The Logic Behind Opt-Outs

Opt-outs are complicated to understand. On a basic level, an opt-out allows a player the choice, during a specified offseason, to nullify his current contract and become a free agent again. How an opt-out affects the value of a contract has been written about plenty — despite the differences in methods or dollar-per-WAR values, it is generally accepted that the inclusion of an opt-out lowers the total salary of the contract.

Given the issues with trying to calculate an exact value of an opt-out — the two biggest challenges being having sparse contract data and the necessity of a reliable future projection system — I tried to explore opt-outs from a theoretical perspective: why would a player ask for an opt-out, and why would a team write one into a contract. Note: the equations were originally in latex, but they lost formatting through submission. They have been replaced with plain text.

From the Player’s Perspective:

A player would sign a contract with an opt-out if he believed the expected present value of the contract was greater than a contract offer without an opt-out.

EPV_opt < EPV_no-opt

The expected present value of the contract without an opt-out (EPV_no-opt) is just the expected present value of the contract itself. The expected present value of the contract with an opt-out (EPV_opt) is more complex.

The expected present value of a contract with an opt-out can be broken down into two components: the expected present value of the pre-opt-out portion of the contract ($latex EPV_{pre\:opt}$) and the expected present value of the post-opt-out portion. Regardless of whether the player opts out or not, the pre-opt-out value of the contract is the same. The post-opt-out value differs, depending on three values: the value of the new contract should the player opt-out ($latex EPV_{opt}$), the value of staying in the current contract and not opting out ($latex EPV_{no\:opt}$), and the probability the player opts out (P opt-out).

EPV_opt = EPV_pre-opt + P_opt * EPV_opt + (1 – P_opt) * EPV_don’t-opt

Given the infinite possibilities after contracts end, EPV_don’t-opt and EPV_opt can have their own massive calculations. Those can be done another time, but note that more goes into each expected present value than it seems at first glance.

A player would sign a contract with an opt-out if he believed the total expected present value of the contract was greater than a contract offer without an opt-out. By including an opt-out, the player is trying to maximize his earning potential — allowing himself to become a free agent again. To do this, he lowers his earning floor — the salary he’d receive if he doesn’t opt-out.

From the Team’s Perspective:

A team would offer an opt-out in their contract if they were looking to spend less money or willing to mitigate risk at the expense of upside.

If the player could earn more in free agency through opting out and has an opt-out, he benefits. He would earn more money than if he didn’t have an opt-out. Similarly, the team would slightly benefit. Though they lose the player to free agency sooner than expected, they paid less for the years they had him on their roster. Though not ideal, this scenario is okay for the team. They received high-level performance for a cheaper salary than they otherwise would have had to pay. Without an opt-out, the team greatly benefits by having a star player under contract at below-market value.

Similarly, if the player would earn less in free agency, he won’t opt out. The player benefits through having guaranteed money, though he has less than if he didn’t have an opt-out in his contract. The team feels similarly — though they have a large amount of payroll stuck in a poor performer, they would have had a larger amount of payroll designated to this player if they didn’t include an opt-out. Without an opt-out, the player benefits through having above-market value pay.

Teams can mitigate financial risk through sacrificing upside by providing a player an opt-out in their contract. The expected return on investment through including an opt-out (EROI opt-out) would have to be greater than the expected return on investment without including an opt-out (EROI no opt).

EROI_opt > EROI_no-opt

If the expected benefit of the contract with an opt-out exceeds that of the contract without the opt-out, the team should include one. As I mentioned above, this scenario caps reward while mitigating financial risk.

The EROI_opt depends on the expected return of investment prior to the opt-out (EROI_pre-opt) and after an unexercised opt-out (EROI_don’t-opt). If the player opts out, the time following his opt-out doesn’t provide any return to the team.

EROI_opt = EROI_pre-opt + (1 – P_opt) * EROI_don’t-opt

Each expected return of investment is a function. For example, EROI_pre-opt can be written as a continuous function that provides an ROI for each level of performance the player is projected to provide. The ROI isn’t binary: a player who barely decides to not opt out provides a much higher ROI than a player who easily decides to not opt out.

Conclusion

Opt-outs are a fascinating wrinkle in contract negotiations. Players can try to maximize their earning ceiling while risking some of their earning floor, while teams can try to minimize their financial risk through sacrificing some of the potential high-end return on investment. Opt-outs are a relatively recent phenomenon, as data science is required to understand the valuations. As analytics grows in baseball, I expect to see more contracts with opt-outs or other forms of value extraction mechanisms, as both teams and players try to do the best they can in negotiations.

This and other analyses can be found on my blog, First Pitch Swinging.