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August 28, 2014

Moonshot

On Regressing Defense

by Robert Arthur


We heard the first blows in the nascent MVP debate of 2014 unfold just last week. At the time, Alex Gordon led all players in fWAR (by a narrow margin), largely on the basis of his extraordinary defense in left field (15 fielding runs above average, fifth highest in MLB). In response, Jeff Passan wrote that the idea of Alex Gordon as the best player in baseball was absurd.

Much wailing and gnashing of teeth ensued. To some of the doubters of sabermetrics, Gordon’s triumph on the leaderboards was yet more proof of the uselessness of WAR(P). To others, arguments against Gordon may have seemed ill-formed.

Fortunately, Gordon no longer leads baseball players in any of the flavors of WAR(P) (whew, argument defused). Even so, Alex Gordon brought to the surface a recurring theme in criticisms of the WAR framework: the weighting of defensive metrics. In theory, a run saved is a run scored. But whereas the relationship between singles, doubles (etc.), and runs produced is easily parsed with linear weights, defense is more difficult to measure. The steps between the events on the field and the runs being saved require more estimation, and that potentially injects more error in the final result.

A natural response to the additional error implicit in defensive measurements is to deem them unreliable and regress them according. ‘Regression’ exists in the sabermetric lexicon as both an abstract concept and a concrete, mathematical transformation. In the abstract sense of the word, to regress a player’s defensive WAR(P), for example, is to mentally adjust his contribution back toward the mean, accounting for the uncertainty in the estimate—exactly what we’d like to do with defense. We can formalize that mathematically by simply multiplying each player’s defensive value, calculated hereabouts as FRAA, by some constant which I’ll call a “regression factor,” r:

FRAAi x r = regressed FRAA of player i

When r is less than one, a player’s defensive contribution is being pushed back towards zero, which is to say the average. For example, at a regression factor of .5, a defensive standout like last year’s Manny Machado loses half of his value, i.e. about 14 runs. Meanwhile, a defensively mediocre player that year, Matt Carpenter, also sheds half of his value, but this only amounts to a single run subtracted. The penalty is thus much stiffer at the extremes, both good and bad. Consider the following graph, which shows the density of players at different FRAA values, with and without a regression factor of .5 applied.

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Related Content:  Kansas City Royals,  Defense,  WAR

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<< Previous Article
Premium Article Skewed Left: A Three-H... (08/28)
<< Previous Column
Moonshot: The Analytic... (08/20)
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Premium Article Moonshot: Time vs. Pac... (09/03)
Next Article >>
Prospects Will Break Y... (08/28)

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