## Roland Garros 2012

French Open draw is out. What’s new? Not much. You get the same old, same old Nadal/Murray vs. Djokovic/Federer set up. So what’s the odds of Djokovic and Federer always in the same half? That’s worth looking into.

For those who are not familiar with the draw process, in Grand Slam tennis, there are 128 players in the main draw. After the seeding is decided, the top 2 players will be placed in each half of the draw, ensuring that best players only meet in the final. Since Federer and Djokovic was never seeded top two in Grand Slam tournaments, theoretically speaking, Djokovic has 50% of the chance to be drawn in Federer’s half of the draw (Federer vice versa), and this seems to be the case in 2006 and most of 2007, before Djokovic ascended in ranking to #4. After Djokovic became a consistent presence in the top 4, therefore a credible contender to the Grand Slam titles, curiously enough he appeared in Federer’s half most of the times. As you can see in the graph, during the 4-year-span from 2008 to 2011, only two times out of a total of 16 they were in different half. And the proportion gets even higher for the so-called fast courts (12 out of 12). And it seems only on clay court (French Open), the two has a more even chance of facing each other in the final.

More astonishingly, since 2008 Wimbledon, they were drawn in the same half for 7 times consecutively. So what’s the probability of that? It’s difficult to calculate that since all these events are not independent. But I did a very crude simulation based on the binomial distribution. It seems the chance of being in the same side of the draw 18 out of 26 times is quite rare, as the case of 7 times in a row (< 5%) being in the same half. So this, combined with a study conducted by ESPN, conspiracy-minded tennis buff would like to know if indeed the draw is fixed to make the game more exciting, or this is really nothing more than the occurrence of small probability events.

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Ron TomaskiMay 29, 2012 at 4:02 pm

[…] thought I’d update my old post about the men’s (in Wimbledon’s case, gentlemen’s) draw since now we have one […]

Djokovic, Federer drawn to meet in Wimbledon semis | SAS® and RJune 22, 2012 at 10:59 pm