Valuing Gerrit Cole’s Opt Out

Last night, Gerrit Cole signed a record-breaking contract with the Yankees. Jay Jaffe broke down the signing, and mentioned one important part: the contract includes a player option after five years. In a contract as lengthy and lucrative as Cole’s, an opt out might seem like mere ornamentation. That’s not the case, though: as Stephen Strasburg’s earlier contract shows, sometimes the market in the future is simply better for a pitcher than we think. With that in mind, I took a stab at valuing the player option.

We use two player projection systems here at FanGraphs, and I ran both of them through the option pricing tool, as well as a hybrid. First, let’s take a look at the most optimistic: Steamer projects Cole for 6.3 WAR this year. From there, I applied a standard 0.5 WAR/year aging penalty and ran the numbers. You can read the methodology here, but as a quick refresher, I take an aging-inclusive projection, then bump each year by a random, normally distributed number to account for fluctuations in talent level.

The bumps persist year-to-year; if Cole improves to a 7 WAR projection for 2021, his mean projection for 2022 would be 6.5 WAR after the aging penalty, and I then apply another random talent bump to that projection. I do the same thing with the cost of a win in free agency; it generally trends upward, but jumps around, and the jumps persist year-to-year.

Cole opts out a surprising amount of the time under these projections:

Cole Opt Out Outcomes (Steamer)
Condition Odds WAR Salary ($m) $/WAR
Opts Out 0.374 31.9 180 5.6
Stays 0.626 29.1 324 11.1
Total 1 30.1 270.1 9.0

But perhaps more surprising is how much better he is in the scenarios when he opts out than he is when he stays. It might sound counterintuitive, but Cole projects for more WAR over five years when opting out than he does over nine years when staying. Why? In many of the scenarios where he declines, the last four years of the deal dip towards replacement level. For him to leave, on the other hand, he has to outperform expectations significantly (or the cost of a win has to spike higher).

How significantly are we talking? Take a look at Cole’s performance and pay in the two scenarios:

Cole Performance Outcomes (Steamer)
Condition Odds WAR (Year 6) Cost of 1 WAR New Contract
Opts Out 0.374 6.5 9.4 214
Stays 0.626 2.2 9.2

On average in the worlds where Cole opts out, he defies aging, looking as good in six years as he does now. In some, he’s a 10 WAR player; in some, a mere 5 WAR, 36-year-old player. You could quibble with the caps teams would be willing to pay for four years of a 10 WAR pitcher, which would tinker with his expected windfall upon opting out, but using a linear cost of a win and the odds of Cole opting out, the option to become a free agent again in five years is worth $26 million to Cole.

Steamer’s projections are the rosiest. If we instead use ZiPS, which starts with a 5 WAR projection but declines more slowly, an early departure becomes less likely:

Cole Opt Out Outcomes (ZiPS)
Condition Odds WAR Salary ($m) $/WAR
Opts Out 0.268 27.5 180 6.5
Stays 0.732 22.9 324 14.2
Total 1 24.1 285.4 11.8

Even in this scenario, however, Cole leaving involves him significantly beating his projections, and the opt out is worth $16 million:

Cole Performance Outcomes (ZiPS)
Condition Odds WAR (Year 6) Cost of 1 WAR New Contract
Opts Out 0.268 6.2 9.4 205
Stays 0.732 1.8 9.2

Finally, I ran a blend of the two projections. The results, as expected, were somewhere in between:

Cole Opt Out Outcomes (Blend)
Condition Odds WAR Salary ($m) $/WAR
Opts Out 0.318 29.7 180 6.1
Stays 0.682 26.0 324 12.5
Total 1 27.2 278.2 10.2

And this time, Cole’s opt out is worth $21 million:

Cole Performance Outcomes (Blend)
Condition Odds WAR (Year 6) Cost of 1 WAR New Contract
Opts Out 0.318 6.4 9.4 210
Stays 0.682 2 9.2

So there you have it. I believe the player option part of Cole’s contract is worth around $20 million. You can disagree with pieces of it; maybe my particular style of random variation doesn’t handle pitchers as well as it does for position players, or maybe the assumption of a linear $/WAR doesn’t work for some extreme outcomes. The overall conclusion, however, seems straightforward: Cole’s player option isn’t a mere trinket, but it also doesn’t significantly change the terms of the deal. Gerrit Cole got paid; and he got paid slightly more due to the exact design of his contract.

We hoped you liked reading Valuing Gerrit Cole’s Opt Out by Ben Clemens!

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Ben is a contributor to FanGraphs. A lifelong Cardinals fan, he got his start writing for Viva El Birdos. He can be found on Twitter @_Ben_Clemens.

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