## Saturday, July 04, 2009

### Is Tiger Woods Irrational?

"Loss Aversion" is a kind of irrationality where people care more about avoiding a loss more than about securing a gain of the same amount. For instance, if one person wins \$50, while another identical person loses \$50, the unlucky gambler will gain more unhappiness than the winner gains happiness. Because of this, people will expend more effort to avoid incurring a loss than they will in pursuit of the identical gain.

This is irrational; if it takes three hours to save a loss of \$20, but you can earn \$10 an hour, you're worse off if you spend the three hours to save the \$20. That's because if you accepted the loss, and instead spent those three hours earning \$30, you'd be \$10 ahead. But since, as it turns out, humans tend to value losses as about twice the value of the identical gain, there should be a tendency to spend time trying to save the \$20 instead of earn the \$30.

The irrational fear of losses is a generalization; it's certainly possible that some people don't have this bias, or at least are aware of it and able to compensate. Life is full of decisions and trade-offs, and you'd think the most successful people would have learned how to be more rational in these situations.

Take golf, for instance. In normal PGA tournament play, your score is just the number of strokes you took. A stroke is a stroke, and so it shouldn't matter if it's a stroke to make birdie (which, if missed, will leave your score unchanged), or a stroke to make par (which, if missed, will make your score one stroke worse). Both strokes are of equal importance. However, the stroke for par may count more in the golfer's mind. That's because, if he doesn't make it, it looks like a loss (his score gets worse). But if he misses a birdie putt, it's just a foregone gain (his score stays the same). If losses irrationally count for twice as much as gains in the golfer's mind, then he should try harder to make the par putt than the birdie putt.

And it turns out he does. According to a recent golf study (.pdf, free download) by Devin G. Pope and Maurice E. Schweitzer, PGA golfers are significantly more likely to make a par putt than the identical birdie putt. It's not even close: overall, the difference is about three percentage points. That's huge: the overall conversion rate for putts is 61 percent, and 3 points out of 61 is about five percent. In baseball terms, it's like a 96-66 team suddenly going 102-60 just by changing an irrational strategy.

Pope and Schweitzer did more than just count putt conversion rates, of course. After all, it's likely that birdie putts are different from par putts in many ways. They might be farther from the hole. They might be in less advantageous places on the green. They are less likely to have followed other putts, which means the golfer doesn't have as good a read of the green. Birdie putts might be associated with different kinds of golfers. They might be associated with different difficulties of greens. And so on, and so forth.

The authors took all these things into consideration. Indeed, their database is so extensive (over 1.6 million putts between 2004 and 2008) that the authors were even able to find thousands of "matching" pairs of putts where one was for birdie and one for par, but where both were in almost exactly the same place on the green, in the same round. The results held: par putts were holed significantly more frequently than birdie putts.

It turns out the difference is mostly length: when pros putted for birdie, they were more likely to leave the putt short than when they were putting for par. The idea is that the birdie golfers are playing conservatively: they want to make sure that if they don't sink the putt, they leave it close to the hole for an easy subsequent shot. On the other hand, the par golfers are scared to miss, because that appears to cost them the loss of a stroke, so they make sure they give it enough weight. For putts of 22.5 feet or longer, birdie putters leave the ball about two inches shorter than par putters.

From a strict strategic standpoint, the conservative play makes little sense. The authors find that after a missed (presumably conservative) birdie try, golfers make the subsequent putt only 0.2 percentage points more often than after a missed (presumably aggressive) par try. So the conservatism costs 3 percentage points, but gains only 0.2 percentage points. Moreover, the gain comes only if the putt is missed: assuming a 50% conversion rate on the original putt, the net gain from conservative play is only 0.1 percentage point!

So why are golfers accepting a much worse first putt for a very, very slight chance at avoiding a three-putt? It must be loss aversion. There are still two possible ways that could manifest itself. It could be that golfers are deliberately trying to hit the ball softer on birdie tries in a conscious effort to be more conservative. Or, it could be that golfers are just trying harder in general on par tries. Either way, that's something that you'd think pros would be able to control, if they realized that what they were doing makes no sense.

Has any golfer figured this out? Apparently not. The authors calculated the effect for each of 188 golfers in their data sample; they got a bell-shaped curve centered around 3.5 percentage points. The "most irrational" golfer's difference was 7 percentage points; the "least irrational" golfer was at half a percentage point. That is: every one of the 188 pro golfers exhibited this bias, to one extent or another. Just as surprising was the finding that the size of the bias was barely correlated with the ranking of the player. Better golfers had less bias, but only very slightly less. Tiger Woods, the best golfer in the world, was almost exactly average in this measure. By eliminating the bias, and shooting birdie putts the same as par putts, Pope and Schweitzer calculate that the average PGA pro will take one stroke off his score for a 72-hole tournament. If a top-20 golfer did this (and none of the other 19 did), his earnings would improve by 22% -- over one million dollars per year.

That's hard to believe, but there it is.

Read the whole study; the authors diced the data many different ways to confirm their thesis, and there are many interesting findings. A New York Times article about the study is here.

P.S. I've been getting lots of spam comments lately, so now comments on older posts (28 days old or more) are moderated. Comments on current posts will continue to appear instantly.

Hat Tip: Inside the Book

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At Monday, July 06, 2009 11:52:00 PM,  Eddy Elfenbein said...

Fascinating post. I think Richard Thaler referred to this as mental accounting, though I'm not sure if I'm using that term properly.

I wonder if there are similar aspects in other sports. For example, are kickers equal in making single point PATs as they are in making 3-point 19-yard FGs.

At Tuesday, July 07, 2009 3:20:00 PM,  doc said...

I read the article, and some of the newspaper stuff about it, and it seems that at least some golfers recognize that the way they approach these putts is irrational...but they do it anyway. That, to me, was one of the most interesting things...

At Tuesday, July 07, 2009 7:03:00 PM,  Phil Birnbaum said...

I wonder if it's something that golfers could change, or if it's such an emotional thing to make par that they can't duplicate their intensity on other shots, even if they wanted to.

You could probably do a study of "clutch hitting" in golf in other ways ... if golfers are tied for first on the 70th hole, do they hit differently off the tee?

At Wednesday, July 08, 2009 12:04:00 PM,  Rodney Fort said...

Thanks forthe post Phil.

I wonder about two other issues:

1) Why can't it just be performance anxiety? I know when I stand over a birdie putt I feel differently than when I stand over a par putt (or, more likely for me, a bogey putt!).

2) Often, what appears to be individually "irrational" is actually rational once the entire equilibrium of competition is accounted for. If a player is trying to win, rather than just minimize their score, perhaps pushing harder on par is optimal and, hence, rational. We know this is true at the end of many golf tourmaments where just finishing three holes with par is sufficient.

Just some thoughts and I'd appreciate your thoughts. For me, whenever EVERYBODY is acting "irrationally" the first thing I do is examine whether I've missed the point.

At Wednesday, July 08, 2009 1:05:00 PM,  Phil Birnbaum said...

Hi, Rodney,

1. I think the authors considered performance anxiety and tried some analyses that showed it wasn't that. I'll look again and get back to you here.

2. I agree ... the fact that *every* golfer does it bothers me a bit. But I can't think of a scenario where it would be rational, and the study looks pretty sound with all the alternatives they tested.

The study did test whether the effect held up by score, and it did. When one golfer needed to make a birdie putt to get to a score of Y, and another golfer need to make his par putt to get to the same score of Y ... the effect still held, that the par putter was much more likely to make his putt than the birdie guy.

So it can't be solely that they're playing to their score.

At Tuesday, August 04, 2009 6:17:00 PM,  KiranR said...

Is this also true for say, eagle putts versus birdie putts? How about the relationship between par putts and bogey putts?

At Tuesday, August 18, 2009 6:33:00 PM,  Brian said...

Very nice article. To add to Rodney's suggestion, wouldn't it seem logical that Tiger Woods plays with the lead more than any other golfer? There has to be a case for conservative putting late in tournaments, especially with the lead.

At Tuesday, December 13, 2011 4:10:00 AM,  Steve Sailer said...

The reason good golfers lag putts short is to reduce the chance of missing the second putt. Did they calculate total strokes or just percentage of putts made? The former is what counts.

A huge fraction of par putts follow chip shots or sand shots where the golfer can watch their ball roll on the green. For example, if you chip your birdie try from off the green six feet past the hole, you get a quite accurate reverse image of the break you'll be facing. That's an easier putt than if you hit it to that location from 150 yards away.

At Tuesday, December 13, 2011 9:09:00 AM,  Phil Birnbaum said...

Steve,

Good points. I don't remember (it's been two years), but I'll reread it when I get a chance.