Update As of this writing, the 2012 Masters is halfway through, so it’s a good time to re-examine the predictions made last April for this year’s tournament.
Scores have been on the decline (a good thing), meaning that for a year greater than any previous year, the probability of a score in the future year being lower than the score from any previous year is greater than 50% (that, incidentally, is the proper way to speak of decreasing trends in time series).
A crude extrapolation on the scores (first picture) said that there was a 95% chance of this year’s final score being between -5 and -17. Before the third round begins, Dufner and Couples are in the lead with -5. Given that the scores from previous rounds are correlated (in the plain English sense) with future scores, we can expect a somewhat higher than average (worse) score Masters this year. This is a long way of saying that my cheap model is in peril (it doesn’t, for example, take weather into effect).
The ages of Masters’ winners hasn’t been changing much (second picture), but this analysis is complicated because a small set of men have won multiple times. Fred Couples is 52 and has won once before, in 1992, when he was 42. If he can keep it up, he’ll be the oldest winner ever. Jack Nicklaus holds the record now, at 46. Chances are that Couples won’t, though. He scored middling for the first round but very well for the second. That implies variability, which lessens the chance he’ll take another green jacket. Jason Dufner, incidentally, is 35.
On the other hand. Jack Nicklaus won the most tournaments: six of them. The interesting thing about this is that it was 11 years from his penultimate to his last win. Couples is in this margin. Incidentally, the last time celebrity (and golfer) Tiger Woods won was in 2005, but he’s +3 and needs an Easter miracle to pull it off.
As before, the margin of victory has been averaging about 2 shots, with most from 0 to roughly 6 (third picture).
Last year’s post follows:
You could see the hunger on the face of Tiger Woods. He wanted to win so badly that he must have been late on his alimony. But his score wasn’t good enough to crack South African Charl Schwartzel, who was both a decade younger than Tiger and decidedly peppier.
Through the tournament, the commentators mentioned that golf is getting younger and tougher. What I don’t know about the sport is a lot. Further, I’ve only played about a dozen times (though I have mastered the perpendicular shot; which is when you aim one direction, but the ball flies off 90 degrees to the left).
My best acquaintance is seeing men standing on Second Avenue early Sunday mornings with bags in hand, forever glancing at their watches, waiting for their rides to some distant (and expensive) course. As I have long said, the beautiful game of petanque is just as frustrating but far cheaper.
Anyway, Schwartzel won with a score 14 under par, which is quite good. Indeed, scores have evinced a general downward trend since the tournament began in 1934.
The dashed red line is the result of a model, which in no way should be taken for reality. The red line is not the data! Even stronger, if we want to ask questions of a time series, we never, not ever, smooth that time series before asking questions. For example, if we want to know if the score in 2011 is lower than the score in, say, 1953, all we have to do is look (in 1953 Ben Hogan scored -14, or 14 under par, thus tying Schwartzel).
What do we mean when we say that scores are decreasing? Merely that the probability of finding scores in latter years which are lower than scores in earlier years is greater than 50%. We can go further and quantify the decrease in a formal model, which is what I did with the red line. That model says the scores decrease by a set amount each year; the amount is 0.08 strokes, which is absurd since strokes can only increase or decrease in whole numbers.
So the model is absurd. It is wrong. But it still might be crudely useful in quantifying the chance that next year’s score will be lower than this year’s (and so on out to 2020). The light blue area to the right shows the scores we expect (with 90% probability) in future years. But since the model is false, these predictions are crude at best. The reason for this long explanation is that this kind of time series modeling is ubiquitous. It doesn’t matter whether the data is, say, global temperatures or Masters’ golf scores. Almost always, these models are much worse than admitted.
Are winners getting younger? Yes and no.
The ages of winners start young, grow older, than begin young again, in a somewhat rough cycle. There is no obvious overall trend up or down. The reason for this is complicated. Every player that one more than once is given their own color and plotting symbol. Look at the open back circles (1963, 1965, 1966, 1972, 1975, and 1986). These are Jack Nicklaus. The black circles form a straight line, increasing. But of course, since Nicklaus aged during these years, the line must be straight.
The more times any one man wins, the more the line will look straight and increasing. In 1949 to 1954, Sam Snead and Ben Hogan were trading wins, producing another upward line. The exception is Jimmy Demaret in 1950, but he also won in 1940 and 1947, producing another line. In recent years, the line is from Tiger Woods (2001, 2002, and 2005). In other words, the straight lines are an artifact produced by the same small set of men winning and having birthdays.
But if we were to re-draw the line showing only the men who won once or, if they won more than once, just their first win, then the ages do not appear to be decreasing (not shown here). Jack Nicklaus was 23 when he first won; so was Severiano Ballesteros when he first won in 1980. Tiger Woods was 22 when he first won in 2001. Schwartzel is 26. And last year’s winner, Phil Mickelson, was 40. The median age of single or first-time winners is 32 and that appears roughly steady.
How about the margin of victory, defined as the number of shots difference between the winner and second place (ties which lead to playoffs are scored 0)?
The median margin is 2 shots, but there are more ties (hence playoffs) and 1 shot leads. There are a few instances of enormous leads. These belong to our usual suspects: Cary Middlecoff (1955), Arnold Palmer (1964), Jack Nicklaus (1965), and Tiger Woods (1997). But these men were of all ages. If we look at a plot of Masters victory margin by age (click to see), no clear signal can be found. There is no clear advantage of youth or experience. Neither is there anything if we look at Masters difference from par by age (click to see); again, youth and experience are in balance.
The conclusion is that scores will probably improve, but that winners do not appear to be growing younger. Youth isn’t everything; experience still counts.