Fun

# Are The Masters Winners Getting Younger And Better? Predictions Update

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:

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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.

Categories: Fun, Statistics

### 20 replies »

1. Doug M says:

Regarding the chart of age of the winning golfer, it suggests a narritive that the sport moves in generations. A cluster of young hot-shots comes onto the scene every 20 years or so, and dominate the sport for an era.

The question would be, are we on the cusp of a the next generational shift. A tougher question than can be answered by data alone.

2. Les Johnson says:

William: your

Youth isnâ€™t everything; experience still counts.

I like to say that old age and treachery will beat youth and skill every time….

Finally, something I know about. 🙂

I don’t doubt today’s players are better on average but there is a lot of other factors to consider.

Over the years Augusta National has had a lot of changes. In 1934, for the first tournament, the course was just 6,800 yards. Today it is 7,435. There were originally 22 sand traps; now there are about double that number. Fairways are considerably narrower today, the greens have been elevated, etc. So, the course is considerably harder now.

More than offsetting this, though, is the HUGE improvement in equipment. Today’s equipment is far superior to what I played with in the 1980s, even. Compared to the 1940s it is like a Ferrari vs a Model-T. Until maybe 15-20 years ago, very few golfers could drive the ball 300 yards. Now many of them boom it out there 330, 350 yards. As for iron play, back in the 1980s I remember most players hitting a 6-iron on the par 3 16th. Now an 8 or even an 9-iron is common.

4. stan says:

Joel,

The biggest difference in the course is the fast greens. When they show Arnie and company playing the course 50 years ago, it’s amazing to see how hard they rapped their putts on those greens.

5. JH says:

All I know is that the Pros make the golf swing look so easy.

6. DAV says:

Watching golf is like watching someone solve a crossword puzzle.

7. Briggs says:

DAV,

Which people do. Wasn’t there a film about an annual crossword puzzle championship? Will Shortz was in it. Poster-sized puzzles being filled out by contestants with erasable markers in front of large, enthusiastic audiences.

8. max says:

Completely off-topic but this is a good graphic representation of the problem with the 95% significance totem of so much modern “science” which I saw yesterday.

http://www.xkcd.com/882/

9. Joel McDade and Stan have touched on one problem with the professor’s comparisons. The game is designed to be a test of a golfer against the course. That is the crux of the battle. The fact there are other humanoids out there undergoing the same struggle at the same time is simply icing on the cake.

Courses have changed so much over the years there simply is no longer a valid comparison. Talk to some of the pros on the Champions Tour [old geezers] and they will say the same. As experienced and skilled as they are, each year they are battling tougher and tougher courses. So that means younger players today on average are notably better than previous generations. The main reason for that, besides the better equipment, is the growth of youth programs such as First Tee and interscholastic competitive golf at the high school level.

Some say skill at golf is almost an unspoken requirement for access to the corporate world. That’s why one sees a large number of corporate tournaments and sponsorship of PGA events. The game is constructed around an “honor code”, so many CEO’s and HR bigwigs use the game to spot check new recruits’ ethical and social development.

10. Speed says:

Is there any human endeavor to which statistics have been more thoroughly and inexpertly applied for so little gain as sports?

11. DAV says:

Briggs,

Could be why they are called puzzles. OTOH, Wheel of Fortune has a following and not all of it caused by Vanna.

12. So, Tiger Woods held the largest margin of victory in 1997, four years before his first win at the age of 22 in 2001? Interesting.

13. j ferguson says:

It may be in golf as it seems to be in music. The top golfers are drawn from a larger cohort where there are many more opportunities to play very serious golf – making it more likely that people with the aptitude and drive will find their way to it. Consider that the guy who would have been a world class golfer 40 years ago but went into electrical engineering is now more likely to find his way into golf. And of course there are many more of those guys.

You could ask where were the other great golfers in 1956? Teaching economics.

Someone here may be closer to today’s symphonies than me, but when I go, even in towns not having widely-praised groups, I still hear marvelous musicians. There was a symphony in a midwest city (not Chicago) in the 60s which had a few good string players and one maybe two top woodwinds, but everyone else would not have made the cut today in even a much lesser city’s group.

They make better horns today. I suspect (but don’t know for sure) that there hasn’t been a lot of change in the other instruments. Again, there are more guys (and gals) with the aptitude and interest, and even a smaller city can have a great orchestra – assuming they can find a way to pay them.

14. Andrew Kennett says:

Max if you think WMB will like that xkcd he should also check out http://xkcd.com/808/

Rob and Briggs,

Tiger was 22 when he won his first Masters in 1997.

16. j ferguson says:

I hadn’t noticed the dates on the comments. Reading down, I came to one by a j ferguson. I read it, concluded that it was pretty good and was getting ready to comment that someone else was using my name and he seemed sharper than me.

We would have to decide who could use it and I would have to confess that I couldn’t match his insight. Then I saw the date and could vaguely remember writing it. What a relief. I do think I’m losing it though.

Some years ago, SWMBO and I were dining in a Wendy’s. She leaned over and whispered “John, look over there. There’s a woman who looks like I might in about 15 years.”

The place had two walls which were essentially mirrors. It was her.

There was dead silence, then we both cracked up.

17. Briggs says:

j ferguson (#2):

Ha ha ha!

18. Your prediction nailed it! Again! How do you do that?

SeÃ±or Ferguson seems astute – with his comments – and wise – to have not replied brashly at Wendy’s.

19. Gary C says:

Fred Couples was 32 not 42 when he won his Masters in 92.