.00024
Edgar Renteria	3958	446	445.44	0.113	0.113	0.00014
Michael Young	4307	536	536.41	0.124	0.125	-0.00009
Jimmy Rollins	4206	499	500.05	0.119	0.119	-0.00025
Ronny Cedeno	3258	398	400.25	0.122	0.123	-0.00069
Hanley Ramirez	4016	466	470.25	0.116	0.117	-0.00106
Alex Cora	1338	163	164.76	0.122	0.123	-0.00131
Geoff Blum	1168	149	150.75	0.128	0.129	-0.00150
Royce Clayton	3338	400	405.01	0.120	0.121	-0.00150
Jose Reyes	3887	443	451.38	0.114	0.116	-0.00215
Angel Berroa	3670	412	420.32	0.112	0.115	-0.00227
Miguel Tejada	4027	465	477.25	0.115	0.119	-0.00304
Derek Jeter	4009	450	464.37	0.112	0.116	-0.00358
Stephen Drew	1475	161	170.45	0.109	0.116	-0.00640
Marco Scutaro	1773	207	218.44	0.117	0.123	-0.00645
Felipe Lopez	4245	438	469.73	0.103	0.111	-0.00747
Aaron W Hill	1273	140	152.71	0.110	0.120	-0.00999