Sunday, October 1, 2017

Drive for Show, Putt for ... Loss Aversion?

TLDR: "The objective of golf is rather simple: complete the hole, round, and tournament in as few strokes as possible."

"However, ... golfers use very different strategies when putting based on how many strokes they have already taken relative to par [which]  can be explained by loss aversion."


"[...] We may expect to see some loss aversion on the putting green. Loss aversion would suggest that golfers care less about making an eagle or birdie putt than they care for making a par or bogey putt."

I find that in expectation "a golfer [makes] a putt for par 22 percentage points more often than if we were to put a ball on the exact same spot of the green and told him he's putting for a birdie."

Aside: Although golf is scored by the total number of strokes an individual required to finish the round, there are a number of odd terms to describe the performance of a golfer on each hole relative to the suggested number of strokes required. A few worth mentioning are:

Par - the suggested number of strokes for the given hole.
Eagle - two strokes less than par.
Birdie - one stroke less than par.
Bogey - one stroke more than par.
Double-Bogey - two strokes more than par.

The objective of golf is rather simple: complete the hole, round, and tournament in as few strokes as possible. However, each hole is given an explicit reference point to judge the quality of a performance on that hole, known as par.

A rational golfer would ignore par as a reference point. Instead, the rational golfer would rely on other pieces of information to inform herself how to approach the hole: distance to pin, location of hazards, the slope of the green, wind speed, etc. However, it has been shown that golfers use very different strategies when putting based on how many strokes they have already taken relative to par.

This phenomenon can be explained by loss aversion. Loss aversion tells us that humans tend to alter their actions to avoid losses more than they would alter their actions to obtain the equivalent gains. Stated alternatively, most people agree that losing $10 is more painful than gaining $10 is pleasing.

In the context of golf, we may expect to see some loss aversion on the putting green. Loss aversion would suggest that golfers care less about making an eagle or birdie putt than they care for making a par or bogey putt. Under this hypothesis, golfers would try much harder to avoid the loss of one stroke (i.e. not miss a putt for par) than they would try to gain one stroke (i.e. make the putt for birdie).

To test this hypothesis, I look at every putt from a 2016 Professional Golfers' Association (PGA) tournament (I apologize, I am only looking at the men's tournaments this time round). The data was collected and uploaded to Github by Brendan Sudol. The final set of data includes information on the tournament, the player, the hole, the par, the count of strokes by the player, and the distance to the pin before and after the shot.

I begin by simply calculating the percent of times each golfer makes a successful putt given the score he is currently lying (i.e. his score for the hole should the putt go in). As I hypothesized, golfers tend to focus to avoid a loss (i.e. not miss a putt for par) significantly more than they do to achieve a win (i.e. make the putt for birdie or eagle).


Now, you may question whether it is fair to look at such average success rates: it is not unreasonable to assume there is some sort of endogeneity in the data. For example, some golfers may specialize in driving the ball from the tee at the expense of quality putting. In this scenario, the golfers that can drive a ball well enough to to the green to set up an eagle putt may need an extra putt or two to save par. If this were true, we would almost necessarily see a low success rate for eagle putts relative to par putts.

For this reason, I calculate the conditional success rate by the score the player is putting for. By conditional, I insinuate controlling for variables such as the tournament, the player, the round within the tournament, the hole, and how far the ball is from the pin.  In other words, in the graph below, we can consider three all-but-identical putts, the only difference is in the golfer's score for the hole should he be successful.

As demonstrated in the graphic above, we would expect a golfer to make a putt for par 22 percentage points more often than if we were to put a ball on the exact same spot of the green and told him he's putting for a birdie.

If this sounds absurd, it is. At the end of the tournament, all that matters is the sum of the total strokes taken throughout each hole. Each individual, even that guy that drives the cart onto the green, is strictly better off by sinking a putt regardless of what the suggested par is for that hole. However, the concept of loss aversion is so innate to humans, even professionals cannot escape it.

Paraphrased by the authors of Scorecasting: "Golfers are so concerned with a loss that they are more aggressive in avoiding a bogey that they are in scoring a birdie."

5 comments:

  1. Wow. That is very interesting. I would have never guessed that all things being equal, the same putt would have a higher percentage based on the higher score for a hole. Well done!

    ReplyDelete
  2. As an avid golfer (have shot par twice in the last 3 years) and a numbers nut, the likely explanation for those % success rates is folks are generally putting for bogey/par from a much shorter distance than for birdies or eagles.

    ReplyDelete
    Replies
    1. First off, congrats on shooting par!

      Secondly, you are certainly correct in saying that a bogey putt likely has a shorter distance to go to the hole than a birdie putt especially if the bogey putt is the second or third putt. This is what I try to show with the first graph.

      To correct for this issue, I use a regression to control for the distance to the pin (among other factors) and display the results using the second graph of the article. That is where I make the assertion that, 'all else equal,' a golfer will make the par putt 22 percentage points more than the birdie putt. It is the mathematical equivalent to placing the ball on the exact same spot and telling the golfer if he is putting for birdie or putting for bogey.

      Delete
  3. Thanks. I am not quite clear how regressing putting distance out (which I think is the discriminating variable) is adding to the theory. I think the loss aversion theory applies better to birdie and eagle putts - you don't want to end up with a par if you are putting for eagle and you don't want to end up with a bogey if you are putting for birdie.

    ReplyDelete
    Replies
    1. I agree, I tried to focus more on the two scenarios in the text: (a) not missing a putt for par vs. (b) make the putt for birdie or eagle. Framed this way, the percentages I calculate align more to the loss aversion story.

      As for the regression, the left-hand side is yes/no did the golfer make the putt, the right-hand side is what the putt was for. This is where some sort of distance control is needed otherwise bogey putts would predict a lot of successes, and you and I both agree they are likely shorter putts.

      Delete