Whether it should be the Red Sox who pay Ellsbury is one of the more difficult questions that the Red Sox are facing this offseason This is Ellsbury’s Dumber-than-Marcel projection for 2014:
+10 Bat + 5 Run + 8 Def + 2 Pos + 18 Def = +43 RAR
So what is a 4-5 win player worth? Tabling for now the issue of how to rate the on-and-off-and-on career of Jacoby Ellsbury, this is the first big question. I have cited now a few times Lewie Pollis’ study of the cost of wins. I grow more convinced the more I read through the discussions that Pollis has it right. Pollis’ study considered the actual cost in salary of the actual wins produced (estimated with WAR) for all players signed through the free agent market. That’s the right approach if you want to determine value of a win, I think. Fangraphs looks at only the first season of FA contracts, and they compare the player’s salary to his projected production rather than his actual production. As Matt Swartz showed (at Fangraphs), it appears that the projections used in Fangraphs’ $/Win calculation have systematically overestimated the expected playing time of free agents in their first seasons, leading to a mis-estimation of $/Win. Further, the out years of contracts cost more on a $/Win scale than the first season, so the average cost of wins goes up for longer-term contracts.
Pollis’ study shows the cost of wins remaining relatively steady for the last few years. Fangraphs by contrast has shown continued free agent contract inflation that outpaces real-world inflation. So if you want to project Ellsbury’s contract, you also have to consider how much inflation you expect over the next five to seven seasons.
However, even though I think Pollis’ study better estimates the true cost of wins, it’s not clear that his numbers are what we should use in projecting salaries. If projections are systematically overprojecting playing time, but we want to estimate how much a player should cost now, before he actually plays any games, we need to use projections ourselves. So if the Dumber-than-Marcels or whatever other (better) projection system overestimates playing time, then I should perhaps be using a number closer to Fangraphs’ than Pollis’.
I don’t have an easy answer to this question, so I’ve decided to do both things. My salary projections use a simple ~0.5 win / year rate of decline. Here are projected “fair” salaries for Ellsbury using both the Fangraphs and Pollis numbers. I have Fangraphs at ~5.5M per win with some inflation, and Pollis at 7M per win with less inflation.
Pollis: 5/122, 6/137, 7/147
Fangraphs: 5/100, 6/114, 7/124
The Pollis projected salaries would probably make the Red Sox solid competitors for Ellsbury’s services, though you can never count out crazy. The Fangraphs numbers look like the sort of offers that a club makes to demonstrate their interest in a free agent who is going to sign elsewhere. How you value a win on the free agent market makes a big difference.