Value over replacement player
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In baseball, value over replacement player (or VORP) tells how much a player contributes offensively and defensively to his team in comparison to a fictitious "replacement player," who is an average fielder at his position and a below average hitter. A replacement player performs at "replacement level," which is the level of performance an average team can expect when trying to replace a player at minimal cost, also known as "freely available talent."
VORP's usefulness is in the fact that it measures contribution at the margin. Other statistics compare players to the league average, which is good for cross-era analysis (example: 90 runs created in 1915 are much better than 90 RC in 1996, because runs were more scarce in 1915). Where league-average comparisons break down, however, are when talking about a player's total, composite contribution to a team. Baseball is a zero-sum game; in other words, you have to score more than zero runs to win a game. It follows, then, that a contribution of any runs helps a team toward a win, no matter how small the contribution. But, the Major Leagues are highly competitive; it is likely that the contribution a marginal player makes, even if it does help a team win one game, is not enough to justify his presence in the Majors. This is where the concept of the replacement level enters the picture.
The currency of baseball is the out. There are a finite number of outs that a team can make in one game: almost always 27 (or 3 outs/inning * 9 innings/game). A player uses said outs to create runs. If you boil everything down, runs and outs are the only meaningful stats in baseball. Outs are easy to calculate: simply take at-bats and subtract hits, then add in various outs that don't count as at-bats: caught stealing, sacrifices, etc. Runs aren't that hard anymore either; use your favorite run-approximation method: runs created, linear weights, equivalent runs, etc. Keith Woolner, who invented VORP, likes to use runs created, but you can really take your pick. Armed with those two numbers (for the player and that player's league), one can finally calculate VORP.
The real controversy of VORP surrounds where the replacement level is set; many equations and methods exist for finding the replacement level, but most will set the level somewhere around 80% of the league average, in terms of runs per out. Now, VORP: Multiply the league average runs per out by the player's total outs; this provides the number of runs an average player would have produced given that certain number of outs to work with. Now multiply that number (of runs) by .8, or whatever level your replacement equations give you; this is the number of runs you could expect a "replacement player" to put up for that number of outs. Simply subtract the replacement's runs created from the player's actual runs created, then, and you have VORP. A word to the wise, though: while the replacement's run total will be park-neutral (by definition), the player's raw numbers won't be. Before calculating the VORP, run the player stats through park factors, normalizing the numbers. The resultant VORP should give a pretty good estimate of how "valuable" the player in question is.