Converting RZR and OOZ to Runs

When I posted yesterday about Revised Zone Rating (RZR) and Out-of-zone plays (OOZ), some readers may have wondered whether these statistics could be translated to runs above average like most of the other defensive metrics.  A few years ago, Colin Wyers developed an algorithm which combined RZR and OOZ and translated these numbers into plays made above average (PMAA) and runs saved above average (RSAA). 

Wyers' algorithm has a lot of steps.  If you don't want to see all the math, you can jump to the table at the bottom of the post and look at the PMAA and RSAA columns.  Anyway,  I'll use Tigers shortstop Jhonny Peralta as an example.  Peralta had the following numbers in 2012:

Innings = 1,278

Balls in Zone (BIZ) =  307

In Zone Plays = 262 

RZR = .853

OOZ = 49

First calculate the average RZR at each position (proportion of all plays in the zone successfully converted to outs) and consider that to be the expected RZR (EXPRZR) for each player.  From that, calculate the plays made in zone above/below the league average (PIZAA) for each player:

          PIZAA  = In Zone Plays - BIZ*EXPRZR

The average RZR for MLB shortstops in 2012 was about .802.  So, Peralta's PIZAA = 262 - 307 x .802 = 16.  Thus, he made an estimated 16 plays in the zone above what would expect from an average shortstop.  

Next, assume that the number of balls hit outside the zone is correlated with the number of innings. Then calculate OOZ per inning for all players combined at each position (EXPORATIO).  Compute, for each player, the plays made outside the zone above/below the MLB average (OOZAA):

          OOZAA = Out of Zone Plays - Innings*EXPORATIO

The EXPORATIO for shortstops in 2012 was .054.  So, Peralta's OOZA was 49 - 1,278 x .054 = -20.  This means that he made an estimated 20 plays outside the zone below what you would expect from an average shortstop.  

Next, combine plays made inside the zone and plays made outside the zone to get plays made above average (PMAA):

           PMAA = PIZAA + OOZAA

Peralta's PMAA was 16 - 20 = -4.  So, he made an estimated 4 fewer plays than would be expected by an average shortstop.  

Chris Dial of Baseball Think Factory estimated that the average play made by a shorstop baseman saves .754 runs, so we can estimate the runs saved/cost (RSAA) by  a shortstop as:

          RSAA = .754*PMAA

For Peralta, that comes out to RSAA=-3.  Thus, Peralta cost the Tigers an estimated three runs defensively compared to an average shortstop.  

Table 1 shows the statistics for Tigers with regular playing time in 2012.  Also included is off-season acquisition Torii Hunter.  According to RSAA, three 2013 starters saved a substantial number of runs in 2012 - center fielder Austin Jackson (+17), second baseman Omar Infante (+12) and right fielder Torii Hunter ( +11).  The only returning starter who was substantially below average was third baseman Miguel Cabrera (-18).

Is this statistic any better than UZR or DRS or other advanced defensive metrics.  Probably not, but it has the advantage of dividing plays into inside the zone and outside the zone, which is information we don't get from other metrics.  As always, take these numbers with a grain of salt.  It is always preferable to look at multiple metrics and years when dealing with defensive data.  

Table 1: Runs Saved Above Average for Tigers Fielders based on RZR and OOZ, 2012

Pos	Player	Inn	RZR	OOZ	PIZAA	OOZAA	PMAA	RSAA
1B	Prince Fielder	1,392	.823	27	7	-2	5	4
2B	Omar Infante	1,246	.836	49	12	5	16	12
3B	Miguel Cabrera	1,322	.682	29	-11	-12	-22	-18
CF	Austin Jackson	1,184	.939	95	4	17	21	17
RF	Torii Hunter	1,112	.910	79	-1	13	13	11
RF	Brennan Boesch	909	.950	35	5	-19	-14	-11
SS	Jhonny Peralta	1,277	.853	49	16	-20	-4	-3

  Data source: FanGraphs.com