4rabet: Bayesian analysis methods and sports betting

Thomas Bayes, born in England around 1701, led a life centered on two research themes: theory and mathematics. It wasn’t until his death in 1761 that he submitted one of his studies, “Solution to the Problem of Chance,” to the Royal Society, with his significant contributions recognized posthumously.

However, it took the advent of desktop computers—200 years later—for Bayes’ work to be truly appreciated and widely acknowledged. Since then, Bayesian analytical methods have found application in various domains, including artificial intelligence. Essentially, the Bayesian approach offers a pragmatic means of utilizing probability and reasoning to navigate uncertain scenarios, including gambling.

This approach involves an iterative process of assessing the probabilities of known future events and subsequently evaluating the impact of new evidence as it arises.

Bayesian Analysis in Sports Betting

Let’s illustrate this theory with a sports betting example, applying it to a scenario involving Bayern Munich. Suppose you believe Bayern Munich has a 50% chance of winning a match. Additionally, you know there’s an 11% chance of rain when they win, compared to a typical 10% chance during Bayern Munich games.

Now, let’s calculate:

– P(A): Probability of Bayern Munich winning = 50%
– P(B): Probability of rain during Bayern Munich match = 10%
– P(B|A): Probability of rain during a Bayern Munich victory = 11%

Upon receiving weather information, Bayesian updating allows you to adjust your odds accordingly. Similar to experts in various fields, including sports betting, you can perform Bayesian updating.

If it rains, you can calculate P(A|B) using the formula: P(A|B) = (P(A) * P(B|A)) / P(B) = (50% * 11%) / 10% = 55%.

Note that P(B|A) / P(B) represents “the probability of B occurring given A,” in this case, 11%/10%.

Given B, simply multiply them together, such as P(A) * P(B|A) / P(B), to update the estimate of A accordingly.

Bettors often sabotage themselves, stubbornly clinging to a specific outcome despite changing circumstances. Bayesian analysis counteracts this tendency by facilitating continuous testing of claims against new evidence, fostering a positive feedback loop that refines event likelihood estimates.

However, Bayesian analysis, like any tool, isn’t a crystal ball. As the adage goes, “Garbage in, garbage out.” Yet, with confidence in your estimates, Bayesian methods can uncover value in sports betting, regardless of what you’re testing.