The strategic jump : the order effect on winning "The Final Three" in long jump competitions

The tournament rules for long jump competitions have changed in recent years. Today, only the three athletes with the best jumps from the five initial attempts are qualified to make an additional sixth jump - a format called The Final Three. In the first implemented version of The Final Three, the top athletes sequentially make one final jump, starting with the athlete ranked third place from the initial attempts. The athlete with the longest jump in this sixth attempt wins the competition, irrespective of achieved results in previous attempts. In this study, we analyze the effect of the athletes' jump order on the probability of winning the competition within this first implemented version of The Final Three. We derive the final's symmetric subgame perfect equilibrium and compute the corresponding equilibrium winning probabilities, given the values assigned to the distributional parameters. The modelling of the game is preceded by a development of a stochastic model for the outcome in long jumping. An athlete affects the distribution of the outcome by choosing where to start her approach run. Our results indicate a last mover advantage, albeit small. The athlete jumping last, wins the final with a probability 0.35, followed by the athlete jumping second with a probability 0.33 to win the final.