Abstract
Simple present value calculations of how a team owner values multi-year player contracts ignore the value of options to defer signing players or release players in subsequent years of the contract. Salary demands for players who use present value calculations of their expected future productivity ignore their valuable options to move to another team over the duration of the contract. Bargaining is then based on the expected future productivity of the player and the net value of the options to the owner and player. In this chapter, we provide a real option model of salary negotiations over two-year contracts. We also identify different conditions that influence the values of the options attached to player contracts.
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Notes
- 1.
A good reference is Copeland and Antikarov (2003).
- 2.
A recent example is the 10-year, $300 million contract signed by Manny Machado with the San Diego Padres in 2019, the third largest total value contract in MLB history. This contract effectively takes the now 26-year-old Machado through the bulk of his remaining playing years, capturing the financial value of most of his remaining options, but not all. The contract includes an option for Machado to leave the team after five seasons.
- 3.
We assume a single team owner although that is often not the case in professional sports leagues. Nevertheless, most leagues require that a single owner be identified if there is a group of owners.
- 4.
Or more precisely, a rate of return that is uncorrelated with the baseball player market, and when there is risk-free borrowing and lending, is equal to the risk-free rate. If there is no risk-free rate, then the relationship of Beta to the return on the market remains intact although the portfolio cannot be shown to be efficient (Fama and French 1994).
- 5.
We imagine a world in which players are like highly variable individual stocks. The risk-adjusted rate might differ from 5% in that case and \( \beta_{ij} \) would differ as well if the portfolio is for all players rather than the capital market. The beta coefficient for the entire league of players (the “market risk”) is equal to one. If we had the MRP for each player and their salary, we could calculate the market risk and then the beta for each “stock” player and the consequent “portfolio” contribution of a team.
- 6.
Rockerbie and Easton (2019) show how to estimate the talent supply elasticity.
- 7.
For simplicity, we are assuming that players are only forward-looking to their next contract in our model. That is, they do not consider the put option to leave the new team they sign with at the end of year one at any point in their new two-year contract.
- 8.
We are assuming he does not manipulate his productivity. Rather it is a random outcome of a process with at least two moments.
- 9.
Although the player has a valuable put option to leave the team to sign with a more lucrative team, we assume that the team owner does not face the decision of releasing the player at the end of one season and signing a more valuable player (in terms of expected MRP). This keeps the exposition simple although it would be an interesting strategy game for team owners to anticipate the future availability of valuable players.
- 10.
This would be consistent with the assumption that the team owner is an expected profit maximizer. In the upper branch of Fig. 3.1, the owner earns a windfall profit, however the owner experiences an unexpected loss in the lower branch. In the two middle branches, the owner just pays the player his expected MRP over the life of the contract.
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Rockerbie, D.W., Easton, S.T. (2020). Contract Options for Buyers and Sellers of Talent. In: Contract Options for Buyers and Sellers of Talent in Professional Sports. Palgrave Pivots in Sports Economics. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-49513-8_3
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