Here’s a bit of very simplistic probability calculation on the outcome of the French Open final, related to my article on the value of a set in tennis.
According to the ATP website, the French Open finalists, Novak Djokovic and Stanislas Wawrinka have contested 56 sets of top level tennis (going back to 2006), with Djokovic winning 40 of them. Using this information, we can derive a very crude estimate of the probability that Djokovic will win a set against Wawrinka: 40/56 is approximately 70%. This might be way off, obviously: some of that data is quite old and Wawrinka has done a little better recently, but who knows…
Using the binomial distribution, based on this probability and an assumption that the results of sets are independent, we can calculate the following probabilities:
Djokovic to win: 84%
Djokovic to win if he wins the first set: 92%
Djokovic to win if he loses the first set: 65%
Djokovic to win if he wins the first two sets: 97%
Djokovic to win if he loses the first two sets: 34%
Djokovic to win if the first two sets are shared: 78%
Djokovic to win from a lead of 2-1: 91%
Djokovic to win from a deficit of 2-1: 49%
Djokovic to win if the match reaches the fifth set: 70%
The thing that stands out for me here is the suggestion that he would still have over a 1/3 chance of winning, even from 2 sets down. This is one way in which the very simple model breaks down in a big way, I suppose. In such a situation, you would probably conclude that Djokovic’s true on-the-day probability of winning a set was less than his long-term results would suggest. There would also be some psychological barriers to overcome, which the model obviously does not account for.