Probabilistic Model of Range - 2007

This is the fourth part of my series on fielding for 2007. The Table of Contents for the series is listed below:

Basic fielding stats
Converting Zone Rating to something useful
Revised Zone Rating
Probabilistic Model of Range
Fielding Bible
Ultimate Zone Rating
Fan Fielding Survey versus range measures
Outfield arms
Ranking the second basemen
Ranking the shortstops
Ranking the third basemen
Ranking the first baseman
Ranking the center fielders
Ranking the right fielders
Ranking the left fielders
What about catchers?

David Pinto at Baseball Musings finished his Probabilistic Model of Range (PMR) tables for 2007 in November. They can be found by scrolling through in his defense archives. 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 2007.

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, 3,724 balls were in play when Placido Polanco was on the field. Based on all the parameters and data for all fielders, it was determined that Polanco should have turned approximatelly 409 balls into outs. In actuality, he turned 420 balls into outs. So he made 11 more plays than would be expected by the typical shortstop (PMAA). If you look at the PMR archives, you will see that the fielders are ranked according to "ratio". For example, Polanco had a 102.67 ratio (outs/predicted outs) which means that he made 2.67% more plays than average.

PMR is similar to zone rating (ZR) and revised zone rating (RZR) but there are some differences. One advantage the PMR system has over ZR and RZR is that it treats balls in different parts of the zone differently. Pinto considers some balls in a zone to be more difficult to reach than others and he takes this into consideration in his algorithm.

PMR has received some criticism for including pop ups for infielders whereas the zone rating systems do not. Some feel that catching pop ups doesn't really have a lot to do with range. I can see their point but I also think there are some fielders who get to a lot of pop ups that others might not have reached. I guess I'm on the fence on that one. One last thing to remember is that different collection systems are used. ZR uses data from STATS, Inc wheras RZR and PMR use data from BIS.

As we did for ZR and RZR, PMAA can be translated into runs saved above average (RSAA) using Chris Dial's method. As usual, PMAA and RSAA can easily be prorated to 150 games (PMAA/150 and RSAA/150). The results for Tigers in 2007 are shown in Table 1 below.

In Table 2, PMR is compared to ZR and RZR on RSAA/150. Using PMR, Curtis Granderson was 19 runs better than average, Brandon Inge (16), Jacque Jones (13) and Polanco (9). All four of them have been above average on all three measures so far. Craig Monroe (-12) is below average for the first time. The systems disagree on Sean Casey and Magglio Ordonez. Miguel Cabrera and Carlos Guillen rated poorly on all three systems.

Table 1: Plays Made and Runs Saved by Tigers fielders in 2007 according to PMR

Pos	player	Inn	outs	pred outs	PMAA	RSAA	PMAA/150	RSAA/150
1B	Casey	989	198	212	-14	-11	-18	-15
2B	Polanco	1,209	420	409	11	8	12	9
3B	Inge	1,310	400	380	20	16	20	16
3B	Cabrera	1,311	330	362	-32	-25	-32	-26
SS	Renteria	1,019	361	365	-4	-3	-5	-4
SS	Guillen	1,074	389	408	-19	-14	-24	-18
LF	Monroe	806	166	175	-9	-7	-14	-12
CF	Granderson	1,285	424	402	22	18	23	19
CF	Jones	645	195	187	8	7	16	13
RF	Ordonez	1,221	261	265	-4	-3	-4	-3

Table 2: Runs Saved Per 150 Games - RZR vs ZR vs PMR

PLAYER	RZR	ZR	PMR
Granderson	34	10	19
Jones	24	9	13
Inge	13	12	16
Polanco	12	4	9
Monroe	9	7	-12
Renteria	5	-9	-4
Ordonez	-5	10	-3
Casey	-8	8	-15
Cabrera	-13	-16	-26
Guillen	-18	-7	-18

Revised Zone Rating

This is the third part of my series on fielding. The Table of Contents for the series is listed below:

Basic fielding stats
Converting Zone Rating to something useful
Revised Zone Rating
Probabilistic Model of Range
Fielding Bible
Ultimate Zone Rating
Fan Fielding Survey versus range measures
Outfield arms
Ranking the second basemen
Ranking the shortstops
Ranking the third basemen
Ranking the first baseman
Ranking the center fielders
Ranking the right fielders
Ranking the left fielders
What about catchers?

After John Dewan left STATS and founded Baseball Info Solutions (BIS), he developed a new version of Zone Rating (ZR) which he called Revised Zone Rating (RZR). There are some differences between ZR and RZR. First, ZR uses data collected by STATS while RZR uses data gathered by BIS.

Another important distinction is that RZR separates balls hit outside a fielder's zone from balls inside a fielder's zone. There are a couple of reasons why it is useful to analyze balls outside the zone separately from balls hit inside the zone. Plays outside of a player's zone are typically more difficult than plays within the zone. Also, although making a large number of plays outside your zone is probably a good thing in most cases, it is possible that a player might be making some plays that a teammate could have handled just as easily. Thus, I think it can be valuable to look at the numbers of plays made inside and outside the zone before combining them.

One more difference between ZR and RZR is that RZR does not give a player extra credit for having both an assist and a putout on a double play. Being able to turn double plays is a valuable skill but a statistic that is mostly a measure of range should not credit two plays to a player that really made one. Thus, I think this is a good improvement.

The Hardball Times database includes the following statistics: Balls In Play within a fielder's zone (BIZ), Plays made in the zone (PLAYS), RZR or percentage of BIZ converted into outs, and plays made outside the zone (OOZ). Justin Inaz who writes the blog "On Baseball and the Reds" has developed an algorithm which combines RZR and OOZ and translates these numbers into plays made above average (PMAA) and runs saved above average (RSAA).

Justin first calculates the proportion of plays made per BIZ for all players combined at each position and considers that to be the expected ratio of plays made in zone (EXPPRATIO). From that, he calculates for each player, the plays made in zone above/below the MLB average (PIZ AA):

PIZ AA = PLAYS - BIZ*EXPPRATIO

He then assumes that the number of balls hit into the zone is correlated with the number of balls hit outside the zone. Considering that assumption, he calculates OOZ per BIZ for all players combined at each position (EXPORATIO). From that, he gets for each player, the plays made outside the zone above/below the MLB average (OOZ AA):

OOZ AA = OOZ - BIZ*EXPORATIO

Finally, he combines plays made inside the zone and plays made outside the zone to get PMAA:

PMAA = PIZ AA + OOZ AA

That can then be translated into Runs Saved Above Average (RSAA) the same way we did with Zone Rating. The results for the Tigers in 2007 are shown in the table below. Justin included results for all players in 2007 in a google spreadsheet.

Using Jacque Jones as an example, Table 1 is read as follows:

INN = Jones played 645 innings in centerfield
RZR = Converted 92.5% of balls hit in zone to outs
OOZ = 35 out of zone plays made
PIZ AA = Given his opportunities, he made 6 more plays in his zone than the average CF
OOZ AA = 8 more plays made out of zone than average
PMAA = 14 more total plays made than average
RSAA = 12 runs saved above average
PMAA/150 = 29 plays made per 150 games above average
RSAA/150 = 24 runs saved per 150 games above average

Table 2 compares RSAA/150 for Revised Zone Rating versus Zone Rating. The first thing to notice is that ZR appears to a bit more conservative than RZR That is, looking at all MLB players, RZR has higher highs and lower lows than ZR. The median still falls right around zero for both measures though as it should. There are some noticeable differences for individual players. First, Renteria is above average on RZR (+5) and below average on ZR (-9). Conversely, Magglio Ordonez is below average on RZ (-5) and above average on ZR (+10). Sean Casey's numbers (-8, 8) also are different for the two measures. This is why it is important to look at more than one range measure.

The way I look at it is that the very good fielders (e.g. Curtis Granderson, Jones, Brandon Inge) perform well on every measure and the poor fielders (e.g Miguel Cabrera, Carlos Guillen) perform poorly on every measure. The fielders who fall between very good and poor will go up and down according to the measure. I'm going to show you a couple of more measures. Then I will take the average of all the measures for each player and rank all the fielders in baseball by position.


Table 1: Plays Made and Runs Saved by Tigers fielders in 2007 according to RZR

POS	PLAYER	INN	RZR	OOZ	PIZ AA	OOZ AA	PMAA	RSAA	PMAA/150	RSAA/150
1B	Casey	989	.707	22	-5	-2	-8	-6	-10	-8
2B	Polanco	1209	.868	39	12	2	14	11	15	12
3B	Inge	1310	.712	63	12	4	16	12	16	13
3B	Cabrera	1311	.627	50	-17	-0	-17	-13	-17	-13
SS	Renteria	1019	.815	49	-0	5	5	4	6	5
SS	Guillen	1074	.801	36	-5	-14	-20	-15	-24	-18
LF	Monroe	806	.852	34	-1	7	6	5	11	9
CF	Granderson	1285	.921	85	12	27	39	33	40	34
CF	Jones	645	.925	35	6	8	14	12	29	24
RF	Ordonez	1221	.906	29	8	-14	-6	-5	-6	-5

Table 2: Runs Saved Per 150 Games - RZR vs ZR

PLAYER	RSAA/150 (RZR)	RSAA/150 (ZR)
Granderson	34	10
Jones	24	9
Inge	13	12
Polanco	12	4
Monroe	9	7
Renteria	5	-9
Ordonez	-5	10
Casey	-8	8
Cabrera	-13	-16
Guillen	-18	-7

Converting Zone Rating to Something Useful

In Part 1 of my 2007 fielding analysis, I ranked the Tigers on range factor and zone rating. Range factor is not so useful now that more sophisticated measures are available. Zone rating is still regarded as one of the better measures and it’s also very accessible throughout the year. In this post, I will explain how Zone Rating can be translated into something more useful than just a percentage. The Table of Contents for the entire fielding series is shown below:

Basic fielding stats
Converting Zone Rating to something useful
Revised Zone Rating
Probabilistic Model of Range
Fielding Bible
Ultimate Zone Rating
Fan Fielding Survey versus range measures
Outfield arms
Ranking the second basemen
Ranking the shortstops
Ranking the third basemen
Ranking the first baseman
Ranking the center fielders
Ranking the right fielders
Ranking the left fielders
What about catchers?

It would be nice if we could change ZR from a percentage to something like plays made above average or runs saved above average. We can not do this precisely without the actual Balls In Zone data from STATS but we can get estimates. Chris Dial, who writes for Baseball Think Factory and has access to some of the data used for calculating ZR, has developed a method for obtaining these kinds of estimates.

Dial takes the average opportunities at each position and the player's zone rating to calculate the number of plays the player made and compares that to the number of plays that a player with league average ZR would have made. The result is Plays Made Above Average (PMAA). He also estimates the approximate run value of a ball in play at each position. His run value methodology is found here. You will notice that, although it varies by position, an extra play made is worth about 0.8 runs on average. Tom Tango explains it more intuitively on his blog. From that, he determines the runs saved a player aggregates above or below the average player at his position (RSAA).

The Table below shows the ZR, PMAA and RSAA for Tigers players in 2007 (those who were with the team in 2007 and those who have been acquired this off-season). PMAA/150 is PMAA prorated to 150 games played. RSAA/150 = RSAA prorated to 150 games played. PMAA/150 and RSAA/150 allow us to better compare players with different numbers of games played. The final column shows how each player ranks on RSAA/150. This may be slightly different from the ZR ranks due to the games played adjustment.

I'll use Jacque Jones as an example. Jones played 645 innings and had a Zone Rating of .904 as a center fielder in 2007. Given his playing time, he made 5 more plays than the average center fielder. This comes out to 4 runs saved above the average center fielder. If we assume the same level of performance over 150 games, Jones would have made 11 plays above average and saved 9 runs above average.

The leading tigers in runs saved per 150 games in 2007 were: Brandon Inge (12), Curtis Granderson (10), Magglio Ordonez (10) and Sean Casey (8). The only Tiger who was below average was Carlos Guillen who had a RSAA/150 of -7. New acquisition Jacques Jones finished 9 runs above average. However, Miguel Cabrera (-16) and Edgar Renteria (-9) were below average. Based on this statistic, it appears that the Tigers did not help their defense during the off-season.

The Replacement Level Yankee Weblog now includes a zone rating database that has Zone Ratings along with conversions to runs saved above average for all players from 1987-2007. Just go to the left sidebar and you'll see a link to the database.


Table 1: Plays Made and Runs Saved by Tigers fielders - 2007

POS	#	Player	Innings	ZR	PMAA	RSAA	PMAA/150	RSAA/150	RSAA/150 Rank
1B	29	Casey	989.0	.886	7	6	10	8	7
2B	28	Polanco	1209.0	.828	5	4	5	4	11
3B	27	Inge	1310.2	.803	15	12	15	12	4
3B	27	Cabrera	1311.2	.714	-20	-16	-20	-16	25
SS	30	Guillen	1074.0	.807	-7	-5	-9	-7	20
SS	30	Renteria	1019.1	.800	-9	-7	-12	-9	23
LF	27	Monroe	806.2	.882	5	4	9	7	10
CF	27	Granderson	1285.0	.908	12	10	12	10	4
CF	27	Jones	645.0	.904	5	4	11	9	6
RF	28	Ordonez	1221.0	.908	11	9	12	10	2