Quantifying Defense

The discussion has been brewing all over the blogosphere over the past few days of the winter with such moves as the Mariners trade of JJ Putz for some defensive studs as well as the Phillies signing of Raul Ibanez about the topic of defense, especially in the outfield.

Fielding has been the toughest thing about baseball to quantify for as long as the game has been played – and still is - for a very long time, the best metric we had was fielding percentage. Fielding percentage is pretty clearly a terrible metric – if a ball is hit 5 feet to the left of me and I decide to just stand at my position and let the ball go by, it’s not an error. However, a good metric would demerit me for this play, since I (and more importantly, the average fielder) could have fielded the ball. Still, my fielding percentage would remain unchanged.

Many advanced systems have arisen since the 1980s, thanks to the breakthrough in play-by-play data recording the locations of batted balls, making it possible to determine the number of chances that a fielder gets over the course of a season. This also makes it possible to determine the number of plays that the average fielder makes over the course of the season. This is the basis behind systems like Dewan’s +/- and Mitchel “MGL” Lichtman’s UZR, and David Pinto’s PMR.

Without examining the way that the computers actually formulate the numbers, we can still take a look at the theory behind it. The first thing to look at is how many runs each defensive play is worth. For this, we turn to linear weights. Linear weights are the basis for stats like wOBA and are derived from the same base/out states as WPA.  These weights are the average run values of each event.

Here are the linear weights for each event for the 2004-2006 seasons:

1B-.465 runs
2B-.775 runs
3B-1.056 runs
HR-1.396 runs
BB-.319 runs
OUT-(-.292) runs

So when JJ Hardy ranges way up the middle and makes a beautiful play, he’s basically turned a single into an out. So he’s turned an event worth -.465 runs to us (the fielding team) and made it into an event worth .292, for a total of (.292 - (-.465)) = .757 runs.

In the outfield, we may even see players saving extra base hits. When Endy Chavez robbed a home run in the NLCS two years ago, he saved (.292 - (-1.396)) = 1.688 runs. However, this also goes the other way around. When Carlos Lee can’t get his fat ass over to a ball down the line and it turns into a double, he effectively costs the team (.775 + .292) = 1.067 runs. To make things easier, we use the value .798 runs/play as the average of these results.

If you can find a player that makes 13 more plays over the course of a 162 season, the team is saving a win. To put that in perspective, for example, ask yourself if Mike Cameron didn’t make 13 more plays last year than Bill Hall the season before in center, or if Ryan Braun didn’t make 13 more plays than Carlos Lee used to in left field.

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2 Responses to “Quantifying Defense”

  1. Kade in Dubuque Says:


  2. Jack Says:

    Essentially, yeah.

    That’s another problem with fielding metrics - this is as simple as it gets.

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