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.”

They Sacrificed for You

As the caravan approached the border, armed guards braced for its arrival. The disparate group of refugees was hopeful they could talk their way through the barrier. As Hans Birkholz dutifully scanned the wall for breaks in the concertina wire, David Harbour and Mike Forde rehearsed the plan. “If Jones pisses them off, we tell them he’s a hired driver and we had no idea that trying to cross the border with a loose-cannon violated Mexican laws against arms importation.” The last car in the caravan carried Dave and Lauri Allen poised to retreat at the first sign of discord on the frontera.

Silverado Golf Course – Slightly Better Than Nothing

A group of a dozen golfers decided to give Scottsdale Silverado Golf Club a second chance. The first chance came nearly a year earlier; we weren’t favorably impressed. But, it seemed unfair to base our opinions on only one data point. Anyone can have a bad day. Perhaps we happened to be there for the only bad day they’d ever inflicted upon golfers. The second chance came Friday, April 21^st.

Based upon our experience on the 21^st, our first experience may have been one of their better days. The second chance was as close to disaster as one can come without seeing a mushroom cloud. Most of us feel fortunate to have escaped the property with our tattered, challenged and abused senses of humor intact.

OrangeTree Very Pretty and the Orange Flower is Sweet, but …

A dozen Camelback golfers took a little road-trip on Friday, November 11^th. For some, it had been years since they had played OrangeTree Golf Course. Others had never played it. When all was said and done and the last putt rolled into the eighteenth hole, the general consensus was … as munis go, it’s a nice course, an interesting layout and a good value. In fact, had we not been spoiled with the great layouts at Camelback, we might even play it again. On a scale of zero to one hundred, OrangeTree averaged a score of sixty-five from the golfers in the group with individual ratings running from fifty-five to seventy-five. To be fair, it is not a muni, but it definitely has a muni feel. That’s not necessarily bad, but don’t expect to come away feeling like you just played an exclusive private club.

The strengths included an interesting layout. It’s mature and many of the holes are quite scenic. They were varied and offered some good golf challenges, however, the course was not a “championship” layout. With a rating of 69.3 and a slope of 119 (from the middle “white” tees), it was more than manageable for most golf skill levels. Fairways tended to have wide landing areas, but greens tended to be small. Miss the green and odds are you’ll be short-sided. With one notable exception, the staff was cordial, friendly and helpful. The biggest positive at OrangeTree is its price. We got a $49 rate in the late morning – cheap by Valley standards. It included the cart, but did not include range balls.

OrangeTree’s weaknesses seemed to be budget related. Greens were a bit “spotty” and hadn’t been rolled since the late Pleistocene. A six foot putt could be a bit of an adventure. Predicting the ball’s roll was like trying to predict the path of a pinball during an earthquake. Tee boxes either hadn’t been moved enough or were too small to allow much movement. They had the appearance of a corn field shortly after harvest. Over all, the course was in “respectable” condition, but that’s about the best that can be said.

More evidence that the drive to reduce expenses may be a touch overly aggressive appeared when I went to wet my towel at the restroom by the sixth hole. As I approached the water fountain outside the little building, it became apparent the fountain hadn’t been functional for quite some time. I went into the bathroom to find water. As I opened the door, I got the impression it wasn’t the spiffiest restroom in the golf world, but as the door closed behind me, the darkness became the cleaning agent. The light didn’t work so I could no longer discern the lack of clean. As my eyes slowly adjusted and a hint of light crawled in through the small window on one wall, I could make out the outline of the bathroom’s features. There was water in the toilet bowl. My towel remained dry. In the dim light, I saw what appeared to be a clipboard with a piece of paper on it. I took it outside to see what I had discovered. It was a “Restroom Cleaning Log – Hole #6”. There was a series of dates beginning with “27-Oct” and running through “19-Apr”. Next to each date was a space for the initials of presumably the person doing the cleaning. There were no initials for any date beyond October 27^th. That wouldn’t have been a problem were it not for the fact that it was November 11^th. If the truth be known, it had probably been cleaned in the previous two weeks, but the person doing the work couldn’t find the clipboard. Remember … it was too dark without a working light in there.

There was one employee that made the day especially memorable. The “starter” seemed to have the personality of Ukrainian prison guard. As some of the members of our group began sharing their starter experiences with me, I couldn’t believe what I was hearing. I thought there’s no way someone could have a position so closely associated with the image of the golf club without having a personality that put a “happy face” on the customer’s golf experience. I suggested that the starter may just have a very dry sense of humor and that the casual onlooker would pick up on it after a brief wait. I decided to get a firsthand look and judge for myself. After a brief exchange with the starter, I stood back and watched as he interfaced with a number of other golfers. I came away concluding that his humor must indeed be bone-dry, so dry in fact, that he came across as a real horse’s ass. But that couldn’t be the case. After all, he was still employed.

Fortunately, other staff members were friendly and helpful. When golfers were “entertained” by three twelve or thirteen year old boys in a yard adjacent to the course, the staff dispatched someone to deal with the homeowner. Mom didn’t seem to grasp the concept of golfers being accosted by boys hurling unmentionable obscenities as not being great for public relations, but the club staff did send an emissary to the scene of the crime in short order when the problem was reported.

The course offered a good value for the money. Where else in the Valley can you get to drive the old style gasoline powered golf carts. The course was fun. It wasn’t in great shape, but it was in good enough shape. It wasn’t extremely challenging, but it was challenging enough. I recommend playing OrangeTree from time to time, particularly if you’re a golfer on a budget.

Mexico, Camelback and Golf

An unnamed member of the group’s best wedge shot was into the fan in his hotel room.

Everyone is back. Everyone survived, but not from a lack of effort. Great dining, super weather, outstanding golf and a party or two (or three or … ). Our trip to Puerto Peñasco was a wonderful event … actually a series of events.

We enjoyed golf at The Links at Las Palomas. The course was in good shape. The layout was interesting and fun. The views were awesome. Matt Flores brought his “A game” and carded a 66, but only because he missed a few putts that could have easily brought him a few strokes lower.

The following day, the group played the Jack Nicklaus designed course at La Vidanta. The course was in immaculate condition. It was an absolutely spectacular layout that offered some real tough golf. I must assume Jack was fighting with Mrs. Nicklaus when he was designing that course and redirected his anger toward us. Scores weren’t as low as they were the previous day, but the experience will not soon be forgotten.

The dining experiences were top notch with (obviously) some great Mexican food, super Italian, German breakfasts, and marvelous sea food. Rocky Point is a shrimping village and we made a serious dent in the fleet’s catch. How fresh were the oysters? We watched as the fisherman hauled them directly from the ocean and put them on our plates. That’s pretty fresh.

Here are a few images from the trip. Others will remain private unless the subjects miss a payment. (Click on any image to enlarge it.)

Camelback Ambiente – In a League of Its Own

With more than 200 golf courses in the Phoenix area, we live in a golfer’s paradise. At its heart is Scottsdale. Some of the great and unquestionably some of the most scenic holes in golf are right here in our backyard. Of the courses that can be accessed without membership, the cream of the crop is the Ambiente course at Camelback Golf Club.

Ambiente is barely a year old, but is already in great shape. Greens are fast and true. Fairways are lush. The vistas are magnificent with backdrops of Camelback Mountain and Mummy Mountain. Every hole on this links style course is encased in flower laden wild areas that are beautiful to look at, but voracious in their hunger for errant shots.

The course design is brilliant. Unlike most “resort courses”, this is not one where you stand on every tee box and let it rip into a wide, hazard free fairway. This is a thinking golfer’s course. It’s real golf. You’ve got to manage your game to score well. There’s potential trouble off of every tee box, even the five pars. If you’re the macho type that reflexively grabs driver on every tee box, chances are this course is going bring you to your knees and take your balls. It’s a course for smart golfers. Even off the tee, club selection is an important consideration.

The course is playable at all levels, but if you’re not a low handicap golfer, don’t fool yourself into thinking you should be playing the back tees. At 7,225 yards, it will give the best golfers everything they can handle. The 245 yard par three fifteenth is one of Ambiente’s signature holes. From the tips, you’re hitting to a two tiered green with water on two sides, a cavernous bunker on the left and another one in front of the green. The seventh hole is a good par five over 600 yards long. The fourteenth is another par five, but it only plays at 580 yards. The greens are interesting and challenging, but fair. Stay below the hole.

Although there is a middle set of tees that bring the course down to 6,630 yards, most golfers will find the “Camel” tees give them all they can handle at 6,123 yards. If you play from this forward tee set and conquer the course, move back to the “Verde” tees the next time you play. But I’m betting you’ll beg for mercy before the course does. It’s still rated at 69.0 with a 124 slope from the forward tees. It’s at 73.9 and 138 from the tips.

Ambiente is one of two courses at Camelback Golf Club. Its sister course, Padre, is a fine course in its own right and a good test of golf, but its character is totally different from Ambiente’s. If you’re in Scottsdale for golf, consider playing both courses. Padre almost has the character of a Florida course while Ambiente is like a walk in Scotland. And you don’t even have to go through airport security to experience the differences.

Camelback’s practice facilities, pro-shop and clubhouse are up there with the best of them. The employees are friendly, well-trained and always ready to help.

If I were visiting Scottsdale and only had time to play one of its 200 courses, it would be Camelback Ambiente. But I live here and play three or four rounds per week. I still pick Ambiente. It just doesn’t get much better.

Course Review – Troon North, the Pinnacle Course

If the price of a round of golf were to correlate well with the quality of the golfing experience, Troon North would be one of golf’s great courses. The GolfNow.com rate is north of a hundred dollars with some tee times calling for a $235 fee. And GolfNow.com generally offers some pretty heavy discounts.

Unfortunately, Troon North is not a world class course. It is a fine course and I recommend playing it. The views are spectacular. The course is fair, at least as fair as a “desert course” can be. But it’s a public course. As a result, it gets a lot of play. It has been my experience that public courses with plenty of play host golfers that don’t seem to know the purpose of the little sand canisters mounted on the carts or the rakes that adorn the sand traps. To some of their customers, ball mark repair is a concept as foreign as a Tibetan poetry reading.

Up Stone Creek without a Paddle

As so often happens, members of Gainey Ranch Golf Club couldn’t arrange to play a routine eighteen hole round at the club they had joined. Once again we were forced to go off-campus to play. In that “the season” was upon us, many courses had raised their rates. Being the bargain conscious group we were, we looked for a deal. What about Stone Creek Golf Club? Most of our guys had never played it; others hadn’t played it in years. I called.

“I’ve got a dozen guys from Gainey Ranch Golf Club that would like to give your course a try next Monday, September 22^nd. What kind of a good rate can you give us?”

The man on the Stone Creek end of the phone paused, but finally said, “I can give you twenty-five dollars per player including range balls, cart and eighteen holes of golf.”