There's a nice article in yesterday's NYT highlighting a study by two Wharton professors, Devin Pope and Maurice Schweitzer, who found that pro golfers were about 3% more likely to make par putts than birdie putts from the same distance and were more likely to leave birdie putts short. Over 72 holes, the "playing it safe" bias on birdie putts cost top players an average of a stroke per tournament , which works out to a $1.1 million average difference in prize money for the top twenty players on the tour, all of whom showed the tendency to make fewer birdie putts than equally difficult par putts.
It's a nice paper, which deals with most of the obvious objections and some of the non-obvious ones as well. (For example, Pope and Schweitzer show that the "playing it safe" bias is not compensated for by an increased probability of making the next putt and that the lower percentage of successful birdie putts at a given distance is not accounted for by their being on more difficult positions on the green.) Assuming for present purposes the validity of the paper's empirical results, I have one minor issue, and a second, more fundamental issue with the claim that the golfers are acting in a suboptimal way by treating birdie putts and par putts differently. First, the secondary point: Considering that the paper is entitled, "Is Tiger Woods Loss Averse?", I wish there had been some discussion of how less aggressive putting for birdies by a player clearly superior to his peers makes some sense, since being in position for a birdie gives Tiger a modest signal that he is on his game and therefore has a strong chance to win the tournament, while putting for a par is a modest signal that he may not be on his game and therefore needs to putt more aggressively to have a good chance to win. Even though that reasoning wouldn't justify anyone but Woods playing it safe as a strategy to win a tournament--and might well not justify his actual degree of conservatism on birdie putts--given that the 188 PGA players studied rose from high schools and clubs where they were probably far superior to their peers, they may in their heart of hearts think of themselves as Tigers and play in a way appropriate for him but not for them, especially if they are also risk-averse and play to do acceptably in the tournament rather than to maximize their expected prize money.
Next, my more fundamental issue. I strongly suspect that the apparently suboptimal difference between how pro golfers deal with birdie putts relative to par putts is part of a package in which apparent irrationality in the form of pattern-oriented, category-based behavior on par and birdie putts is conducive overall to the best level of performance of a complex physical and mental act. In their putts and other shots, pro golfers are able to overcome problems of overconcentration as well as underconcentration, of excessive attention to a goal as well as insufficient attention, of blending the conscious and the unconscious, in a way that weaker golfers are not. Doing so may well involve pattern-oriented behavior such as treating birdie and par putts slightly differently, which incurs some cost taken by itself but which contributes to the overall high-performing equilibrium of the pro golfer. Effectively countering the "yips" and the internal tension between duty--"you must make this putt"--and letting go likely involves some degree of pattern-oriented, category-based conduct like different behavior on birdie and par putts.
The problem with my problem with Pope and Schweitzer's paper is that, without more, it amounts simply to a "the pros play optimally" assertion. One way to test my claim would be a study of whether pointing out the "play it safe" bias to pros improves their performance relative to a control group of pros who don't hear about the bias. I would say no. (Good luck to anyone in getting pro golfers to cooperate with such a study...) Another way to make the claim better is to specify better how the calculating side of the brain if unchecked by a pattern-oriented side will run astray. That better model may itself have problems with testability, but would move the discussion beyond a simple assertion that the pros are rational after all.
One way to start constructing a better specified model: Suppose optimal putting depends on an optimal blend of conscious and unconscious factors. Calculative reasoning is always in danger of allying with the conscious side and bringing on the yips. Pattern-oriented principles, even if flawed in themselves, help counter that unfortunate tendency of calculation, and can do more good than harm.
Another sport in which I believe that top level players could be shown to behave less optimally in some situations than others is baseball; my intuition is that pitchers could be shown to waste the next pitch more than is optimal on 0-2 counts, given the pitcher's command of the strike zone as shown by their behavior on other counts. (The analysis would be trickier than with the golf study because it is indeed rational to waste the next pitch somewhat more on 0-2 than other counts.) I suspect the psychology here is similar to that in golf, in that "relaxing" on the 0-2 pitch and the birdie putt are behavior that is sensible overall given the workings of the human brain and body, though irrational if taken in isolation.
