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Wednesday, July 11, 2007

2007 Yankee Defense at the All Star Break

Wrapping up my All Star Break review of the Yankees so far, here's how their defense rates by zone rating. If you want to read a good explanation about zone rating, you should read this article by Chris Dial, but I am going to run through an example as well, to try and clarify exactly what the numbers that will follow mean.

I could pick on Derek Jeter, but I'm not going to go there. Instead I'm going to look at the brightest spot on the Yankee defense so far, Robinson Cano. We all know Cano's been a disappointment on offense, but let's look at his defense.

To help clarify the numbers I'm about to run through, here's the Stats Inc. Zone Rating grid, with the 2B area of responsiblity highlighted.



Any ball hit in that highlighted area that is converted into an out at least 50% of the time is considered a fieldable chance for a second baseman. This is based on observation by Stats Inc. scorers, but there are three people scoring these at every game and they score them independently to help cut down on subjectivity.

When a fielder has a ball hit into their zone of responsiblity, they are given a fieldable chance, which is the denominator in ZR. When they convert that into an out, it's considered a play made. When a fielder makes a play that is not his defined zone, it gets added to his chances and plays made so they get credit for it. The question is if they get enough credit for doing so, which is one limitation of zone rating. Another limitation is the zones of responsiblity are fixed, and do not account for positioning. This is a limitation when trying to assess a player's actual talent, but as far as their value in any given time, I don't think it's much of one. If a player is not put into position to make more plays than he is, that means they are not as valuable to their team as they should be, regardless of who is responsible for the positioning.

ZR is expressed as a three digit decimal from 0 to 1, and it's just plays made divided by fieldable chances. So if a player has 10 fieldable chances hit into his defined zone and converts 8 of them into outs, his ZR is .800. Plays are either made or not made in ZR. If a player makes an error, it's no worse than if their range never let them get to the ball in the first place.

So let's get back to Cano. Cano has played 84 games this season, and 747 defensive innings at second base. He has seen 274 fieldable chances, and has a ZR of .880. So we multiply his fieldable chances by .880 to get his plays made, which is 241.

The next thing we do is multiply the chances that Cano has had times the average ZR, to get an average plays made. This assumes that the types of chances a player faces over the course of a period are the same, and it's not necessarily true. Players could have stretches where they face easier chances or more difficult chances, which is why you will see players' defensive numbers fluctuate from season. Again, I consider this a limitation when trying to assess a player's ability, but not their value. This is the type of thing that should even out over time, which makes multi-year zone rating a decent gauge of a player's defensive talent.

In the American League, the average 2B has a ZR of .831. I separate the leagues because I've noticed systemic differences in the infields, and I assume it's at least partly due to pitchers "hitting." So, using the .831 avg ZR times Cano's 274 chances, we get an average plays made of 228. We subtract this from Cano's actual plays made to get a difference. 241 - 228 = 13, so Cano has converted 13 more plays into outs than average. This difference is then multiplied by the average run value of a play at that position, which was calculated by Dial and is based on the linear weights values of the single or XBH that the play would turn into if it is not made, as well as the marginal value of the out that was not recorded.

Here are the run values for the average plays at each position.

POS RV
1B: .798
2B: .754
3B: .800
CF: .842
LF: .831
RF: .843
SS: .753

For 2B, the average play is worth .754 runs, so we multiply that by Cano's +13 plays made and get a runs saved above average of 10. To calculate this over a full season, you just divide the runs saved by the innings played and multiply by 1440 innings.

Credit for this methodology goes to Chris Dial and his article Dr. StrangeGlove or: How I Learned to Stop Worrying and Love Zone Rating and to Chone Smith and his article Tweaking Zone Rating. Without them breaking zone rating down this clearly for me I never would have been able to understand it.

The same basic idea is used for figuring out all players except pitchers and catchers, and here are the numbers for the Yanks.

Player	TM	LG	Pos	G	GS	INN	PO	A	E	DP	Ch	PM	ZR	Avg ZR	AvgPM	Diff	RS	RS/162
Cano, Robinson	NYY	AL	2B	84	84	747	178	271	6	78	274	241	.880	.831	228	13	10	19
Rodriguez, Alex	NYY	AL	3B	83	83	724	63	149	5	15	207	168	.812	.762	158	10	8	16
Cabrera, Melky	NYY	AL	CF	59	48	445	154	5	1	1	166	152	.916	.889	148	4	4	12
Cabrera, Melky	NYY	AL	LF	18	16	142	34	2	0	0	34	31	.912	.872	30	1	1	11
Cairo, Miguel	NYY	AL	3B	7	3	35	1	9	1	2	10	9	.900	.762	8	1	1	45
Cairo, Miguel	NYY	AL	SS	8	2	36.2	3	15	0	1	18	16	.889	.824	15	1	1	35
Thompson, Kevin	NYY	AL	RF	4	2	18	6	0	0	0	5	5	1.000	.859	4	1	1	48
Cabrera, Melky	NYY	AL	RF	4	3	26	3	0	0	0	3	3	1.000	.859	3	0	0	20
Giambi, Jason	NYY	AL	1B	2	2	14	11	1	0	3	2	2	1.000	.842	2	0	0	26
Basak, Chris	NYY	AL	3B	2	0	3	0	1	0	0	1	1	1.000	.762	1	0	0	91
Posada, Jorge	NYY	AL	1B	1	1	6	6	0	0	1	0	0	.000	.842	0	0	0	0
Damon, Johnny	NYY	AL	1B	3	0	4.1	4	0	1	1	0	0	.000	.842	0	0	0	0
Nieves, Wil	NYY	AL	1B	1	0	1	1	0	0	0	0	0	.000	.842	0	0	0	0
Phillips, Andy	NYY	AL	3B	2	0	2	1	0	0	0	0	0	.000	.762	0	0	0	0
Thompson, Kevin	NYY	AL	CF	1	0	1	0	0	0	0	0	0	.000	.889	0	0	0	0
Basak, Chris	NYY	AL	SS	1	0	1	0	0	0	0	0	0	.000	.824	0	0	0	0
Thompson, Kevin	NYY	AL	LF	4	1	13.2	5	0	0	0	6	5	.833	.872	5	0	0	-21
Phillips, Andy	NYY	AL	1B	13	10	90.1	85	4	0	12	16	13	.813	.842	13	0	0	-6
Cairo, Miguel	NYY	AL	2B	2	2	17	5	6	0	0	8	6	.750	.831	7	-1	0	-41
Cairo, Miguel	NYY	AL	LF	3	1	13	2	0	0	0	3	2	.667	.872	3	-1	-1	-57
Phelps, Josh	NYY	AL	1B	29	20	162.2	167	9	3	16	27	22	.815	.842	23	-1	-1	-5
Abreu, Bobby	NYY	AL	RF	84	81	720	156	2	4	0	183	156	.852	.859	157	-1	-1	-2
Damon, Johnny	NYY	AL	LF	1	1	9	1	0	0	0	3	1	.333	.872	3	-2	-1	-215
Damon, Johnny	NYY	AL	CF	41	38	318	106	1	0	0	119	104	.874	.889	106	-2	-1	-7
Mientkiewicz, Doug	NYY	AL	1B	48	36	330.1	353	14	2	46	59	47	.797	.842	50	-3	-2	-9
Cairo, Miguel	NYY	AL	1B	21	17	155.1	161	9	4	16	42	32	.762	.842	35	-3	-3	-25
Matsui, Hideki	NYY	AL	LF	68	67	586.1	131	4	2	0	152	127	.836	.872	132	-5	-5	-11
Jeter, Derek	NYY	AL	SS	84	83	726.1	128	246	13	69	295	227	.769	.824	243	-16	-12	-24
Total				678	601	5345.2	1765	748	42	261	1633	1370	.839	.840	1371	-1	-1	-2

Legend
INN - Innings
PO - Putouts
A - Assists
E - Errors
DP - Double plays
Ch - Fieldable chances
PM - Plays made
ZR - Zone Rating
AvgZR - Average ZR
AvgPM - Average PM
Diff - PM minus AvgPM
RS - Runs saved
RS/162 - Runs saved pro-rated to 162 games

So yeah, Cano's been great. Also great, Alex Rodriguez, who has rebounded from two sub-par years at third after a solid 2004 defensively. Melky's flashing a plus glove in LF and CF and this doesn't even include his arm.

The rest of the numbers seem to match my observations pretty well, although I'd have pegged Abreu to be a little worse and Matsui to be a bit better. This is part of the reason I've grown fond of zone rating. It's freely available, it's easy to convert to runs, and for the most part the players I think are good and bad defenders show up as such in ZR.

These numbers are not meant to be an absolute assessment of either a players' defensive ability or value. First of all, we're dealing with a small sample size. The difference between Jeter being average or horrible is about one play a week. Second of all, as I've listed above, there are limitations in zone rating which need to be acknowledged and understood. Over at Bronx Banter the other day there was a heated discussion about defensive metrics and their pros and cons. The way I described it to someone over there is this. Let's say you have a group of hitters, and the only thing you know about him is their batting averages. Would you prefer to use your visual observations of the players' abilities and whether they have good at bats, or would you rather use batting average to determine their skill at least partially, even acknowledging that batting average has limitations? That's kind of where I think defensive metrics should fall into place.

For catchers, I use a combination of passed balls and stolen base percentage. It's not a great method because pitchers deserve some of the blame for stolen bases, but again, if we think of it in terms of value instead of ability it's better than nothing.

NAME	GP	GS	INN	TC	PO	A	E	DP	FPCT	PB	SB	CS	CS%	CERA	RS	RS/150
Jorge Posada, NYY	77	68	621	427	394	30	3	2	.993	3	61	19	0.24	4.42	-3	-7
Wil Nieves, NYY	21	18	142	105	99	5	1	1	.990	0	17	5	0.23	4.12	-1	-5
Josh Phelps, NYY	1	0	1	0	0	0	0	0	.000	0	0	0	0	0	0	0

Posada's defense has typically been average or slightly below, but he was great last year. He's back below average this year, but he's hitting more than well enough to compensate. Wil Nieves has a wonderful smile, which is apparently all he needs to have to be the Yankees' backup catcher.

With the pitching, offense and defense all assessed it's time to see where everyone on the Yankees ranks in terms of overall value, so here you go.

Last	BR	DR	PR	TR
Rodriguez	33	8		42
Wang			18	18
Posada	19	-3		16
Bruney			8	8
Cano	-2	10		8
Myers			7	7
Clemens			6	6
Matsui	8	-5		4
Rivera			3	3
Villone			3	3
Jeter	15	-12		2
Pettitte			2	2
Hughes			2	2
Britton			2	2
Giambi	1	0		2
Proctor			1	1
Cabrera	-5	5		1
Mussina			0	0
Ramirez			0	0
Phillips	0	0		0
Basak	0	0		0
Rasner			-1	-1
Thompson	-1	0		-1
Pavano			-1	-1
Henn			-1	-1
Farnsworth			-1	-1
Bean			-2	-2
Wright			-3	-3
Vizcaino			-3	-3
Desalvo			-3	-3
Phelps	-3	-1		-4
Clippard			-4	-4
Karstens			-5	-5
Damon	-4	-3		-6
Cairo	-5	-2		-7
Abreu	-6	-1		-7
Nieves	-7	-1		-8
Mientkiewicz	-6	-2		-8
Igawa			-13	-13
Total	38	-6	15	47

BR = Batting runs
DR = Defensive runs
PR = Pitching runs
TR = Total runs

I'd take Bruney and Myers's high ranking with a big grain of salt. It may be better to use a linear weights type formula for relievers' value to the team since ERA or RA can hide their performances with inherited runners.

I was surprised to see that Cano's defense makes him such a plus contributor, but I guess that's the case at least by this methodology. If you want to get angry, you can figure out how much the "contributions" of Abreu, Mientkiewicz and Igawa have cost the team this year.