Given an analysis of every pair of competitors in a race, how may I determine the probability of any given competitor winning the race?
For example, what is the probability of competitor 2 winning the following race? P(Cx Win) means the probability of Competitor x winning.
Cx Cy P(Cx Win) P(Cy Win) ---------------------------------- 1 2 0.3 0.7 1 3 0.4 0.6 1 4 0.9 0.1 2 3 0.8 0.2 2 4 0.7 0.3 3 4 0.9 0.1
I have tried to calculate a 'rating' for each competitor by adding their individual win probabilities. For example the rating for C1 would be 1.6. The rating for C2 would be 2.2 etc. I've tried different ways to use this rating to find the probability of the competitor winning, however my gut feel tells me something is wrong.
Is there a mathematical solution to this problem?