This is a review of the NBA guaranteed contracts research conducted by Arup Sen and J. Bradford Rice, applying a Bayesian model and simple OLS regression.
In the world of sports, it always seems that players play better in the last year of their contract than they do during the earlier years. Teams then seem to offer these players huge contracts in order to retain them, only to see their performance fall as they start the new contract, a situation that is especially frustrating for the fans of the game. Unlike many other sports, basketball contracts are of a simple, fixed-wage design and rarely include incentive clauses. Is this pattern of increased effort in the last year of a player’s contract a true phenomenon or simply a figment of the fans’ imaginations?
Fixed-effects estimates indicate that players’ efficiency score in the final year of a multi-year deal is significantly higher than in the prior year.
The interaction between the player and team is modeled as a 3-period principal-agent game. The principal is risk neutral and the agent is risk averse. During the 3-period game, the player chooses what effort to expel in each period even though the salary for that period was previously negotiated. The outcome is achieved at the end of every period and depends on the player’s inherent ability, the level of effort exerted and a random component. The player, as well as the team, has some belief regarding the player’s ability and this is updated in a Bayesian fashion by the team at the conclusion of every period. As the player is earning a guaranteed wage for the period, the only incentive to put in the effort is pride and the ability to affect future wages.
Contracts that cover the first 2 periods of a player’s life are analyzed. Results indicate that players signing such a contract will increase their effort level over the life span of the contract. While one period contracts are more beneficial for the team, the agent’s risk aversion steps into play. The players value security and will make some wage concessions per period in order to sign a longer guaranteed contract. This concession allows the team to compensate for any loss of effort. Finally, more experienced players demonstrate a smaller variety of effort levels over the course of their contract than less experienced players do. This is a result of the fact that the ability of more experienced players is better known by the team, which can result in negative consequences if the player is putting out less than optimal effort.
Testing the hypothesis that player effort and performance will improve as the expiry date of the current contract nears is tested using a simple OLS regression of performance on the years remaining in the contract. The dataset-includes information on 657 NBA players including their contract terms, annual performance across several dimensions, information on team performance and physical characteristics. Effort decreases the most right after a new contract has been signed.
This information enables analysts and coaches to determine just what the decrease in effort after the beginning of a contract actually is in order to determine terms for future contracts. Coaches, being aware of this phenomenon, can better strategically plan the team for the year, knowing which players are nearing the end of their contract and therefore will put in maximum effort versus those just starting a new contract. Players nearing the end of the contract will be more effective players for the team, assuming a similar level of ability.
Are teams unaware of this phenomenon? No, of course not, teams anticipate the drop of effort level for a player and contract terms are decided with this in mind.
Analytics Used: Bayesian Model, Simple OLS Regression
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