US Open Daily Graph - Hewitt vs Del Potro

Earlier this week, I posted my first attempt at a tennis win probability graph, using Victoria Duval's come from behind upset over Samantha Stosur as an example. I am going to try to make this a daily feature for the remainder of the US Open. Each day, I will pick a particularly noteworthy match and publish its win probability graph. As I don't follow tennis too closely, I am open to suggestions as to which match to feature.

For today's post, I am using Leyton Hewitt's upset victory over Juan Martin Del Potro. As with my Duval graph, I am calibrating the inputs to the model such that the initial probability matches the betting consensus (Hewitt with a 12.8% win probability). See the table at the bottom of the graph for the assumed serve and return point probabilities.

Victoria Duval Pulls off the Upset with a Key Six Point Streak

The first big upset of the 2013 US Open occurred Tuesday night, with 296th ranked Victoria Duval defeating 11th ranked (and 2011 US Open champion) Samantha Stosur. Match highlights, plus Victoria's giddy post-game interview, here.

I had been playing around with an in-match win probability model for tennis (similar to my NBA model), and this seemed like a good test case. Tennis probability is actually easier to model than fixed timed sports like basketball and football. For tennis, all you really need to specify is the probability of winning a point (both when serving and returning). The rest is just a calculation of the branching probabilities (somewhat tedious, but straightforward).

As with the NBA, I am not the first to attempt this. Jeff Sackmann (of HeavyTopspin.com) compiled win probability graphs for a large sample of 2011 matches. For a more math-centric view of things (with infinite series!), take a look at Ian Stewart's collection of mathematical recreation essays, Game, Set and Math (my original introduction to the application of math to sports). Or check here for a closed formula solution for winning a single game.