# Comparing the Performance of Baseball Players: A Multiple-Output Approach

By Koop, Gary | Journal of the American Statistical Association, September 2002 | Go to article overview

# Comparing the Performance of Baseball Players: A Multiple-Output Approach

Koop, Gary, Journal of the American Statistical Association

1. INTRODUCTION

Many of the statistical methods used in this article are adapted from the economics literature, and hence some economic terminology is used. That is, baseball players (like firms in an economic context) are viewed as producing outputs given firm characteristics (e.g., a batter produces the "output" hits, which depends on his situation, including what team he plays for, etc.). In an economics context, typically firms operate with different output mixes, just as in baseball batters have different mixes of hits (e.g., singles, doubles, home runs). By looking at the best firms in different regions of output space, the economist can trace out a production possibilities curve, which measures the maximum feasible combinations of outputs that can be produced. In baseball, the best batters can be considered in different regions of output space and trace out a comparable curve. For instance, Mark McGwire might heavily influence the production possibilities curve in the power dimensions, whereas Tony Gwynn might have in fluence in batting average dimensions. Once this production possibilities curve is estimated, individuals can be compared to it. Because the curve reflects best practice, an average player will lie inside the curve. As discussed later, a number between o and 1 can be calculated that reflects how far the player is from the nearest point on the curve. Following the economics literature, to this number is called efficiency. So, for instance, a certain player may have an efficiency of .8. This number has a simple, intuitive interpretation: The player under consideration is only 80% as productive as the best players with a comparable output mix. In other words, the proposed methodology enables comparison of any player with similar players and provides an easily interpretable, single-number summary of a player's performance. Furthermore, the methodology incorporates all of the outputs that a batter produces and corrects for the player's situation (e.g., playing in a particularly good or bad hitter's park).

The output aggregator in this first approach provides a sensible efficiency measure, performance as percentage of best comparable player (see Sec. …

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