Sometimes a Rare Event is Just Rare

At PTG, I just saw a talk by Katarina Pijetlovic of Tallinn University of Technology, on alleged irregularities in ITF draws for Wimbledon and the US and Australian Opens.  Apparently, in the past 12 of these events Roger Federer and Novak Djoikovic were drawn into the same half of the tournament and Andy Roddick and Rafael Nadal were drawn into the same half of the draw.

In any one event the odds of such an outcome are 1 in 2, and across 12 such events, 1 in 4,096 (0.5 to the 12).  The suspicion, Pijetlovic explains, is that there was some nefarious goings on in the draw process.  She pointed to a recent analysis by ESPN of tennis draws which showed that the US Open draws were outliers with respect to the low ranking of players faced by the top seeded player in the first round.

What is going on here? Cheating? Subterfuge?

Pijetlovic expressed doubt because the drawn are done in public with a person (usually a former tennis player) pulling names out of a container (often a trophy).  But still, she said . . .

I for one am not convinced by either of these analyses that there is anything here as they lack a coherent theory  - What benefit would conferred to the tournament?  Is there collusion across tournaments to pair Feder/Djoikovic and Roddick/Nadal?  Why connect the US Open draws with the top 4 seeds across three tournaments?  Why neglect the French Open?

I asked Pijetlovic about it in the Q&A and she said that the statistics were not impossible but were improbable. Fair enough. But there are an awful lot of things that happen in sport. Some much so that rare events are sometimes observed and the joint probability of rare but otherwise unconnected events will be smaller still.

To observe a rare event (or several) and to conclude that there is more to it requires more than just rareness. Otherwise it is just data mining. Sometimes, the luck of the draw is just the luck of the draw.