| Abstract: |
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. |