The need for a Bayesian approach in betting

Following the Copa America this year, Dominic Cortis became the witness to two stunning statistical events. During this tournament, Mexico broke two records. Read on to find out how these records were conflicting in nature and what that means for using statistics in betting.

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The first Mexican national team record is an unbeaten run of 22 games. As Brazil was eliminated by Peru, Mexico was being touted as possible winners. Indeed the handful of Mexicans I met in the Golden State believed they have a shot at going all the way, even to beat then-favourites Argentina.

Their unbeaten run was however stopped by another record – their biggest ever loss in a seven goal deficit to eventual winners Chile. Let’s just say the Mexican Taquerías were a bit on the quieter side that evening.

However this provides us with another difficulty faced in modelling: how much to trust past results? As financial products state “Past performance is not a predictor of future results”.

The Bayesian approach

Odds may not apply in a generic fashion for every scenario. One can then use a Bayesian approach, where uncertainty is quantified and trust in a model is expressed in terms of how much one can believe the parameters used.

Mexico’s unbeaten run of 22 games was stopped by their biggest loss ever in a 7 goal deficit to eventual winners Chile.

Typically parameters used in models are assumed to follow a distribution of their own. To learn more about the application of standard deviation to measure betting probabilities go to the article How to use deviation for betting.

Will Kurt uses the analogy of Han Solo to explain how to apply Bayesian techniques. I would highly recommend to read the article, even if summarised here.

Kurt points out that in a scene of “The Empire Strikes Back”, Han Solo successfully flies the Millennium Falcon through an asteroid field even if advised by C3P0 that the probability of making it through is almost 4000 to 1.

C3P0 is not wrong, but he forgot to consider the fact that Han Solo is badass (literally quoting Will here, please excuse the plagiarism).

4000:1 outcomes are uncommon. 5000:1 outcomes are more-so but just in case someone forgot, Leicester City won the Premiership at these odds. Did the bookies dismiss that Leicester City FC were badass too just like C3P0 did?

Well, the Gems and Rhinestones blog states it as it is: we don’t know what the correct odds should have been. In the blog, we find that if the variance per team is doubled, the odds on Leicester should have been around 265. Just as a comparison, Pinnacle’s odds for next season, which are updated to the new information from 2015/16 are currently 21.00*.

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Source: pinnacle.com