Who Makes The Best PIZAA In Baseball?

Most of the readers of this blog have checked out the advanced fielding statistics at sites like FanGraphs and Baseball-Reference from time to time.  A metric such as Defensive Runs Saved (DRS) give us an idea of a player’s overall fielding performance.  It is given as runs saved above what would be expected from the average player at the given position.  It is discussed in more detail in the fielding glossary.

You may also have noticed two additional columns at FanGraphs labeled RZR and OOZ.  These are the Revised Zone Rating statistics developed by John Dewan, president of Baseball Info Solutions.  Dewan later developed the more detailed DRS metric.   The Revised Zone Rating system is comprised of the following measures:

1. Balls in play within a fielder’s zone (BIZ)
2. Plays made in the zone (Plays)
3. Proportion of balls in zone converted into outs (RZR)
4. Plays made outside the zone (OOZ)

A play is considered to be inside a positional zone if half the balls hit into that area are converted into outs by all the players in baseball at that position.  While the Revised Zone Rating system is less sophisticated than DRS, it is useful because it separates the plays a player made inside his zone from the plays outside his zone.  The data, of course, should be interpreted with caution as is the case with all defensive metrics especially with the increasing trend of defensive shifts.

Table 1 below shows how the distinction between in-zone and out-of-zone plays can be useful.  Phillies shortstop Jimmy Rollins converted 334 out of 407 (82.1%) of balls in his zone into outs in 2013.  Brewers shortstop Jean Segura had a similar number of balls hit into his zone (402) but had a smaller RZR (77.9%).  Conversely, Rollins made fewer out-of-zone plays (49) than Segura (98).  These data suggest that Rollins may have been the steadier fielder on balls hit in the shortstop zone but that Segura was better at making difficult plays.

Table 1: Revised Zone Rating Statistics for Jimmy Rollins and Jean Segura, 2013

Player	BIZ	Plays	RZR	OOZ
Jimmy Rollins	407	334	.821	49
Jean Segura	402	313	.779	98

 Data source: FanGraphs.com  

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 (who has since been hired by the Houston Astros) 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 and I'm not going to repeat the whole process here.  If you want see all the math, you can read my post from last year.

Table 2 below shows the MLB leaders among shortstops in 2013.  The top shortstop in the majors was Andrelton Simmons of the Braves with 33 PMAA. The 33 plays made can be broken down into two parts: 30 Plays in Zone Above Average (PIZAA) and 3 Plays Out of Zone Above Average (OOZAA).  PIZAA and OOZAA may be two of the most amusing acronyms out there and you are probably relieved that I didn't show all the math.  Simply stated though, Simmons was exceptional on plays in the shortstop zone and slightly above average outside the zone.

The final column of the table shows that Simmons saving an estimated 25 runs for the Braves.  Simmons was also rated as spectacular by DRS (+41), Baseball-Reference's Total Zone (+30) and Baseball Prospectus' FRAA (+27).  

Former Tigers shortstop Jhonny Peralta had -2 PIZAA and -1 OOZA which shows that he was about average both inside and outside the zone.  This might be a surprising result, but if we look at two years of data (2013-2013), we see the Jhonny we know:  +14 in the zone and minus -21 outside the zone. 

Tigers current shortstop Jose Iglesias has unexpected number the last two years: +6 PIZAA and -1 OOZA but that's based on under 800 innings.  I would guess that his outside-the-zone play will rate much better in the future.

 
Table 2: Runs Saved by MLB Shortstops According to RZR, OOZ, 2013

Player	Team	Inn	RZR	OOZ	PIZ AA	OOZ AA	PMAA	RSAA
Andrelton Simmons	ATL	1,352	.876	73	30	3	33	25
Clint Barmes	PIT	804	.843	60	9	18	27	21
Pete Kozma	STL	1,051	.838	69	12	14	26	19
Jean Segura	MIL	1,251	.779	98	-10	33	23	17
Troy Tulowitzki	COL	1,029	.862	51	20	-3	17	13
Yunel Escobar	TBR	1,320	.782	90	-7	21	14	11
Pedro Florimon	MIN	1,099	.838	58	12	1	13	10
Alcides Escobar	KCR	1,388	.790	89	-4	17	12	9
Ian Desmond	WSN	1,400	.844	69	15	-4	11	9
Brendan Ryan	- -	854	.759	64	-12	19	8	6
Elvis Andrus	TEX	1,288	.822	63	6	-4	2	1
Zack Cozart	CIN	1,308	.849	54	15	-14	1	1
Alexei Ramirez	CHW	1,400	.820	65	7	-8	-1	-1
Starlin Castro	CHC	1,418	.804	72	0	-2	-2	-1
Brandon Crawford	SFG	1,226	.813	58	3	-6	-2	-2
Jhonny Peralta	DET	935	.796	48	-2	-1	-3	-2
Everth Cabrera	SDP	847	.804	41	0	-3	-3	-2
J.J. Hardy	BAL	1,417	.804	69	0	-5	-5	-3
Didi Gregorius	ARI	894	.795	43	-2	-4	-6	-4
Stephen Drew	BOS	1,093	.788	55	-4	-2	-6	-5
Adeiny Hechavarria	MIA	1,297	.801	61	-1	-7	-8	-6
Asdrubal Cabrera	CLE	1,099	.788	51	-4	-6	-10	-8
Jimmy Rollins	PHI	1,318	.821	49	7	-20	-13	-9
Omar Quintanilla	NYM	814	.771	33	-8	-9	-17	-13
Jed Lowrie	OAK	1,023	.758	43	-11	-10	-22	-16
Erick Aybar	LAA	1,203	.736	59	-21	-4	-25	-19

Data Source: FanGraphs.com