Probabilistic Model for Range

In an earlier post, I discussed the difficulty of measuring range or the ability of fielders to turn batted balls into outs. In that post, I defined range factor and zone rating and gave the limitations of each measure. Here, I’ll talk about David Pinto’s Probabilistic Model of Range.(PMR).

He uses STATS Inc. data to obtain information about each ball put in play – direction, type of hit (ground, fly, line drive, bunt, pop up) and intensity of hit (soft, medium, hard). For each direction/type/intensity combination, he uses something called Maximum Likelihood Estimation to calculate the probability of an out for each of the 9 fielders. Based on these probabilities, he calculates the predicted number of outs for an average defender at each position on each team. He then compares this to the actual number of outs made.

For example, the table below shows that there were 1,233 balls put in play in games when Omar Infante played shortstop. Based on the PMR, the average shortstop should have made 157.18 (or 158) successful plays on the balls that were hit. Infante actually made 171 plays. This was14 (or 8.8%) more than expected. Interestingly, this was the best percentage in baseball for shortstops with 500 or more balls in play when they were in the game. Looking at ground balls only (GB), Infante made 4.7% more plays than expected. Carlos Guillen, made 2.9% fewer plays than expected and 2,7% more plays than expected on ground balls.

At second base, Placido Polanco made 4.2% more plays than expected while Infante made 1.6% fewer than expected. So based on these somewhat small sample sizes, Infante had better range at shortstop than at second base. Orlando Hudson was baseball’s leader with an amazing 18.6% plays more than expected. Pinto has not given ground ball only numbers for second basemen yet.

Pinto has only posted results for middle infielders so far. I’ll add the results for other positions as they become available.

Table: Probabilistic Model of Range

Player	Pos.	Type of Hit	BIP	Outs	Pred. Outs	Diff	% Diff
Infante	SS	Any	1233	171	157.18	13.82	8.79
Infante	SS	GB	567	131	125.07	5.93	4.74
Guillen	SS	Any	1934	240	247.06	-7.06	-2.86
Guillen	SS	GB	950	203	197.69	5.31	2.69
Polanco	2B	Any	3001	336	322.35	13.65	4.23
Infante	2B	Any	1810	190	193.21	-3.21	-1.66
Hudson	2B	Any	3318	490	413.33	76.67	18.55