Should the Red Sox Re-Sign Jacoby Ellsbury, Part I: The Cost of Wins

Come back, Jacoby! (RLRS photo)

Come back, Jacoby! (RLRS photo)

The most recent news on Jacoby Ellsbury and the Red Sox is not good for those of us who are fans of the speedy center fielder. Peter Abraham at the Globe reports that while the Red Sox want to re-sign Ellsbury, they consider him a “long shot” at this point. There is a ton of money floating around baseball at the moment (Ricky Nolasco is looking for $100M, for serious like), and if you presume Robinson Cano ain’t signing with no Mets, then Ellsbury is the best free agent on the market. He is going to get paid.

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.

8 thoughts on “Should the Red Sox Re-Sign Jacoby Ellsbury, Part I: The Cost of Wins

  1. Dave H

    I’ll post this in every Ellsbury/Sox FA thread I can find: 6/$120m is an easy call for me. The Sox have a high replacement level, and they need stars. Ellsbury is a perfect fit for this team. If you’re convinced that JBJ will be a star, then he takes over for Gomes/Nava at some point, and Victorino after that.

    Has anyone reconsidered the linear cost of wins model in the wake of Pollis’s study? Previously it seemed likely that stars saw more years, not more salary. If you use actual wins instead of projected, and all years instead of the first, is the result the same?

  2. Darren

    My takeaways from the Pollis article:

    –In the discussion at the bottom, Cameron says that Fangraphs dollar figures had not been adjusted to account for their unifying replacement level. Tango, on his site, calculates that doing so brings Fangraphs’ numbers up to $5.7M.

    –Pollis’s chart shows the number bouncing back and forth between $6M and $7M the last few years. He concludes from this that the price of a win is $7M–I would say his study shows it to be more like $6.5M.

    So, overall, we’re quibbling between $5.7M and $6.5M. Not a huge difference and I’d certainly be comfortable using $6M as an easy shorthand. That number, plus some inflation, probably puts us somewhere in between MCOA’s two estimations above:


  3. Jose

    I wouldn’t do seven years unless the cost was unrealistically low. The number for five and six years look reasonable to me.

  4. Piehole


    I said on another thread that the Sox should go for an absurd amount for a 3-year contract. Like 3/75. But since that doesn’t now look absurd enough, 3/81 with 3 option years based on incentives that automatically kick in if he plays 150/300/450 games over the first 3 years at around $20mm each. But since that’s bitching expensive, if he goes on the 60-day DL or misses 100 games, the Sox get a team option year at $500k. This reduces risk for the Sox since if he’s not playing you cut him loose after 3 years, and if he’s not playing, the cheap team option brings his contract value way down. 3-year deals for LOTS of money should be every team’s standard operating procedure.

    But a straight 6 year contract for Ellsbury with no protection for the team is absurd. If there’s a buyer out there willing to go that length for him, “Goodbye Jacoby. Been nice knowin’ ya. Don’t let the door hit you in the ass.”

  5. Dave H

    @Piehole: I don’t think that’s a realistic expectation given how the market works. First, there’s not going to be anything about the 60-day DL – I doubt there will be much in the way of injury risk taken on by the player and certainly not anything that the team has total control over. Second, there’s a reason that star players get longer contracts. It makes more sense for the player, who is probably relatively risk adverse, to give the team a discount in AAV in exchange for more guaranteed years.

    Some 6-year contracts for Ellsbury would be absurd, but some would be quite reasonable – you can’t focus only on the length and not the money. As great as their strategy was last year, in retrospect having Drew and Napoli for another year at the same AAV would have been even better.

  6. IronChefChrisWok

    I don’t have problems wiht paying a 4 win player, the question will always be “will Jacoby be a 4 win player going forward”

  7. Clarence Thomas is Visiting RLRS (scott)

    I like Ellsbury at anything up to Crawford money. I’ll be a bit disappointed if he signs elsewhere for less than 7/140.

    I also think that people might be right to disagree with my position- Ellsbury is definitely high risk/high reward and a 6 or 7 year contract could be an albatross if he continues to get hurt or his skills decline rapidly. But he’s proven that he’s a superstar player when healthy, and I’m willing to pay for the chance to get those 6 WAR years. (Of course, it’s not my money, so that’s only saying so much).

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