Section 4: Bayes’ Theorem and Sports Betting Touts
A brief discussion of Bayesian probability is relevant to begin an examination of the claims of sports betting ‘touts.’ Bayes’ theorem relates to the conditional probability and marginal probabilities of two given events, where both events have non-zero probabilities. In other words, it examines an outcome based on the known background distribution from whence that outcome arose.
The basic idea is perhaps most easily explained through this common example: A patient in Country X sees his doctor to determine whether he is suffering from disease Y. A preliminary test is administered, and the test comes up positive. The doctor administering the preliminary test already knows that 5% of the inhabitants of Country X suffer from disease Y. Through extensive research, the doctor also know that when the patient actually has the disease, the test will come up positive 100% of the time (there will never be a false negative), and when a patient does not have the disease, the test will erroneously come up positive 10% of the time (a false positive).
Given that the patient’s test came up positive, what is the probability that he actually has the disease? Initial reactions are generally that the probability is high – after all, the test was positive, so therefore the patient will probably actually have the disease somewhere around 90% of the time! In actuality, this results-based logic falls apart when examined from a Bayesian perspective, and when we consider the background distribution.
Ninety five percent of inhabitants do not have the disease, but 10% of them get a false positive anyway. Only 5% of inhabitants actually do have the disease, and all of them come up positive. Thus, only about 1/3 of the total number of positive results are from people who actually suffer from the disease. When a population of 1000 people is tested, 50 will suffer from disease Y and will test positive, while the other 950 will be healthy. Yet 95 out of the other 950 will still be given a false positive, and thus 95 out of the 145 total positive tests will actually be false. We know that the patient took the test, and we know that the test was positive – but all that tells us is that the patient is a member of that group of 145 people whose tests were positive. Thus, it is not quite time to despair – there is still 65.5% chance that he is in fact not suffering from disease Y!
The patient in Country X was horrified to see a positive test result, because he assumed that it was almost certain (~90%) that he had the disease, while in reality the probability was only 34.5%. Many touts use this same false, results-oriented trickery to fool customers into thinking that they are beating the lines, when in fact they are just lucky.
Consider that if 5% of sports bettors can actually beat the lines in the long run, and 80% of those are winners over a 2 year period, and 95% of bettors are hacks who are just flipping coins , and 20% of them are winners over a 2 year period (due to variance), then this means that 82.6% of bettors who are winners over a 2 year period are actually hacks who are long term losers!
Thus we stumble upon the golden tout philosophy: there are so many hacks out there, that some portion of them are going to experience several standard deviations of variance, and will be winners over a period of several years, despite the fact that they are ‘truly’ long term losers – in practicality, that adds up to hundreds of touts who have built huge winning records through blind luck, and are selling their picks to an unwitting public. Yet despite their record, these Bayesian touts have at best a 50% win rate looking forward, if not worse.
An even simpler way to examine this is through Warren Buffet’s famous quarter game: say all 300 million Americans paired up and flipped a quarter, with the winner keeping the loser’s coin. The next day, the 150 million winners would pair up and flip, and again the winner would keep the loser’s quarter. The survivors would repeat this for 22 days, at which point 71 players would be left, each having amassed a fortune of $1.04 million in quarters. The world would praise these 71 incredible flippers, laud them as geniuses of coin calling, and examine in minute detail what exactly it was that made them so good at calling heads or tails. No doubt dozens of books titled, “How I Became a Millionaire in Three Weeks doing nothing other than Flipping Quarters” would be published. This scenario seems laughably ridiculous, but this is almost exactly what sports betting touts who sell their picks to an unwitting public are doing! Touts base all of their results on past metrics which hold no predictive value, and disappear as soon as they have a bad season only to reappear with a new name and website when they run hot again.
So how can a smart investor figure out which touts are sharps with a positive expectation for future performance, and which are just members of a large crowd of losers who happened to hit a lucky streak? How can he tell which claims are significant, meaningful indications of future success, and which are nothing more than lucky hot streaks?
1. Justification for success:
An analyst with extremely complex statistical metrics, such as my math model, is more likely to be successful in the future than a gambler who won 30 out of 50 games, but can’t offer a reason other than, “I’m the million dollar man, I just pick locks.”
2. A very, very large sample size:
Some touts sell their entire product based on a 15-0 hot streak, or winning 60 out of 100 games. Sample sizes this small are completely meaningless. If you flip 100 coins over and over, you’ll get heads 60 or more times about 1 out of every 30 times, which is pretty frequent when you consider the number of touts there are trying to sell their picks based on tiny sample sizes.
On the other hand, my college football Best Bets have gone 1322-1065-41 (55.4%), my NFL Best Bets have gone 916-767-40 (54.4%) and my basketball picks have gone 6649-5687-244 (53.9%) over my 30 year career as a public handicapper. Now that is a meaningful sample size, and every statistical test, measured to the highest degree of certainty, would conclude that I am without question able to beat the Vegas line over time. To be fair, the line has gotten sharper over my career and it as not as easy to win as it used to be, but I continue to sharpen my analytical tools to say ahead of the odds makers.
3. Clear statement of records:
Many touts fudge their numbers by quoting ridiculously selective, meaningless statistics. Claims of, “90% winning percentage on Thursday night inter-conference games,” or “undefeated on Monday nights in November,” abound in the tout industry. Numbers such as these which are artificially created ex post facto are so ridiculous that any serious investor should quickly learn to ignore them.
I care about only one statistic: my overall record. Do not be fooled by the lucky few touts that emerge with hot streaks every year. There are so many thousands of touts spouting drivel that a few of them are bound to get lucky once in awhile. I have reasons to expect future success to match my past record, and I have been a consistent winner for 30 years. I don’t win every year but the stock market doesn’t go up every year either. However, my Best Bets, and the stock market, are both good investments over time and it is important for gamblers to think more like investors. Gamblers tend to think in the short term while investors think long term. Be an investor, not a gambler.