Paul Kedrosky is intrigued by a claim about golf strategy

While eating lunch and idly scanning subtitles of today’s broadcast of golf’s PGA Championship, I saw an analyst make an interesting claim. He said that the best putters in professional golf make more three putts (taking three putts to get the ball in the cup) than does the average professional golfer. Why? Because, he argued, the best putters hit the ball more firmly and confidently, with the result that if they miss their ball often ends up further past the hole. That causes them to 3-putt more often than do “lag” putters who are just trying to get the ball into the hole with no nastiness.

The hypothesis is that the better putters take more risks. That is, there is a trade-off between average return (few putts on average) and risk (chance of a big loss: three putts.)

His is a data-driven blog and he confronts the claim with a plot suggesting the opposite: better putters have fewer three-puts. However, there are reasons to quibble with the data (starting a long distance from the green, it would be nearly impossible to hole out with a single putt. In these cases good putters will two-putt, average putters will three-putt. The hypothesis is really about putting from around 10 feet and so the data needs to control for distance, as suggested to me by Mallesh Pai. Alternatively, instead of looking at cross-sectional data we could get data on a single player and compare his risk-taking behavior on easier greens, where he is effectively a better putter, versus more difficult greens.)

And anyway, who needs data when the theory is relatively straightforward. Any individual golfer has a risk-return tradeoff. He can putt firmly and try to increase the chance of holing out in one, at the cost of an increase in the chance of a three-putt if he misses and goes far past the hole. The golfer chooses the riskiness of his putts to optimize that tradeoff. Now, we can formalize what it means to be a better putter: for an equal increase in risk of a three-putt he gets a larger increase in the probability of a one-putt. Then we can analyze how this shift in the PPF (putt-possibility-frontier) affects his risk-taking.

Textbook Econ-1 micro tells us that there are two effects that go in opposite directions. First, the substitution effect tells us that because a better putter faces a lower relative price (in terms of increased risk) from going for a lower score, he will take advantage of this by taking more risk and consequently succumbing to more three-putts. (This assumes diminishing Marginal Rate of Substitution, a natural assumption here.) But, there is an income effect as well. His better putting skills enable him to *both *lower his risk and lower his average number of putts, and he will take advantage of this as well. (We are assuming here that lower risk and lower score are both normal goods.) The income effect points in the direction of fewer three-putts.

So the theoretical conclusions are ambiguous in general, but there is one case in which the original claim is clearly borne out. Consider putts from about 8 feet out. Competent golfers can, if they choose, play safely and virtually ensure they will hole out with two putts. Competent, but not excellent golfers, have a PPF whose slope is greater than 1: to increase the probability of a 1-putt, they must increase by even more the probability of a three-putt. Any movement along such a PPF away from the sure-thing two-putt not only increases risk, but also increases the expected number of putts. Its unambiguosly a bad move. So competent, but not excellent golfers will be at a corner solution on 8 foot putts, always two-putting.

On the other hand, better golfers have a flatter PPF and can, at least marginally, reduce their average number of putts by taking on risk. Some of these better golfers, in some situations, will choose to do this, and run the risk of three-putting.

Thanks to Mallesh Pai for the pointer.

## 4 comments

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August 19, 2009 at 12:49 am

ShrikWhat about controlling for the chicken-egg factor, and similar circular reasoning?

i.e. do you define a good putter as one who makes two-putts consistently? if so, doesn’t the starting definition defeat the hypothesis?

August 19, 2009 at 6:53 pm

econ phdThere is a bit of an endogeneity problem here, because the statistic used is putts per green in regulation. On average (not necessarily in specific cases), the people with lower putts per green in regulation are going to be the better ball-strikers (I say this without hard proof, but would be virtually certain the data would back me up) which is to say: they find themselves closer to the hole once on the green in regulation. This also means that with easier first putts, they are less likely to three putt. Hence, I would conjecture that if you had 100 clones on the putting green, all of whom were heterogeneous ball-strikers, that you would get a graph that looked exactly like that on the blog. Hence, 3 putts and lower putts per GIR are potentially going to be correlated even if the putting skill between two golfers on opposite ends of the scatter plot is identical.

One statistic that I used to keep when I was playing more seriously is feet of putts holed per round. That is to say, if every putt you sink in a round is 2 feet, that’s 36 feet of putts holed during the round. This way you abstract from all other factors that could hide just how long the putts you have been holing are. With sufficient data, this provides the truest measure of putting skill that I know of. Comparing this statistic to 3 putts per round would give a more accurate idea of the correlation between tendency to 3 putt and putting skill.

Of course, this statistic is not kept by any tour I know of, but I know for sure that certain players do keep this statistic for themselves. Perhaps with a little prodding the PGA tour could start it and this debate could be more satisfactorily settled😛

August 19, 2009 at 8:49 pm

Derk JonesYou claim “who needs data when the theory is relatively straightforward” and start out with some interesting observations before quickly reaching the conclusion that “the theoretical conclusions are ambiguous in general”.

How does Paul’s data stack up against your points? I’m sure he would send you the data so you could break things down further. Come on, if you’re going to do a theoretical analysis put a bit more effort into it.

December 11, 2009 at 6:31 am

Golf Channel and Equipment ReviewsLook !..Risk and Return in Golf