Which Center Fielders Made the Plays that Mattered Most?

Jeff Zimmerman posted an interesting article on Friday. It prompted me to try to analyze the relationship between (i) an outfielder’s ability to make plays, and (ii) an outfielder’s ability to save runs. From my analysis below, the relationship is not as hand-in-glove as I initially would have thought.

From what I understood about Jeff’s article, he advanced a new defensive metric called “PMR,” which stands for Plays Made Ratio. Jeff calculated this ratio using data from Inside Edge, which categorizes every ball in play into one of six buckets. Jeff explains:

Most of the fielding data falls into two categories. The zero percentage plays are just that, impossible plays, and make up 23.2% of all the balls in play. Balls in this bucket are never caught and always have a 0% value. The other major range is the Routine Plays or the 90% to 100% bin. Defenders make outs on 97.9% of these plays, which make up 64.0% of all the plays in the field; the 2.1% which aren’t made are mostly errors. In total, 87.2% of all plays are graded out as either automatic hits or outs; it is the final ~13% which really determine if a defender is above or below average.

Between almost always and never, four categories remain. Even though each category has a defined range, like 40% to 60%, the average amount of plays made is not exactly in the middle of each range. Here are the actual percentage of plays made in each of the four ranges.

Range	Actual Percentage
1% to 10%	6%
10% to 40%	29%
40% to 60%	58%
60% to 90%	81%

With these league average values and each individual player’s values, a ratio of number of plays made compared to the league average value can be calculated. To have the same output of stats like FIP- and wRC+, I put Plays Made Ratio on a 100 scale where a value like 125 is 25% better than the league average. Here is the long form formula and Jason Heyward’s value determined for an example.

Plays Made Ratio = ((Plays made from 1% to 90%)/((1% to 10% chances * .063%)+( 10% to 40% chances * .289)+ (40% to 60% chances * .576) + (60% to 90% chances * .805))) * 100

Heyward’s Plays Made Ratio = ((1+10+9+26)/((14*.063)+(16*.289)+(9*.576)+(27*.805)))*100

Heyward’s Plays Made Ratio = (46/32.4)*100

Heyward’s Plays Made Ratio = 142

Heyward had a heck of a season. Of the 66 playable balls hit to him, normally only 32 of them would have been caught for an out. Heyward was able to get to 46 of them, or 42% better than the league average. He has consistently had above league average values with a 133 value in 2012 and 125 in 2013.

Jeff posits that the new PFM metric gives us new insight that FanGraphs current go-to defensive metric (Ultimate Zone Rating) does not:

Now remember this stat [PMR] only looks at how often a fielder would have made the play considering their position on the field. The team could be playing its outfielders back to prevent a double or their infielders in for a bunt which could put the defender out of position. Additionally, it doesn’t look at the final results of the play (at least for now). If Sir Dive Alot is playing in the outfield and he loves to try to catch every ball hit his way, then he will get to a few extra flyballs by diving all the time, but those he doesn’t get to will pass him by for more doubles and triples. Also, an outfielder could be good at making plays while coming in versus going deep; balls which fall in over his head would be more damaging than those which fall for shallow singles. While his Plays Made Ratio may be high, the number of runs he saves, as seen by UZR or Defensive Runs Saved, may be lower by comparison.

This got me thinking about the relationship between a player’s PMR and his UZR, and, more specifically, his RngR. As I understand RngR, it is the component of UZR that estimates the number of runs a player saves, or surrenders, due to his range. RngR isolates the contribution a player’s range makes to his Ultimate Zone Rating by ignoring the contributions from his arm and his ability to limit errors.

Intuitively, it would make sense that a player’s PMR and his RngR would be strongly correlated. In other words, a player whose range allows him to make more plays than average would also be the same type of player whose range would allow him to save more runs than average. A simple two-by-two matrix, with RngR along the left side and PMR along the top would show the following quadrants:

	Below Average PMR	Above Average PMR
Above Average RngR	(1) Poor range/saves runs(?)	(2) Good range/saves runs
Below Average RngR	(3) Poor range/surrenders runs	(4) Good range/surrenders runs(?)

My intuition is that players would fall in either quadrant (2) or quadrant (3). The interesting questions arise with players that would fall in quadrant (1) (those who exhibit poor range, but whose range saves runs), and in quadrant (4) (those who exhibit good range, but whose range does not save runs). There are several explanations for why a player may fall into quadrant (1) or (4).

Jeff noted three possible explanations.  First, a player may be overly aggressive, which would may lead to more outs (a higher PMR) but also more misplays resulting in doubles and triples (a lower RngR). Second, “an outfielder could be good at making plays while coming in versus going deep; balls which fall in over his head would be more damaging than those which fall for shallow singles. While his Plays Made Ratio may be high, the number of runs he saves, as seen by UZR or Defensive Runs Saved, may be lower by comparison.” Third, a player (or his team) may be particularly well adept at positioning himself, which would amplify his RngR rating, but not necessarily his PMR (as Jeff noted when discussing Nick Markakis).

How does the relationship between PMR and RngR look if it is applied to actual players? To find out, I looked at all center fielders who between 2012 and 2014 had at least 70 “total chances” (defined by Inside Edge as balls hit to that fielder where there is between a 1% and 90% likelihood that the ball is caught). That provided me a list of 18 center fielders. Next, I calculated each player’s rate-based RngR/150 (calculated by his total RngR divided by the innings he played in center field, multiplied by nine, multiplied by 150). That revealed the following table:

Name	PMR	RngR/150
Jacoby Ellsbury	128	11.5
Lorenzo Cain	127	19.5
Mike Trout	126	3.9
Michael Bourn	122	4.4
Ben Revere	122	-3.0
Andrew McCutchen	120	-1.5
Denard Span	116	4.0
Carlos Gomez	114	11.2
Dexter Fowler	114	-12.0
Juan Lagares	108	18.7
Coco Crisp	106	-2.3
Jon Jay	105	3.2
Adam Jones	90	-5.7
Leonys Martin	89	0.6
Austin Jackson	88	-1.2
Colby Rasmus	87	2.7
Angel Pagan	87	-2.4
B.J. Upton	80	-0.6

A scatter chart of this information looks like this. I also added a best-fit line to the scatter plot. My intuition that a player’s RngR/150 would be strongly correlated with his PMR is contradicted by this data. In fact, according to this data, (and based on my very limited skillset at statistical analysis, which may be completely incorrect), only 15% of the runs saved due to these 18 center fielders’ range can be explained by their Plays Made Ratio.

Even more interesting than the two-by-two matrix characterization introduced above, are the points on the scatter plot that are either way above (Juan Lagares and Lorenzo Cain) and way below (Dexter Fowler) the linear trendline.

The data suggest that Lagares/Cain and Fowler have similar range in center field, but that the former use their range to save more runs than the latter. One possible implication of this information is that Fowler is not optimizing his ability and that through better decision-making (such as being more aggressive or less aggressive on fly balls) or better positioning he could save more runs. As discussed earlier, it could also mean that Fowler is not (relatively) adept at playing balls hit over his head or in the gap, which leads to more doubles and triples.

On a larger scale, a possible implication of this data is that teams could significantly improve the amount of runs their center fielders save by (i) coaching their center fielders to make optimal decisions regarding their aggressiveness and (ii) properly positioning their center fielders. I would be curious to analyze what is the optimal amount of aggression a center fielder would have in going after balls hit to the outfield, the optimal way to position himself. For example, is it better to play shallow and be aggressive in cutting off singles (which Lagares has a reputation of doing) or to play deep? Those questions are best answered in a follow-up post/article.