Why I bet Golf. Spoiler: Sine functions model performance.
By: M Hayes
Tags: Golf, Gambling, Probability, Data Science

“Everyone should gamble a little bit every day, in case you are walking around lucky and don’t know it”

-According to my mother, Satchel Paige said that-

Apocryphal? Like Satchels true age, who knows?

I bet on golf. Specifically head-to-head (H2H) tournament matchups on the PGA tour. For the uninitiated H2H matchups are who beats who within the tournament. If player A plays poorly and finishes 140th out of 156 players but player B finishes 147th. Player A wins. Simple as that. If they tie, the bet is returned. If Player A finishes behind Player B, the bet loses.

Okay why do I bet golf? Compulsion? Boredom? The belief that I have a statistical edge? Yes, I believe I have a statistical edge although I won’t exclude boredom or compulsion. I believe I have a statistical edge-at least for the time being. A strong edge. I will assert that golf is currently an inefficient betting market that can be exploited. You can make money. Like playing Texas Holdem circa 2003. Or unrestricted card counting at blackjack. Eventually golf will become an efficient market where betting advantages shrink or disappear altogether. That is just the nature of the game. Whether its AI (call me), Wall Street quants, a Bill Benter analog or Billy Walters et al — Golf lines will change. The market will become more efficient. This article may accelerate that inevitable conclusion somewhat, but I would like to plant my flag and declare victory before that happens. Note, if you are into gambling or probability and don’t know Bill Benter, you should: https://www.bloomberg.com/news/features/2018-05-03/the-gambler-who-cracked-the-horse-racing-code. All genuflect. His white paper describing his horse racing algorithm is also worth a read.

Let’s do a little deeper dive. Why do I think I have a statistical advantage? Golf is more data rich than the average or even above average gambler realizes. I mean seriously data rich. Beat up Elon Musk and steal his lunch money at recess data rich. If golf were genetics, you could get 17 generations of fruit flies in an hour. Cure human disease, if not ignorance. 75% of PGA tournaments have field sizes of 120 players or more. In any one PGA tournament the number of H2H permutations is N*(N-1)/2 where N equals field size. In a tournament of 156 players (very common) there are 12,090 H2H match-ups available to analyze. While only 30 or so match-ups may be posted as weekly betting options, the prior data available to study statistical patterns is massive. In any 12-month period you might have ~400,000 H2H data points. (Note 1). In the 150-year history of baseball, there have only been 235,000 games played. So, 7 months of golf is equal to the entire history of baseball. Golf is data rich y’all. Overnight crypto billionaire rich. I disappeared into the rabbit hole of golf data a year ago and am just now emerging. I wish I had packed more snacks and several changes of underwear. Wait I work at home, so just snacks.

…what have I discovered. Golf betting is situational, and players have defined rhythms to peak performance. In golf, scoring averages don’t matter. Let me repeat scoring averages don’t matter! They mean nothing. Scoring averages at the venue in question were relevant during the height of the pandemic but no longer. Player rhythms matter! It took me a year and maybe 1200 hours to find the rhythms, but they are there. Maybe if I hadn’t taken LSD every day during that 1976 semester of Fourier transforms, I could have cut my research time in half but, oh well. Fourier transforms bored the fuck out of me. Still do. Sorry Dr. Chan. Thank you Dr. Johnson. Still, sine functions FTW.

Wait what? Lets circle back. To channel the late Slim Pickens “What in the Wide Wide World of Sports is going on here”? Are you telling me golf has bio rhythms? You mean you bet on the Gemini v the Capricorn during the equinox? Spoiler, never bet on the Capricorn. Of course I always bet on Max Homa v Joel (porn ‘stache) Dahmen ! Facetiousness aside, Im saying there are peak harmonics (for lack of a better term) correlated with performance. Alternatively, what I’m saying is that there is a defined pattern to optimal performance. That so called rogue data points might have an underlying explanation. That there is a defined lead up to peak performance and a defined declination following peak performance. Or patterns that maintain peak performance. At least individual peak performance. Data points that might appear rogue or random in other sports can be validated in golf due to massive data sets available. D.E Shaw didn’t validate “ghost patterns” in financial markets with tiny data sets, he had a more than a few popsicle sticks available to do his homework assignment. Or so I’m inferring. Golf has millions of popsicle sticks. You can build anything. Hey look it’s a dreamsicle Large Hadron Collider. Is that Burning Man? One more time, golf is data rich. Especially if you are willing to work a little.

Okay but real talk does back testing in golf and finding patterns yield a positive ROI betting on golf. The answer is a a qualified yes. There are some exquisite modeling techniques (Note 2) available in golf that will confidently predict the outcome of randomly generated H2H matchups that will NOT work when betting. That will not produce a positive ROI or even win at the predicted rate. Guys setting handicapping lines and choosing match-ups available to the betting public are very smart…very clever. Whether generated by Hidden Markov models, Alchemy, Las Vegas Voodoo or the imaginary Bayes-Nostradamus model, most golf matchups posted for betting fall outside the lines of traditional analysis. And throughout my years of handicapping, I seem to be victim of the Heisenberg Uncertainty Principle of Handicapping — observe a trend and in so doing, change its nature. Instant reversion to the mean. As a countermeasure, when I analyze golf and find a pattern, I always do binomial distributions. I generally don’t blink for a binomial distribution under a 100,000:1. In excel, I use this: 1/(1-binomdist(numbers, trials, probability, true))>100,000. But if you spend enough time analyzing golf you will find patterns with binomial distributions in excess of 1E+8. Sometimes 9 or 10. Ive seen one at 1.5E+15 (Note 3). And that should give you a little confidence when throwing your 20 quid at a match-up that you’re making a statistically sound betting decision. You may not win the individual bet, but over time a strong definable ROI will emerge. Are there strong definable patterns in golf? Yes! I will articulate my strongest one in an abstract manner. Read on.

Let’s get right to it: Let A1 and B1 be variables associated with Player A & B. Let C equal (Note 4) be a constant. Then, if delta sine (lets call it dsin) defined as sine (C*A1) — sine (C*B1)>.2, player A beats Player B 63.23% of the time (Note 5). Nothing else matters. 51,106 data points from a random sampling of 245,677 H2H matchups (Note 6) back up this assertion. Data used from 10–04–18 to 10–28–21. Done over and out. Im stealing your girlfriend. See ya. Nerds rule. Gold medal. Give me a tiny flag and let me do an eight second victory lap around the kiddie pool. USA! USA! In actual matchups posted since Jan 9, 2020 through current, dsin>.2 has occurred 611 times out of 2629 match-ups for a win % of 59.74%. ROI of 11.48%. If we only look at tournaments with elite fields dsin is a phenomenal 68.8% with a 28.39% ROI. 183–83. 266 matchups fitting this criterion since Jan 9, 2020. This unbelievable win % and ROI might be just an arbitrary but highly misleading stat in another sport, but in golf we have maybe 40x additional data points available to confirm the validity of dsin. For the record back testing would suggest that among elite players where dsin>.2 a future win rate of 65–66% with an ROI of 20–22% is more realistic. At least while golf remains inefficient. So we have gotten a little lucky, not a problem.

There are other patterns besides dsin in golf but dsin provides at least one foundation for golf analysis and betting. In addition, like the intersection of dsin and elite tournaments, we can look at other data sets or the intersection of one or more multiple data sets to identify matchups that show a positive ROI. Then we can look at the union of intersecting sets to generate a global set of matchups that will most likely generate a positive ROI. Currently I use six variables to analyze matchups. Strength of Schedule (SOS) is one of those variables. In general SOS is not equal to nor correlated to purse money. Note: What I have not been able to do is to generate a unique estimated win % per match up to take advantage of the Kelly Criterion for optimal bankroll growth. That has proven to be an endeavor with a very short half-life. Variables which are well behaved in back testing are poorly behaved within posted matchups. I wonder if I can lure Benter out of retirement? I have fruit roll-ups.

Golf can be beaten. You can be that guy in Michigan who beat up the state lottery for a few years. Golf can be beaten-at least for the near term if you do your homework. Especially if you can connect variables to your golf database not easily observable to the betting public. Weather data, specifically pollen counts anyone?

Good luck.

M99.

I’d like to acknowledge the Lloyd Danzig article here on Medium: https://medium.com/@lloyddanzig/quantitative-sports-betting-6976e1ceaf0f. While not directly relevant to the material here, that article provided a departure point never previously available to me. It fundamentally changed my approach to analyzing data. Without it, I’d be lost. I wouldn’t even know here the rabbit hole was. And while there were days where I wished I had never found the rabbit hole, ultimately Im grateful. Lloyd Danzig is brilliant. I do have some thoughts on P(A,B) though…big thoughts. Expect a prequel. Teaser: F(X,Y)= X*Y/(1-X-Y+2*X*Y) for 0<X,Y,<1. Independent if not original (??) discovery. While F(X,Y) was a trivial derivation, its utility is impressive and I suspect many future applications will be found. Another victory lap around the kiddie pool.

1. In addition to the final tournament results, there is an additional data trove of data from H2H matchups by individual rounds. That could increase your data set by 3.5x.

2. Ive found one technique in particular using F(X,Y) & P(A,B) referenced above that is exquisite. Doesn’t work for betting, but it sure is pretty otherwise.

3. Yeah there are a few bullshit filters in that one, but there is truth in there somewhere.

4. As I write this article, I realize that C is likely not a constant but presumably variable by player. Time to pack more snacks. Small refinements are foreseeable. Major refinements are possible.

5. Im not going to reveal A1 or B1. However, should you want to reverse engineer this, you might want to string a guitar with piano strings. Or play around with fret patterns, there aren’t that many permutations.

6. Subsequent to the 1st draft of this article, I found a formula to calculate all permutations for all players within a tournament simultaneously. Then I sum the results. Other than a self-reassuring audit check, no need to generate ~250K random H2H matchups. Dsin is actually better than indicated above. 189258–102710 for a .6482 Win% over the last 96 tournaments. While dsin can fluctuate with and is partially correlated to player abilities, dsin has an easily observable higher amplitude among top rated players than average tour players. That’s great news for handicapping H2H matchups, as generally the posted betting matchups are restricted to top rated players.