Fielding Bible Stats at FanGraphs

You may have noticed that FanGraphs recently added some new defensive statistics. It's too early in the season to analyze player fielding but I will be using these measures a lot in the future.  So, I'll take some time today to explain them.  Much of this post was abstracted directly from my book Beyond Batting Average which discusses these and many other statistics in great detail.

The newly listed FanGraphs statistics were originally published in the Fielding Bible - Volume II and are based on John Dewan's plus/minus system.  The two statistics most people will be using most often are

rPM - plus/minus runs saved

DRS - defensive runs saved.

The Fielding Bible system is similar to Mitchel Lichtman's Ultimate Zone Rating (UZR) which has been at FanGraphs for a while.  Both systems use detailed play-by-play data on location and type of batted ball from Baseball Info Solutions (BIS).  The methods are similar in theory but use somewhat different algorithms and thus produce varying results for some players.

BIS video scouts watch videotape of every MLB game and every play is entered into a database which includes exact direction, distance, speed and type of every batted ball. Direction and distance are entered by simply recording the exact location of the ball on a replica of the field shown on the computer screen. The speed of a batted ball is recorded as soft, medium and hard.  Each play is also categorized according to batted ball type: groundball, line drive, fly ball, fliner (a cross between a fly ball and a line drive) or bunt.

Dewan first published the plus/minus methodology and results in The Fielding Bible in 2006 and added enhancements in the The Fielding Bible – Volume II in 2009.  The plus/minus system breaks the field into small areas and determines the probabilities of players making plays in each area based on location, speed (hard, medium, soft) and batted ball type (ground ball, fly ball, line drive, bunt).  The system uses these probabilities to determine how many outs each player was expected to make and how many he actually did make in comparison to the average player.

Dewan explains that each type of play (e.g. softly hit ground ball hit into the hole between short and third) has a difficulty determined by how many times all fielders in MLB converted that play into an out.  For example, if that play was made 30% of the time, then a player gets a score of +0.70 for making that play.  If he doesn't make that play, then he gets a -0.30 score.

The scores on all of a player’s plays are summed to compute his +/- rating.  This rating represents how many plays the player made above or below the number of plays an average player at his position would have been expected to make given the same opportunities. For example, Adam Everett had a +/- of +9 in 2009 indicating that he made nine more plays than the average shortstop would have been expected to make given the same opportunities. 

Dewan converts plays made above average to defensive runs above average using situational run expectancies.  Based on these expectancies, Dewan determined that each plus/minus point for a shortstop is worth 0.76 runs.  For example, Everett cost his team 9 x 0.76 = 7 runs in comparison to the average shortstop.  For outfielders and corner infielders, Dewan adjusts the +/- figure for the potential of individual balls going for extra bases. The result is the rPM statistic.

Dewan also introduced defensive runs saved (DRS) in The Fielding Bible – Volume II.  DRS is an extension of the plus/minus system.  In addition to +/- runs saved, DRS includes other sources of runs saved by position:

rSB - stolen base runs cost/saved for catchers

rGDP - Double play runs cost/saved for infielders

rARM - Arm runs cost/saved for outfielders

rHR - home run runs cost/saved for outfielders

For example, Everett had 7 plus/minus runs and -1 double play runs for a total of 6 DRS in 2009. This is similar to his UZR of 5.3.  So DRS serves as a confirmation of UZR in this case.  Some players do not match so closely on DRS and UZR but that is a topic for another day.  For now, I'll say a little more about the four additional statistics listed above.

The rSB measure is based on the number of stolen bases and the success rate against an individual catcher.  However, it also takes into account the stolen bases and success rate against the pitchers they caught.  So, if one pitcher on a staff was bad at holding base runners and one catcher caught a disproportionate number of that pitcher's games (compared to other catchers on the same team), the catcher will not be unduly penalized for something that wasn't his fault.  Gerald Laird saved the Tigers nine more stolen bases above what would have been expected from the average catcher in 2009.  Each stolen base saved is worth .62 runs so Laird had a MLB leading seven rSB.

The rPM statistic looks at how many plays a player made above what an average player would have been expected to make but does not give a player credit for turning double plays.  The Fielding Bible system counts the number of times an infielder had opportunity to be involved in a double play (including fielding balls and making pivots) and how many times he successfully participated in a double play.  Like the other statistics above, rGDP is converted to runs cost/saved.  Adam Everett had a -1 rGDP so he cost the Tigers one run on double play balls in 2009.

The rPM statistic only considers an outfielder's ability to make catches and does not consider the outfielders arm.  The rARM statistic gives an outfielder credit for his ability to throw runners out and to prevent runners from advancing. For example, when a batter hits a single to left field with a runner on first and second base unoccupied, the runner either stops at second or attempts to advance to third.  If the runner stops at second, then the outfielder would get credit for a hold.  If the runner is thrown out at third, then the outfielder is credited with a kill.

For each outfielder, Dewan counts the numbers of advancement opportunities, holds and kills.  He then determines how each outfielder compares to league average in both kills and holds.  Finally, using situational run expectancies (e.g. How likely is it for a run to score with a man on first and third and no outs compared to a runner on first and one out?), he then calculates runs saved above/below average for each outfielder.  Bobby Abreu was the MLB leader with 11 runs saved with his throwing arm in 2009. If we only look at Abreu's rPM of -10, he rates as a poor outfielder.  However, if we add his arm rating to the equation, his final DRS is +1.

BIS also tracks how many times outfielders caught balls that would have been home runs if the ball was not caught.  That is, the ball was heading over the fence and the outfielder either reached over the wall and pulled it back in or caught it just before it would have gone out.  Adam Jones saved the Orioles an MLB best six runs with home run saving catches (rHR) in 2009.

Fan Fielding Survey versus range measures

This is the seventh part of my series on fielding in 2007. The table of contents for the entire 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?

Today, I'm going to revisit Tom Tango's Fan Fielding Survey. Tango anually conducts a survey on defensive skills which many of you completed last year. For those of you who are not familiar with the survey, he asked fans to rate the fielding skills of players on their favorite teams just based on observation and instructed them not to use any stats at all. As you can see on the ballot, fans were asked to scout players on reaction/instincts, acceleration/first few steps, speed, hands, release/footwork, throwing strength and throwing accuracy.

He then tabulated the results which can be seen in detail on his site. Each player ends up with a score between 0 and 100 on each of the 7 skills. Tango explains that the league average rating for each of the 7 categories is 50 and that a player with a rating of 70 or better is in top 16% in the league.

Tango also came up with an idea on how to turn these ratings into runs scored above average. First, weighted averages are created for each player based on the importance of the skills at his position. The weights are shown on Table 1 below. I'm not exactly sure how he decided upon these weights but they make intuitive sense. For example, a third baseman's arm strength carries more weight than his speed. On the other hand, speed and acceleration are very important for outfielders.

Table 1: Weights for skills on fan fielding survey

Pos	Instincts	First Steps	Speed	Hands	Release	Arm Strength	Accuracy
C	1.3	0.3	0.3	1.3	1.3	1.3	1.3
1B	1.6	1.6	0.4	1.6	0.8	0.4	0.4
2B	1.6	1.6	0.8	1.6	0.8	0.4	0.4
SS	1.5	1.5	0.7	0.7	1.5	0.7	0.4
3B	0.9	0.9	0.5	0.9	0.9	1.9	0.9
LF	1.0	2.0	2.0	1.0	0.5	0.3	0.3
CF	1.0	1.9	1.9	1.0	0.5	0.5	0.2
RF	0.9	1.9	1.9	0.9	0.5	0.5	0.5

Once the weighted average is computed for a player, you then subtract from it the average score for all players at his position. I did this for all players and compared the distribution of scores to the distribution of runs scored per 150 games (RSAA/150) for PMR and RZR. It turned out that the distributions were very similar with standard deviations of 14 for PMR, 15 for RZR and 15 for fan fielding. Thus, I used these scores as RSAA/150 estimates for fan fielding.

Tango recommended multiplying the result by .7 to get run estimates because he was comparing to the UZR distribution which had a smaller standard Deviation (at least in 2003). I don't have all the UZR scores so I compared to distributions which I did have.

The results for the Tigers are in Table 2. If you are skeptical that you can turn fan observations into run estimates, then just think of the results as above or below average skill for the position.Table 3 compares the range measures discussed previously with the fan fielding estimate. The Fan Fielding results for the Tiger players correlate reasonably well with the range measures. Players that did well on the range measures - Curtis Granderson , Brandon Inge and Placido Polanco - were also given high scores by the fans. The fans also agreed that Carlos Guillen was a poor fielder last year. Magglio Ordonez and Sean Casey who went up or down according to the measure, were ranked below average by the fans.

One player who was ranked radically lower by the fans was Jacque Jones. There are a couple possible reasons for this. First, the Cubs had only 25 voters and there was a low agreement among them in (.55) in rating Jones. This makes me think that a small number of fans may have brought down his average. Another reason was that the range measures do not consider an outfielder's ability to prevent base runners from advancing with his arm and, according to the fans, Jones has poor throwing skills. I'll talk more about throwing arms shortly.

Table 2: Fan Fielding Scores for Tigers - 2007

POS	Player	n	instinct	first step	speed	hands	release	arm strength	accuracy	RSAA/150
1B	Casey	44	57	20	11	71	43	37	45	-4
2B	Polanco	52	81	67	54	89	86	56	89	17
3B	Inge	53	83	83	68	73	75	91	62	17
3B	Cabrera	9	55	29	28	42	51	73	33	-12
CF	Granderson	52	82	84	81	81	63	47	45	9
CF	Jones	25	47	62	66	53	32	25	6	-15
LF	Monroe	38	37	46	47	38	49	58	48	3
RF	Ordonez	50	52	39	36	52	45	48	51	-11
SS	Renteria	22	64	52	52	67	70	61	72	-1
SS	Guillen	52	52	41	42	29	38	47	31	-22

Table 3: Comparison of runs of RSAA/150 across methods

PLAYER	RZR	ZR	PMR	+/-	UZR	FFS
Granderson	34	10	19	18	18	9
Jones	24	9	13	42	N/A	-15
Inge	13	12	16	18	12	17
Polanco	12	4	9	8	N/A	17
Monroe	9	7	-12	N/A	N/A	3
Renteria	5	-9	-4	N/A	N/A	-1
Ordonez	-5	10	-3	N/A	14	-10
Casey	-8	8	-15	N/A	8	-4
Cabrera	-13	-16	-26	-20	-28	-12
Guillen	-18	-7	-18	N/A	-24	-22

Fielding Bible - 2007

This is the fifth 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?

Before I discuss The Fielding Bible system, I want to direct you to a database which SG has constructed over at the Replacement Level Yankees Weblog. He has put together detailed Zone Rating data from 1987-2007 including translations into runs saved above average. You can find it on the left sidebar of that site under "Fun Stuff". SG obviously put a lot of work into it and it's a valuable resource.

Now back to my analysis...

John Dewan's Fielding Bible plus/minus system has many similar features to Zone Rating (ZR), Revised Zone Rating (RZR) and especially Probabilistic Model of Range (PMR). The system is described briefly on the Fielding Bible web site. The site also has various other excerpts from their 2006 book and they are worth reading because they explain fairly complex concepts quite clearly.

On the web site, they describe how video scouts watch every play of every major league game and record information about location , distance, speed (soft/medium/hard) and type of hit (groundball, liner, flyball, bunt, fliner (somewhere between fly and liner) for each play. It's the same data collection system used for RZR and PMR but the three systems have somewhat different methods of processing the data.

In the Fielding Bible +/- system, each type play (e.g soft hit ground ball hit into the hole between short and third) has a difficulty which is determined by how many times major league fielders convert that play into an out. For example, if that play was made 30% of the time, the a player gets a score of +.70 for making that play. If he doesn't make that play, he gets a -.30. All the scores on all the plays are summed for a player to get his +/- rating. The rating represents how many plays the player made above or below those an average player at his position would make.

So +/- is equivalent to PMAA (plays made above average) which we calculated for all the other systems. As usual PMAA can then be converted to RSAA as described in Chris Dial's article. Also, PMAA and RSAA can be prorated to 150 games to get PMAA/150 and RSAA/150.

There is no Fielding Bible book this year but Baseball Info Solutions did release 2007 data for about half the players - the ten leading fielders and the five worst fielders at each position. The available results for the Tigers in 2007 are summarized in Table 1 below. You can see that the following players were among the 10 best at their positions: Jacques Jones (42 runs saved above average per 150 games), Brandon Inge (+18), Curtis Granderson (+18), and Placido Polanco (+8). Miguel Cabrera (-20) finished among the bottom five third basemen.

Table 2 compares the Tigers on ZR, RZR, PMR and +/-. It can be seen that Jones, Inge, Granderson and Polanco ranked well on all 4 systems and that Cabrera ranked poorly in each case.

Table 1: Plays Made and Runs Saved by Tigers fielders in 2007 according to +/-

Pos	player	Inn	PMAA	RSAA	PMAA/150	RSAA/150
1B	Casey	989	N/A	N/A	N/A	N/A
2B	Polanco	1,209	10	8	11	8
3B	Inge	1,310	22	18	22	18
3B	Cabrera	1,311	-24	-19	-24	-20
SS	Guillen	1,074	N/A	N/A	N/A	N/A
SS	Renteria	1,019	N/A	N/A	N/A	N/A
LF	Monroe	806	N/A	N/A	N/A	N/A
CF	Jones	645	24	20	50	42
CF	Granderson	1,285	21	18	22	18
RF	Ordonez	1,221	N/A	N/A	N/A	N/A

Table 2: Runs Saved Per 150 Games - RZR,ZR, PMR and +/-

PLAYER	RZR	ZR	PMR	+/-
Granderson	34	10	19	18
Jones	24	9	13	42
Inge	13	12	16	18
Polanco	12	4	9	8
Monroe	9	7	-12	N/A
Renteria	5	-9	-4	N/A
Ordonez	-5	10	-3	N/A
Casey	-8	8	-15	N/A
Cabrera	-13	-16	-26	-20
Guillen	-18	-7	-18	N/A