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.