There’s frequently-cited baseball statistic, “value over replacement player”. It’s misleading and incorrect.
A player’s statistics can be approximately converted into wins and losses. A “replacement player” is someone earning the minimum salary. The idea is to compare the player’s performance to a “replacement player”. It’s frequently cited as cost per win.
Suppose a player’s “value over replacement player” is 5 wins. The team won 5 more games with that player, compared to what a minimum salary player would have produced. If the player is paid $10M, then the team paid $2M per win.
One fallacy is that this statistic can be unfair to superstar players. One year, Derek Jeter was the highest paid player and one of the statistically best players. However, according to “cost per win”, the Yankees weren’t getting a bargain. I already wrote about this.
The fallacy is that “replacement player” isn’t a minimum salary player. For a small-market team, the replacement is a minimum salary player. For the Yankees or another big-market team, the “replacement” would be one of the top free agents. If the Yankees didn’t have Derek Jeter, they wouldn’t have a minimum salary shortstop; they would get the top free agent. Derek Jeter’s value shouldn’t be compared to a replacement player. He should be compared to one of the top 15 players the Yankees would otherwise have.
For example, Alex Rodriguez is out for a few months with surgery. They Yankees didn’t pick up a minimum salary replacement. The Yankees signed Kevin Youkilis for $12M.
Also, the “value over replacement player” analysis indirectly converts statistics to wins and losses. Using modern sabermetrics, it’s possible to evaluate the win/loss effect of each play. Getting a homerun when the game is tied is worth a lot more than getting a homerun when the game isn’t close. Instead of indirectly converting statistics to wins and losses, this could be directly calculated. After each play, evaluate whether the team’s chance of winning increased or decreased. Then, you can figure out how many wins each player produced.
There are serious flaws with the “value over replacement player” analysis. Instead of converting statistics into wins and losses, a play-by-play analysis would be more accurate. On big market teams, the “replacement player” is not a minimum salary player, but rather one of the top free agents.