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October 31, 2006

Melky's Defense by the Week
by SG

One of the things I wanted to do this season in order to better understand how to assess the value players bring defensively was to track defense weekly. My hope was that doing this would allow me to see any patterns or changes in time periods, rather than a single year-end number.

Regular readers are already pretty familiar with the method of evaluating that I've been using recently, the heart of which is Stats Inc's zone rating. If you are, you can skip the next two paragraphs. For those who aren't familiar with it, Chris Dial wrote one of the most thorough explanations about the system. For those who don't feel like reading the link, zone rating is a number between 0 and 1, that represents the percentage of fieldable plays a player makes. In other words, if a player has 100 opportunies to make a play, and converts 85 of them into outs, his zone rating would be .850.

I like ZR because it is freely available on several sites (including ESPN and CNNSI), and also because it generally matches what my eyes see fairly well. With the work done by Dial and Sean Smith, it's now pretty straightforward to convert ZR to a run value, which lets us at least attempt to quantify a player's defensive contributions.

Now, ZR has some limitations, like any fielding metric. It does not factor in the speed of batted balls, so a team that gives up more hard-hit balls may look worse than they deserve to, when it's actually the pitchers' fault. It's also scored by people, although it is done by a team of three people who sit separately to cut down on human bias. Also, it does not account for positioning or shifts, so a player being played out of position will be penalized for not being able to make a play he may have made if he was in his normal position. There appear to be park factors in several stadiums (notably those with high walls), although we are making some inroads in figuring out how to handle these. Lastly, it does not handle plays made out of zone well, as they end up getting lumped into plays in zone. So keep all these factors in mind when looking at numbers based on zone rating, and account for the error bars inherent in these numbers.

When you think of Zone Rating, all it is is plays made/plays available. If a play is not made due to an error, it is no more or less meaningful than a play that is not made due to a fielder's lack of range. This is a fundamental part of understanding defensive value, that is usually overlooked by the mainstream media. Fielding percentage doesn't mean a damn thing, really.

So now that the explanation is out of the way, here are the numbers that you need to calculate a player's defensive contribution.

Chances/Plays available - This is available on CNNSI, but if you don't have this number handy you can calculate an approximation of this. To do that, you would do the following.

For 1B, it's best to use a historic approximation of the chances most 1B see per inning, which is 0.198112. So a 1B who plays 1000 innings would have 198 chances, typically. It's best to use the actual chances from CNNSI, but if that's not available this should be close enough.

For all other IF, we can figure out the plays availabe by using their plays made (assists), and dividing by their zone rating. So a player who has 250 assists and a ZR of .825 would have had 303 plays available to them.

For OF, we can do the same thing, substituting putouts as plays made instead of assists.

We then need to calculate the average ZR at each position and from there we can see how many plays above/below average a player makes. Each position has an associated run value for the plays they make or fail to make, and those are listed here. We would multiply these run values times the plays made above/below average to get a run value.

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

For OF, I then add in a value for runs saved by their arm by comparing their assists to the league average at the same position.

So now that this has all been explained, let's run through it with an example, which in this case is going to be Melky Cabrera. A lot of people want to see Melky as the full time LF in 2007 because he seems to be a pretty big upgrade over Hideki Matsui, who has been about a -10 LF in his Yankee tenure. However, the numbers don't really mesh with this perception.

This season, Melky had 256 playable chances, and converted 208 of them into outs. 208/256 = .816, his ZR. The average AL LF had a ZR of .844, so the average LF would have made 216 plays. So Melky made 8 fewer plays than average, which we then multiply by .831, to get a run value of around -7 for zone outs. Melky had 12 assists in 998.2 innings, the average LF would have had 8. Assists are worth about one full run, so we give Melky a plus 4 for his arm, which makes his overall defensive value around -3.

So here's Melky's chart for the season, by week. There's a lot of rounding in the charts below so if things don't look like they add up to what's displayed here in some columns, that's why.

The encouraging thing in this set of numbers is that you can see that Melky struggled quite a bit over his first 30 games, although his arm helped make his defensive value decent.

In this chart, ZR is the ZR by week.

A ZR of .769 over a full season would be really bad. It would mean he would make somewhere on the order of 25 fewer plays than average. Thankfully, things were better in his last 85 games, as far as zone outs, although baserunners seemed to gradually learn that running on Melky is foolish.

An .837 ZR is still below average, although not terribly so. Matsui's career ZR in LF is .834, but he's also getting older and his arm is not nearly as good as Melky's. With what appears to be a dearth of options at first base in the free agent market, I wonder if the Yankees should consider Matsui's offer to play 1B.

I think Melky has the potential to end up being pretty solid in the OF eventually, and 990 innings is a pretty small sample size, so I wouldn't read too much into these numbers. It's just a little bit of information to try and quantify what we watched.

If anyone wants to see similar splits for other players, let me know.