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.

One for You Number Junkies

I can’t help myself. Statistics have intrigued me since I was a little kid. I read Darrell Huff’s “How to Lie with Statistics” when I was in the fourth grade. I was calculating the “Earned Run Averages” of baseball pitchers when I was in the third grade. Statistics are my drug of choice. What are the odds?

Stats overallWednesday’s golf match on the Ambiente course was played under the agitated hand of Mother Nature. Winds for most of the competition hovered around ten knots and gusted to twenty for most of the day. For the most part, winds were at our backs for the first ten holes then spit in our faces for the last seven. As expected, some of the players chanted the mantra of how difficult it was to score with the wind whistling as it did. However, I observed no instance where the wind blew only as one particular player put his ball on the tee and stopped when another prepared to tee off. Everyone played the same course under the same conditions. In other words, it was a fair match.

But for the number junkies, it was an opportunity to evaluate the impact of the wind. So like a kid in a candy store, I dug in. Here’s what I found after analyzing 2,606 rounds of golf played from the Camel tees of the Ambiente golf course.

  • Under “normal” circumstances, the back nine on Ambiente plays about a tenth of the stroke easier than the front side. That’s probably not terribly significant statistically – call it even.


  • With ten knot winds like we had Wednesday, scores were relatively unaffected when the wind was at our back. You no doubt got a little distance boost, but shot making was complicated by the need to estimate the effective distance. Everything seemed to work itself out with (if anything) a slight increase in difficulty.


  • When the wind was in our faces, we still suffered the same complication of estimating correct distances, however, that problem was compounded by the loss of distance when hitting into a headwind. The end result is the back nine played a little over one full stroke harder than the front side. Little slices were big slices; little hooks were big hooks. The back nine played at least one full stroke more difficult than did the front.


  • The biggest positive impact on scores when the wind was at our back came on the par five holes. The biggest negative impact appeared on the shortest holes. Yes, with these observations, it’s clear I have a keen sense of the obvious.


  • With the wind in our face, the reverse was true, i.e., longer holes issued greater punishments, another revelation of the obvious kind.


What can we learn from all this? It’s harder to play in the wind!

Upon closer scrutiny, there probably are some little tidbits that can be extracted from the data that will give you a competitive edge. But in the final analysis, it will undoubtedly amount to the following adage; “smart golf” carries a premium under adverse conditions. You might want to give a little more consideration to club selection. “Grip it and rip it” is NOT necessarily the best advice for windy days.

With all that said, here are a couple of quotes to put in your quiver for defense against number junkies.

“There are three kinds of untruths: lies, damned lies and statistics.”

“Torture numbers enough and they will confess to anything.”

“Four out of three people have trouble with fractions.”

Finally, one more statistic that conclusively proves it is well within the realm of possibility to play well in high winds. Observe the scorecard. Then congratulate Dr. Bill Yarbrough.

Yarbrough Ace

Don’t Jump! Life Is Worth Living!

hangmans-nooseI pen this missive to encourage today’s competitors to not commit suicide. Yes, it was horrible. Yes, you looked like someone that isn’t ready to play on the big course, like someone who should be sticking to the course where putting through the witch’s mouth is nirvana, where you’re a hero if your first shot gets past the blades of the windmill. Most of you (like I played well) should have been putting with a white cane rather than a $300 putter. But sometimes, that’s the way the cookie bounces. And besides, the way you played today, even if you tried to shoot yourself, you’d most likely miss anyway.

I am a mathematician. To me, statistics have always been more exotic that any porn I’ve yet to see. Today’s statistics were true hard core. Here they are!


At first glance, they are merely numbers, cold, hard, uncaring numbers. But look closer. Note the following …

The average “differential” was 11.0. “Big deal,” you say? Consider this; the average differential is normally on the order of 3.0 strokes. As a group, we were nearly four times the average today.

The average score was 91.1. With the handicaps carried by the group, the average score should have been roughly 85. The average was six strokes higher than expected!

Under normal circumstances, the average score to handicap is plus three, i.e., three strokes over the difference between course rating and gross score. Generally, about one in five golfers will shoot his handicap or better.

Here are the facts …

No one, not a single golfer shot better than four strokes over handicap today. One golfer (name withheld to protect the guilty) shot 24 strokes over handicap. Another was 19 over handicap.

Why did this happen? Because the course (Padre) was in a bad, very, very bad, mood. The greens were lightning fast, the fairways were as receptive as my first wife with a headache, the wind was constantly changing. I haven’t seen the golf gods this pissed off in years.

Now the up-side …

Everybody had to compete on the same course. If you had a bad day, so did everyone else. The field was level. Quitcherbichen.

Many moons ago – in my days of climbing the big mountains – I learned  that when the mountain’s in a bad mood, she’s not going to have any guests. On other days, she embraces even the novice climbers. Such is the case with a golf course. The Padre was not accepting guests today. If you survived, you did well.

There were some great shots hit out there today. In fact, on one hole (#2), I had six of them.

Wednesday’s another day. Suck it up. Play well. The field is level. If it’s tough for you, it’s tough for everyone. Oh my! I say that, but I’m going to quit golf altogether if I don’t do better, a lot better.

Kennedy’s Flourish Before Winter in Winnipeg

Bob Kennedy kicks in a putt

After Wednesday’s torrid competition, it wasn’t surprising to see scores fall back into the statistically “normal” range, at least for most of the golfers that is. The big exception was Bob Kennedy. Bob recorded a net 63 with an outstanding round on the Camelback Ambiente course. Given his handicap, that’s a better than 200-to-1 odds round of golf. It really paid off in the day game, especially after his partner, Maddie Levy, posted a 10-to-1 odds round. They walked away with half the pot for winning the front side and then escaped with the other half of the pot by winning the back side by one stroke over Jack Summers and Jim Funk.

Speaking of Jack Summers, he continued to play with a hot hand with a one-over-par 73. When his handicap hits bottom, it will probably be the lowest he’s seen in ages.

Low Net

  1. 63 – Bob Kennedy
  2. 67 – Jack Summers
  3. 68 – David Harbour

Low Gross

  1. 73 – Jack Summers
  2. 81 – Maddie Levy
  3. 82 – Bob Kennedy and Howard Jones

The course seemed to play a little tougher – or should I say, less easy – than it did Wednesday. There were only nine birdies in the group. Bob Ewing accounted for one third of that total. Summers, Jones and Bob Kennedy claimed the rest. The scores returned to normal with players averaging three strokes over handicap. The weather was perfect. The course is in great condition. And smiles decorated the faces of all the participants – even Sandy Wiener’s!

Cooler Weather – Hotter Golf

Ron Dobkin – eleven below handicap

It defied explanation. Fifteen Camelback golfers decided to bring their “A” games to the course all on the same day. Scores averaged more than three strokes below what would have normally been expected. Forty percent of the field posted scores in the 70s on the Ambiente course. Some golfers played very well; others played better than that.

Ron Dobkin rode his well-earned 21 handicap in route to a gross 79, net 58. He was eleven strokes under his handicap. It was his best round in two years. Interestingly enough, the competition was so tough that Dobkin’s net 58 only got his team a tie for second place. Regardless, it was a spectacular effort.

Dr. Jack Summer – gross 71

Dr. Jack Summers took medalist honors with a fine one-under-par 71. Bob Ewing was another competitor carding a super round five strokes under his handicap. Seven of fifteen golfers shot below handicap. Statistically, a golfer normally shoots three strokes over handicap. I’m not sure what virus had infected the field, but if it could be bottled and sold, there would be an insatiable market.

Low Net

  1. 58 – Ron Dobkin
  2. 64 – Bob Ewing
  3. 65 – Jack Summers

Low Gross

  1. 71 – Jack Summer
  2. 72 – Matt Flores
  3. 76 – Mike Smothermon

It was indeed an unusual day. With only fifteen golfers, it’s notable there were twenty gross birdies. Every single hole on the front side yielded at least one birdie. The third hole gave up four of them. There were eleven net eagles and one net double-eagle. Ron Dobkin had a net one on the challenging ninth hole. More than eighty percent of the scores recorded were net pars or better. The average gross score was 82! If I were to pick one word to describe Wednesday’s play … Wow!

In the Spirit of the Season – the Gift of Camaraderie

Bob Sznewajs' team takes first place
Bob Sznewajs’ team takes first place

Camelback golfers teamed up with golfers from Gainey Ranch in a fun event Friday. The competitors played on the magnificent Ambiente course at Camelback Golf Club. Not only does Ambiente offer a spectacular Scottish links style course, it is in immaculate condition. Unquestionably, it’s the finest course in the area.

Van Ark wins low gross
Van Ark wins low gross

When the last man walked off the course, the team of Bob Sznewajs, Roland Brendel and Howard Jones had conquered the field. Playing a Modified Stableford format with the team’s best ball, they were exceptionally strong racking up 36 points. The team of Mark Van Ark, Pat Collins and Howard Garr played extremely well scoring 33 points. On any other day, that would have probably been good enough to easily beat the field. Ron Dobkin and David Harbour both played well, but didn’t get the support needed from their teams to climb to the top.

Low Gross

  1. Mark Van Ark – 76
  2. Roland Brendel – 78
  3. Howard Jones – 79

Low Net

  1. Howard Jones – 63
  2. Mark Van Ark – 66
  3. David Harbour – 69

Everyone finished with a smile. With absolutely perfect weather, a fabulous course and great company, it was a wonderful day to be in Scottsdale, Arizona. There were no snow shovels, no mukluks and no signs of frostbite. Some place better to tee it up? I can’t imagine where that would be.

Here’s a look at the “net scores” turned in on the day. We played from the forward tees (equivalent in slope and rating to the middle tees at Gainey) so the course was far gentler than it could have been.Stats20141219

Gobble, Gobble, Gobble . . .

Ogrin speaks with the mortals while standing on water.

Men’s Day, one day before Thanksgiving:  If you were wondering who the turkeys were and your names are not Nichols or Ogrin, then look in the mirror.  On a day when the course beat up 95% of the field, the team of Mike Nichols, Bailey Ogrin and guests from the law firm of Caprio & Crown won a “no contest” verdict with a nine point thrashing of the rest of the field.  Not only did they eat our dinner, but most of the desert as well with Bailey gobbling up five skins, Nichols & Crown one each leaving two left overs for Vlah and Hourihan.

As for the mere mortals with team scores clustered between 130 & 135, they were only 9 points behind the winners at 121.

Continue reading “Gobble, Gobble, Gobble . . .”