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Notwithstanding his recent knee surgery, Tiger Woods will be the overwhelming favourite to win next week's U.S. Open at the Torrey Pines Golf Course in La Jolla, Calif.
Meanwhile, Lorena Ochoa is the favourite to win every tournament she plays, and she's leading this week's LPGA Championship after two rounds. It's logical to make them huge favourites week after week.
Or is it logical? Woods has won 64, or 29 per cent, of the 221 PGA Tour events he's played as a professional. Ochoa has won 23, or 17 per cent, of 133 tournaments since she joined the LPGA Tour. Woods has won three of five tournaments this year and Ochoa six of nine. But both lose far more often over the long run than they win.
"There's a mathematical point here that's relevant," John Allen Paulos, a mathematics professor at Temple University in Philadelphia, said recently in a telephone interview. "It's the distinction between most likely and likely. If you tell somebody to flip a coin 100 times, the most likely number of heads is 50. It's not likely that you'll get 50, it's just the most likely."
Paulos has written a series of popular books exposing our widespread ignorance of his subject. His books include A Mathematician Reads the Newspaper, in which he dissects the errors journalists frequently make. His most recent book is Irreligion: A Mathematician Explains Why the Arguments for God Just Don't Add Up.
Paulos has noticed an uptick in interest in the application of mathematics to the analysis of sports. He's aware of what Woods has been doing and was interested in the degree to which odds makers and laymen in their conversation make him such a favourite. He's the 7-to-4 favourite next week at Sportsbook.com.
"Quant types used to be derided in sports," Paulos said. "Now they're accorded a good deal of respect."
He was thinking of books such as Michael Lewis's Moneyball, for one, and other examinations of baseball in particular.
"The best hitter in baseball at any given time is the most likely to get a hit," Paulos explained by way of making an analogy to Woods. "But even the best hitter will get a hit only 35 per cent of the time. Likewise with Tiger Woods, he's the most likely to win, but even for him it's not likely. It's easy to conflate these two notions because likely is in both of them, but most likely doesn't imply likely."
Think about it for a moment. Woods has won six tournaments at Torrey Pines, and now will try to win a major there. It's natural that he should be a huge favourite there, or at any tournament given how many more tournaments he's won than any other contemporary player.
Phil Mickelson, with whom Woods will play the first two rounds, has won 33, or 9 per cent, of 358 PGA Tour events he's played as a professional. He's won three tournaments at Torrey Pines, which he pretty well considers his home course because he grew up nearby. His record is superb, but it's nowhere near what Woods has done. No wonder Woods will be so heavily favoured.
Even so, as Paulos pointed out, the math doesn't justify the odds. Other factors besides the data play into the assessment of Woods's chances.
"People don't just rely on the numbers," he said. "There's psychology, and the oddsmakers worry about herd-like effects. If everybody puts their money down on him, will they be able to cover it?"
Woods has generated enormous, and unrealistic, expectations. He's won 13, or 29 per cent, of the 45 majors he's played as a professional. That's so impressive as to be beyond comment. Still, he's also not won 32, or 71 per cent, of the majors he's played.
That latter figure should be sobering for everybody, including readers, writers, and the television analysts who will inundate viewers with material about Woods. They might prepare by reading Paulos' book Innumeracy, the mathematical equivalent of illiteracy. Along these lines, Paulos referred to the "cognitive illusions all of us subscribe to."
Woods is the most likely of all players to win the U.S. Open. The same thing goes this weekend for Ochoa. But are they likely to win? The math says no. Maybe Lorie Kane of Charlottetown will win the LPGA Championship. She's eight-under par and in third place, two shots behind Ochoa.
"You never know what's going to happen," Ochoa herself said. "There are so many good players on the course."
There's a voice of reason. Who knows? Maybe Ochoa is familiar with Paulos' work. Or, likely, or most likely, she appreciates how difficult it is to win.
