# Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football

By Wayne Winston | Go to book overview

9
THE VALUE OF REPLACEMENT PLAYERS

In this chapter we will learn how to use the Player Win Averages discussed in chapter 8 to evaluate trade offers and calculate a player's fair salary (based on his previous year's performance).

VORPP: Value of a Replacement Player Points

The key tool involved in our analysis will be the Value of a Replacement Player Points (VORPP), which was developed by Keith Woolner, formerly of the Baseball Prospectus and now an executive for the Cleveland Indians. You may recall in several earlier chapters we compared a player's batting, pitching, and/or fielding performance to that of an average player. Although such comparisons are interesting, they do not really help us determine the true value of a player. We know that players create value by doing good things. Woolner appears to be the first person to have realized that players also create value by keeping bad players out of the lineup. Woolner asked what a team would do if a player were injured. The team often brings up from the minor leagues a player whose salary is very low (let's say 0). In theory there is a near inexhaustible supply of such players (called replacement players). To define a replacement player for, say, second basemen, Woolner would put the second basemen in descending order of plate appearances and define the replacement second basemen to be those who rank in the bottom 20% of this list. Woolner calculated that a lineup consisting totally of replacement players would generate a season record of 44–118 (winning four more games than the 1962 New York Mets).

Recall from chapter 8 that for each game a team finishes below .500 they will earn —2,000 SAGWIN points. Therefore, a team of replacement players should end the season with —74,000 points. Ignoring the relatively

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