# Probability for Nth Place in Race from Bradley-Terry Model Inputs and Outputs

I have created a motorcycle race prediction model that is given pairs of racers and outputs the probability of each rider beating the other in each pairwise comparison. That info is then processed using the Bradley-Terry model to determine each rider's probability of winning.

With that information (pairwise probabilities and winning probabilities), how may I calculate the probability of each rider finishing in nth place?

So far, I've tinkered with the Harville method, which has been pointed out to have some unrealistic assumptions. I'm currently working with the method in https://github.com/microprediction/winning, but I'm not totally sure I understand the output can be used to determine the probability of each racer finishing in a specific position.

I'd like to know if there is anything obvious I can do with the info & models I'm currently using and/or if there are other models I should look into.

Much help from: Peter Cotton (https://math.stackexchange.com/users/92982/peter-cotton), Given every horse's probability of winning a race, what is the probability that a specific horse will finish 2nd and 3rd?, URL (version: 2021-09-10): https://math.stackexchange.com/q/3260483

• Please share a minimum reproducible dataset and code to help others tinker with the problem Sep 5, 2022 at 19:00