Abstract
In a sports league, team owners can expect to increase player performance, and the team's winning percentage or profits, by providing a win bonus on top of the players’ fixed salary level. In some clubs, the guaranteed player salary is relatively low and the premium, in case of a winning game, relatively high, whereas in other clubs, hardly any win bonus is paid. In this theoretical paper, we investigate what the impact of a win bonus is on the winning percentage, the competitive balance, the owner profits, and the overall quality in a professional sports league.
The model we start from is an extension of the well-known Quirk and Fort (1992) two-team model and we introduce a premium system consisting of a win bonus that is paid on top of a fixed salary. Assuming that players are motivated to increase effort if their salary depends on the winning percentage, we derive the Nash-Cournot equilibrium under both the profit and a win maximization hypothesis.
The impact of a premium system turns out to be rather complex, given the fact that clubs react to the strategies of other clubs in the league. The team that introduces a premium system can expect to increase its profits or its winning percentage by paying a bonus combined with a reduced fixed salary. A crucial factor, though, is the players’ response to the win bonus. If the team's effort is not enhanced enough by the bonus, the team's profits and wining percentage can go down. Also the effect that an increased winning percentage has on the current season revenue is an important factor.
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