After Serena Williams’ triumph in the Australian Open women’s singles final last weekend, many commentators pointed out her seemingly odd streak: She’s won the year’s first Grand Slam tournament in each of the last four odd-numbered years. ESPN, inevitably, asked, “What are the odds?”
Not so remote. She’s played in 10 Australian Opens, six of them in odd-numbered years. Assuming her probability of winning was the same in each of them, there’s a six in 10 chance that the first would have happened in an odd-numbered year; if it did, a five in nine chance that the next one would, and so on. Multiply the four probabilities, and you’d realize we’d expect her to have won in four odd-numbered years 7.1% of the time. Four even-numbered years would have been just as interesting, and that had a 0.5% chance of happening, so this streak is about a one-in-13 chance. That’s a far cry from, say, a perfect game in baseball.
Of course, you might argue that it’s significant that the two Australian Opens that Williams missed during her 12-year Slams career have both come in even-numbered years. So if we calculate the probability of her winning four of the tournaments in odd-numbered years out of six even and six odd, it’s just 3%. But she’d have the same chance to win four in even years, so the total probability of such a seemingly abnormal event is a rather normal 6.1%.
But it’s really only in the last seven years that Williams was a consistent threat to win the Australian Open. From 1998 to 2001, she entered 14 Grand Slam singles draws and won just once. In 2002 she skipped the tournament due to injury, then won the next four Slams. So in the last seven years, she’s played in six Australian Opens, four of them in odd-numbered years. There’s a 6.7% chance all four would have fallen in odd-numbered years. No matter how you slice it, Williams’s streak isn’t that odd, just a somewhat quirky coincidence.