How Streaky is Tiger Woods?

The first PGA Tour event of the year, each year, is the tournament whose ancestral name is the Tournament of Champions. (It currently sports a "Hyundai" before that phrase, having emerged from the depths of being called the "Mercedes Championships.") It's played in Hawaii, and its field consists of all and only those players who won a tournament the previous year (and who want to play in it), as you might expect from the name. This year, Dustin Johnson won the Hyundai Tournament of Champions, but he did it in slightly odd fashion. Or, well, the whole tournament happened in slightly odd fashion. For some reason, apparently, the Tour decided to shift the TOC to a Monday finish. But then Friday, Saturday, and Sunday all featured ridiculously high winds that made it impossible to play any golf. (Actually they played a few holes and then cancelled play, erasing the scores that had been put up in the little half-rounds.) Eventually they were able to play on Monday, when they got in 36 holes, and on Tuesday, when they got in another 18, making a 54-hole tournament that they could call official. And Dustin Johnson won it. My dad and I had been speculating that, if Dustin were to win this week's Hawaiian Open with a nice low score, he might set an all-time record for furthest under par in a span of seven days, since he would get in an unusually high seven rounds in that span.

Except... a few minutes ago, Dustin withdrew from the Hawaiian Open with flu-like symptoms. He had been playing rather miserably anyway, and was going to miss the cut. Ah well.

It got us thinking about how likely it is for a player to win in back-to-back weeks. You could imagine that players would feel awfully drained after a win (though not as much as if they didn't get any time off, as Dustin did here), but you could also imagine that someone who was playing well in Week X would be likely still to be playing well in Week X+1. The problem in trying to analyze this is that most players scarcely win any tournaments at all. Dustin Johnson, for instance, has 7 wins in 120 events (not counting this week, which'll push the denominator to 121). That's a winning percentage of 5.83%, or .058 in baseball format. That's low. If you assume that the two weeks are purely independent of one another, and that the 7-for-120 winning percentage represents Dustin's "true talent," he would have only an 0.34% chance of winning both of any two arbitrarily-chosen tournaments, including if those tournaments are in back-to-back weeks. In other words, if a player like Dustin Johnson played his whole career and never won in back-to-back weeks, we shouldn't be too surprised, and the difference between his having 0 back-to-back wins and having 1 or 2 of them wouldn't really be that significant.

There is one player, however, for whom that concern does not apply: Tiger Woods. He has 74 career wins in just 293 events, for a winning percentage of 25.3%, or .253, which is higher than that of the 40-120 1962 New York Mets. Each of the Mets' contests was against one other opponent, so without knowing anything else we'd expect them to have won 50% of their games. Each of Tiger's contests tends to be against over 100 other players, so knowing nothing else we'd expect him to win less than 1% of his tournaments. And yet, Tiger's got a better winning ratio than those Mets. Man they were bad, and man he's good. And, in particular, he's good enough to permit meaningful analysis of his winning tendencies when playing back-to-back weeks.

If you assume independence, Tiger should be winning both tournaments about 6.4% of the time that he plays in consecutive weeks. Also, he should fail to win a tournament about 55.9% of the time that he plays in consecutive weeks, leaving an expected 37.8% of the time that he'd win one but not the other. Over the course of his long career, he has played two weeks in a row 91 times. (Note that some of those windows overlap, i.e. if Tiger played three consecutive weeks, I count that as two separate windows, both of which include the middle week.) Our expected percentages under an assumption of independence would work out to about 5.8 two-win windows, 34.3 one-win windows, and 50.8 no-win windows. Instead, Tiger has 9 two-win windows, 28 one-win windows, and 54 no-win windows, which translate to percentages of 9.9%, 30.8%, and 59.3%, respectively.