Musings of a Forensic Statistician

“There are three kinds of untruths, lies, damned lies, and statistics.” Mark Twain is often credited with that statement, but what are the odds?

“Torture numbers enough and they will confess to anything.” Gregg Easterbrook gets the credit for that one, but it might have been lifted from Twain.

I’ve always loved numbers. As a young baseball fanatic, I learned how to calculate a pitcher’s “earned run average” (ERA) by the time I was in the third grade. Baseball has given us some of the world’s greatest multi-dimensional mathematicians. Yogi Berra famously said, “Ninety-percent of the game is half mental.” Top that Stephen Hawking.

Discussions of golf numbers and statistics in the last few days seems to have raised some eyebrows. The USGA applied its PCC (playing condition calculation) to our Monday round. The PCC was triggered by a statistical setpoint in the GHIN system. To address some of the questions, I ran an analysis of golfer’s performances as a function of the course and tees played.

Those that saw the report seemed surprised that with over four thousand data points, golfers playing the yellow tees on the Padre course averaged more than five strokes over their handicap index. Yet, with over six thousand data points from Ambiente’s Camel tees, players averaged about two-and-a-half strokes over their indices.

Is that statistically significant? More than 10,000 data points! Hell yes! The numbers are saying something. The question is “What are they telling us?”

If you’re not a “numbers person”, the answer is “Who cares?” You can stop reading now. But if your curiosity beckons, read on. Who knows? Maybe a more in-depth understanding can lead to your gain.

I’m only going to comment on the performance differences between Ambiente (Camel) and Padre (Yellow). Both courses are roughly 6,100 yards in length. Although they’re admittedly somewhat different in their personalities, both courses are subject to the same weather, winds, temperatures, etc. In a nutshell, we’re comparing apples-to-apples.

(If you’re interested in looking at the numbers associated with the nearly 100 courses played by our golfers over the past six years, you can see them here. I’ll be anxious to hear your thoughts and interpretations.)

Statistically, the difference in the average to handicap between the two courses is huge. A half stroke – maybe not, but it’s nearly double the difference. That is not reasonably possible without further explanation. Here are some possibilities for your consideration:

  1. The USGA course rating and slope evaluations are not accurate. If after 10,000 or so rounds, the differences are so pronounced, the obvious conclusion in my mind is that one course is rated substantially too low and/or the other one is rated too high. A statistical analysis of the mathematical structure of the USGA Handicap System strongly suggests that scores should average roughly three strokes over handicap. This neglects performance differences in handicap ranges and some other minor variables. If we drill-down on the question, it may suggest the course slope rating in also in error.
  2. Statistical “hysteresis”. Simply put (is it too late for that?), assume a person plays twenty rounds on Padre and ends up with a handicap that is three strokes too high. When that golfer then plays twenty rounds on Ambiente, he’ll be inclined to play significantly better relative to his now elevated handicap. When he completes twenty or so rounds on Ambiente and now returns to Padre, his handicap is too low. In reality, this does “explain” the numbers; it only shines a light on their consequences. The course rating/slope of one or both should be reviewed.
  3. Golfers with vanity handicaps prefer Padre. OK, now I’m really stretching it, but let’s not rule it out. Sometimes, it’s the “old guys” (of which I am now one) that are probably more inclined to scrape the four-foot putts, hit “breakfast ball”, and forget how many strokes were actually taken… that prefer Padre. After all, Padre players have access to more bathrooms, fewer fairway traps, and fewer snakes, coyotes, bobcats, and other predators. Play Ambiente and you’re two-and-a-half miles from the clubhouse at the turn. Those are pretty dangerous waters for an old boat.
  4. Club “management” is messing with the courses. Frankly, this isn’t speculation; it’s a reality. Most if not all golf course’s management “manipulates” the course a bit to improve pace-of-play. Camelback is no different. The tees on both Camelback courses are periodically moved forward due to a variety of factors, profitability no doubt being the most obvious. In the most egregious case, the green tees on #18 Ambiente occasionally get set forward to take the long shot over the wash out of play. That cuts 70 to 80 yards off the “rated” length of the hole. That alone results in a 0.4 reduction in the course rating. Similar, but less dramatic moves have been made on other holes. After analyzing hundreds of rounds of golf, the rating from the Verde tees when compared to other tee sets is a full stroke-and-half too low… or the tees are intentionally set a full stroke-and-a-half closer than designed when the AGA rated the course.
  5. Padre is the preferred course for sand-baggers. I suggest this as a possible explanation, but I don’t really believe it. Nonetheless, if a golfer inclined toward a little padding of his handicap is preparing for an upcoming tournament where a higher handicap would be beneficial, the Padre course would definitely give him an edge in getting his handicap to a competitive level. He could play his best and still get a two to three stroke bump without violating an rules of golf. On top of that, if he’s a proponent of the NMAPYDN school of golf (“Never make a putt you don’t need”), he could work the Padre course into a five or six stroke competitive edge by tournament time.
  6. Economics could contribute to some of the performance difference between the courses. The rack-rates and the guest rates are higher on Ambiente than they are on Padre. Perhaps someone who is more cost-conscious tends to reduce expenses on practice and play frequency. If so, his handicap becomes less responsive to change. Non-members also tend to play other courses more often. If those other courses are more fairly rated, performance relative to handicap on Padre will suffer.

There are other possibilities and I will delight in hearing your suggestions. But with more than 10,000 data points, it’s irrefutable that something is amiss. As the “forensic statistician”, I’m inclined to argue the Padre course is not rated properly (suggestion #1) and/or Camelback management is lax in its efforts to consistently setup the course according to its AGA rated conditions.

Recognizing the reality doesn’t mean it’s all bad. There sits in the Member’s Lounge a large trophy called “The Camel Cup”. It is currently in possession of the golfers of the J-Golf Group at Camelback in large part because some deceitful and diabolical tournament organizer deemed the Padre course as the field of battle and solicited the help of the Camelback ground’s crew in setting the pins in devilish locations prior to the tournament. The poor guys from Gainey Ranch never knew what hit them. I guess it makes sense that an unfair situation puts one side at a disadvantage, but the other side ends up with the advantage. Having a grasp of statistics can pay dividends, especially when you realize that it is said, “Four out of three people have trouble with fractions.”