How to Value Opt-Outs

Yoenis Cespedes' opt-out could be valued at nearly $70 million with a strong 2016 season. (via Arturo Pardavila III)

Yoenis Cespedes’ opt-out could be valued at nearly $70 million with a strong 2016. (via Arturo Pardavila III)

As the ever-expanding revenue of Major League Baseball filters through to larger player contracts, those contracts get inevitably more complicated. Before there was as much money to go around, players benefited from guaranteed contracts that could ensure a certain lifestyle. Even though a player’s value was highly variable, the player benefited from his pay not being so. Teams bought the risk from the player. As these contracts get larger, teams are now selling off some of that risk to players.

The big wave of contracts that appeared over the last decade involved multi-year, guaranteed deals for young players that bought out arbitration years well before a player was eligible. This type of contract was actually the player selling some extra risk to the team and getting a guaranteed sum of money in case he fizzled out before reaching arbitration. Such a risk is considerable for players, because getting that money in the bank is the difference between having the lifestyle of a wealthy person and not. The difference between earning $1 million and $11 million over a career is far larger than the difference between earning $11 million and $21 million. Players are willing to hedge against the risk of earning $1 million in their careers.

On the other hand, players who have reached free agency generally have earned much more than they would ever need. Few players will ever need to work again outside of baseball, so they no longer have such a fear of injury or decline hurting their livelihood. Players have little need to hedge against the risk of disappearing from the game with a mere $21 million. In fact, they may have an appetite for upside risk in some cases—which is why you see more deals with “opt-outs” given to free agents nowadays.

Valuing these provisions is important for teams over the long run. Front office decision-making has moved away from just talent evaluation, and now requires some understanding of economic and financial concepts. Teams take a major downside when they are to pay a player like David Price $127 million after an opt-out; this was an agreement to pay Price $127 million for 2019-22, only if he does not appear to be worth it after 2018. It is a guarantee to pay above market value!

Does that mean that teams are being foolish to even offer opt-outs, as the commissioner recently suggested? No way! These are deals are simply transferring risk between player and team. Saying that opt-outs are foolish for teams is akin to saying financial firms should not sell put options. Believe me—if these were valueless, somebody would have noticed by now.

I recently put a dollar value on several of these opt-outs in January at MLB Trade Rumors, and added several more recently. Most of the recent opt-outs subtracted about 10 to 15 percent off the sticker value of the deals, relative to how large they would have been without opt-outs attached. In this article, I will break out how to put a value on these and delve into the research behind those valuations.

Since we are trying to figure out how much a player would have earned absent an opt-out in his contract, we want to start by working backwards from what he received with his opt-out. While he may be overrated or underrated in terms of his effect on the win column, that is a separate issue. You also want to use the approximate marginal dollar value per WAR that teams are using on the free agent market—WAR in general may also be overpriced or underpriced, but that would again be a separate issue. We want to know how much a player in the given market would make. The most recent analysis I did was here, so I will use these forecasts of future dollar per WAR costs.

Everyone knows that projections are going to be wrong, but that is not what we are talking about here. Projections are wrong because even if you know the exact talent level of a player, a season of data is just not that large of a sample. If you knew the exact batting average talent level of a player, the standard deviation of his actual batting average is 20 points, so a .260 talented hitter in 500 plate appearances will hit under .240 or over .280 a third of the time.

The key to properly valuing opt-outs is forecasting how much projections change.

We know that we will never know for sure how good a player is—this is a known unknown. Furthermore, we know that our estimate of how good a player will be in the future will change over time.

When you are valuing opt-outs, knowing how your expectations will change over time is exactly what you need to model. A player will opt out in the future if his market value at that time is high enough that it exceeds the amount he is owed after his opt-out. Suppose we think right now going into 2016 that Justin Upton will be a 2.9 WAR player who will be worth $93 million from 2018-21, and is owed only $88.5 million for that time period if he does not opt out. The odds are next to nothing that going into 2018 we still value his 2018-21 production at exactly $93 million. The only question is how much higher or lower we expect it to be. Is the standard deviation of his expected value $20 million? Is it $60 million?

To estimate this, we need a way to see how much future year projections are likely to change. We probably will not learn anything crazy about the aging process of baseball players over the next couple years. And while I do factor in some variability in my forecast dollar per WAR, the primary question is how much different from 2.9 WAR we should expect Upton to be worth in 2018 once we observe his 2016-17 performance.

I used a quick and dirty method of estimating this—I used a regression analysis to see how the three most recent seasons of WAR (weighted 5/4/3) would forecast WAR two seasons out (so how 2013-15 WAR would predict 2018 WAR) and then zero seasons out (so how 2015-17 WAR would predict 2018 WAR). I compared how much those basic forecasts changed. How did 2018 projections look as of November 2015 versus November 2017?

As it turned out, the average difference in projections was about 1.0 WAR if you limited them only to the kinds of players who actually get opt-outs—players older than 26 years old who had a weighted average of at least 2 WAR over the past three seasons and positive WAR the season before. But 1.0 WAR is a very high estimate—after all, we would hope that teams are using more sophisticated methods than just weighting the last three years of WAR. How much better is beyond the scope of a project like this, so I guessed how much better teams could do than my quick and dirty estimate. Roughly 30 percent better sounded right to me, so I assumed that a WAR forecast two years in the future would change by 0.7 as it got closer. This was naturally a little lower for opt-outs that came one year from now, like Yoenis Cespedes‘, and higher for opt-outs that came three years from now, like Price’s.

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The rest of the assumptions I used were relatively typical approximations like those you see in regular sabermetric websites. I assumed that players’ forecasted WAR declines by about 0.25 WAR in their late 20s and 0.5 WAR in their 30s. I assumed that the dollar per WAR estimate I linked to above was also likely to change a little a couple years into the future—I figured by about $200,000 per WAR in either direction. And then I approximated the likelihood of players opting out based on their baseline WAR forecast and the standard deviation of WAR. This is frequently close to even odds.

Making adjustments was necessary for each of these cases to even out. Discovering the opt-out value requires moving the guess of initial WAR value up or down until the expected value of the upside is equal to the downside. The upside is the expected value provided above the contract cost pre-opt-out. The downside is the expected cost of the contract above the value, conditional on the player opting out, multiplied by the probability that he opts out.

Mathematically, the breakeven point is when:

Expected Value(pre-opt-out) – Salary(pre-opt-out)

=

Probability(opt-out) * (Salary(post-opt-out) – Expected Value(post-opt-out | not opting out))

Most of the assumptions tended to have relatively limited effect on the approximate value of the opt-out. The key parameter is the standard deviation of forecasted WAR, which affects that last term reflecting the expected value post-opt-out conditional on not opting out. Further research into how projections change over time as the year in question gets closer could shine more light on that term, but I believe 0.7 WAR for these types of players is probably a pretty good estimate. Individual players’ opt-out values also varied based on initial WAR forecast, time until opt-out.

This shows the importance of the variance around a player’s projection—players’ talent levels are not their mean projections. As contracts get more sophisticated, the concept of players’ talent levels consisting of a variance (in addition to just their mean projection) is essential to pricing. Furthermore, using more proper pricing methods than simple dollars per WAR analysis becomes very important as well. These opt-outs are the latest stage in baseball player contracts, but knowing how to measure variance and price options is likely to be essential for many of these deals.


Matt writes for FanGraphs and The Hardball Times, and models arbitration salaries for MLB Trade Rumors. Follow him on Twitter @Matt_Swa.
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tz
Guest
tz

Very well stated. Because of the differences between the baseball “market” and financial markets, it would be difficult to ever model a market-consistent value of player contract options to the degree of fit that one could model financial options. But your choices for parameters, especially the “Marcel” type proxy for the market’s projection of player value, serve well in giving a consistent analysis of contracts with and without opt-outs. The only fly in the ointment is projecting the variance in the change in projected value, but again I think your approach makes proper use of publicly available information. As a… Read more »

Dave T
Guest
Dave T

Very good post, and this point – “This shows the importance of the variance around a player’s projection” – really hits the nail on the head for me. As Matt correctly notes, an opt-out is just a player option, specifically a put option. One of the basic conclusions of options pricing models is that options on more volatile (i.e., higher variance) assets are more valuable.