Bayes’ Rule Applications in Sports Betting
The instant gratification and excitement that comes with gambling is undoubtedly addicting. Many gamblers believe their superstitions and good luck charms will someday pay off in a big way. However, as the math has shown time and time again, casinos are rigged against the players in the long run. Aside from the highly skilled card counters at the blackjack tables, the expected value of any casino guest is negative, statistically speaking. But with the Supreme Court lifting the federal ban on sports betting in 2018, there is now a new avenue for bettors to explore, specifically the mathematically minded.
One of the biggest issues with applying Bayes’ Rule to real-life situations is the inability to accurately assign probabilities to uncertain events. This is especially true in sports betting, where analysts must quantify what they know about the probability of a future event to then predict the significance of new data as it become available. However, there are plenty of scenarios where it is not only feasible but could be extremely helpful to use Bayesian analysis to predict the outcomes of sporting events. For example, weather data is becoming increasingly more accurate as technology advances, and we can estimate the probability of a certain weather event with high confidence. This leaves the sports bettor with only one variable left to their own interpretation.
Suppose we know that the probability of there being a tailwind when World Champion sprinter Christian Coleman competes is 0.9. Further assume that the probability of there being a tailwind in a race given Christian Coleman wins is 0.95. Since we can find information about weather patterns before a race begins, we can perform a Bayesian update to find the odds of Christian Coleman winning so that we can decide if placing a bet on him would give us a positive expected value. The only guesswork that we would have to do is estimating the probability that Coleman wins a race, which is tricky to actually calculate considering we would have to know the head-to-head records against all his competitors and set an arbitrary date to start our analysis. Here we will assume the probability that he wins is 0.85. If there is a tailwind, then we know that P(A|B) = P(A)*P(B|A)/P(B) = (0.85*0.95)/0.9 = approximately 0.897. If your calculated probability based on Bayes’ Rule is better than the implied odds of the bookie or casino, then you should consider placing a bet on that sporting event.