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Using Stats to Try and Take
Roger Federer's Measure

September 12, 2005 5:54 p.m.

Roger Federer isn't yet the best-ever men's tennis player -- he has to win eight more Grand Slam tournaments just to match Pete Sampras's record 14. But he already holds a more-remarkable record: He's won 23 straight tournament-final matches, last losing to Jiri Novak in July 2003.

That's far more impressive than his current winning streak of 24 matches and his hard-court streak of 35, because in finals, Mr. Federer often plays the world's best players. During his streak, he's beaten Andy Roddick five times, Lleyton Hewitt three times, Marat Safin twice and Andre Agassi twice -- including at the U.S. Open on Sunday. Bjorn Borg and John McEnroe shared the previous Open-era record for wins in finals, with a mere 12. (The record on the women's side is 25, by Margaret Court in 1972-1974, when competitive balance wasn't what it is today.)

How improbable is this feat? To get an idea, I checked in with Stephen Clarke, a professor at Australia's Swinburne University of Technology who has studied tennis statistics, and who ran some numbers of its own.

The roughest guess is that Mr. Federer had a 50% chance of winning each final, since presumably the players who advance to the finals are close in ability. Multiply 50% 23 times, and you get one in 8.4 million. That's like flipping a coin 23 times and landing heads each time.

But, of course, that's overstating the case, because Mr. Federer is a better than one in two shot against anyone in the world. He's gone 71-3 this year and 158-12 during his streak, winning 92.94% of his matches. Multiply 92.94% 23 times, and you get just one in five -- not that impressive a feat.

But this is vastly understating the magnitude of his achievement, because, again, his odds of winning finals should be lower than in earlier rounds. So here's a rough effort to compute his odds: We compiled the winning percentages in finals of four of his closest competitors during the streak -- Messrs. Roddick, Hewitt, Agassi and Safin, and Rafael Nadal -- omitting all those losses they racked up to Mr. Federer. Their combined record in finals not featuring Mr. Federer was 29-8, or 78.4%. Multiply that by itself 23 times, and you get one in 270. That's a rough measure of how unlikely it would be for any of the top players other than Mr. Federer to win 23 finals in a row -- even if their wildest dreams had been answered and Mr. Federer hadn't been playing the last two years.
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