Golf Erotica for Mathematicians

Math chalkboardI recently received an email from one of our golfers asking for an explanation of the “Odds” column on the Gross Score Report found at the bottom of the “Match Sign-Ups” page on this site. It dawned on me that others may have that same question. What follows is a copy of my response to the email.

If you have something important to do, like watch your grass grow or look for dust bunnies under your couch, skip everything in black below and go directly to the answer in red at the bottom of this diatribe. Either way, let me know if you have any other questions. Cheers.

What time is it, you ask? Let me tell you how to build a watch!

Years ago, the number crunchers at the U.S.G.A. analyzed (I presume) a couple million rounds of golf. They built a chart showing the probabilities that someone with a given handicap index would shoot a particular gross score on a golf course with a specified rating and slope. That chart was published in the USGA magazine and a variety of other places. When I saw it, I was enraptured. (Mathematicians and engineers like me are frequently aroused by statistical challenges. Yes, we’re a strange lot.)

When I saw the chart, I was driven to analyze the data in much greater detail. I called the USGA and spoke with someone in the appropriate department. I asked if they would share the raw data with me. The guy was aghast. “We don’t share our data with the public” he responded with arrogant contempt dripping from his voice. When I told him I wasn’t “the public” that I was in fact a USGA member, he was almost as impressed as if I had told him I was owned a pencil and knew how to use it. He wouldn’t budge. I’ve always been of the ilk that the only challenges worth pursuing are those that aren’t supposed to be possible. The guy just made me more determined than ever.

I set about the task of mapping all the data points from the chart that I thought necessary to accomplish the task. I then performed a nonlinear multiple regression analysis on all the manufactured data. I developed the following formula:
With that formula, I can produce a reasonably reliable estimate of the probability of a person shooting a given score.

Since I developed this tool, I have entered many tens of thousands of rounds of golf into my personal database. The formula has proven to be quite accurate when applied to my database, so the snooty dude at the USGA can go suck on his own database.

Needless to say, my formula – like the USGA predictor – is contingent upon a number of assumptions that suggest stasis, i.e., the golfer isn’t in the midst of a series of lessons, hasn’t had his legs cut off and the course is properly rated. Nonetheless, it provides an interesting metric that’s useful in a number of ways, some not terribly obvious. Think about using it as a tool for the handicap police to root out cheaters and sandbaggers.

So, in answer to your question … the “Odds” column reflects the probability that the golfer will shoot the score that was turned in. If the number appears in brackets, it means the number is actually the inverse of the probability, i.e. less than even odds.