Great Expectations

Finally, the men’s bracket at the Western and Southern Open tennis tournament stayed still long enough for me to model it. Here are the results:

This table is sorted by the player’s official world ranking, which is how the top 16 players in the bracket were initially seeded. While the ATP rank is obviously correlated with skill to some extent, it’s not the best available way to assess relative skill. For the purposes of the model, the primary indicator of skill is the odds offered on Betfair, a clearinghouse for sports wagering, on Friday night before the tourney started. ATP rank was the secondary sort, where the Betfair odds were equal, and for the qualifiers and lucky losers.

There are some biases in the Betfair odds. One is that there were no odds quoted for qualifiers and those who became lucky losers, so those folks all go to the bottom of the list, even though some of them would, no doubt, have been quoted at shorter odds if it had been known that they’d be in the main draw. There’s also a distinct bias in favor of Americans. John Isner has the eleventh best ATP ranking, but had the fourth shortest betting odds, presumably reflecting the assumption that he’d do particularly well in familiar surroundings in front of a supportive crowd.

Note that the simulation is for the bracket before any games had been played. Now, of course, the winnings of about half the field are known with certainty because they’ve already been eliminated – they earn $17,700 if they were eliminated in the first round, or $32,780 if eliminated in the second. The point here is not to predict anyone’s actual outcome, but rather to show how the peculiar practices of the ATP with regard to filling their brackets cause some odd anomalies.

Here’s a doozy. The seven qualifiers – Smith, Youzhny, Dolgopolov, Eubanks, Marterer Krueger, and Sousa – collectively can expect to earn $228,451. But the seven players they beat in the qualifying finals collectively expect $250,320! At it turned out, the qualifiers would have done better, on average, if they’d lost that last qualifying match, and taken their chances to be lucky losers.

There’s more to be said about these results, but that will have to wait for tomorrow.