Optimal Starting Height for Pole-Vaulting

We have constructed a model for computing the expected height a pole-vaulter will clear when he starts his vaulting at a predetermined height, provided that the bar is raised in constant steps. The model uses conditional joint probabilities that the pole-vaulter will clear certain heights in one of the three possible trial vaults at each height, provided that he has already vaulted a certain number of times. These probabilities decrease as the number of vaults increases. The optimal starting height for pole-vaulting is determined by searching for the starting height that will maximize the expected height cleared. An approach is outlined for deriving the required probabilities from easily obtainable data. The model and its assumptions are validated with a numerical example, and a comparison is shown between pre- and post-optimal results.