Thomas Bayes was born around 1701 in England, and divided his life between studying matters theological and mathematical. It wasn’t until after his death in 1761 that one of his studies “An Essay towards solving a Problem in the Doctrine of Chances” was submitted to the England’s Royal Society and posthumously acknowledged the significance of his work.
It took, however, until the advent of desktop computers – 200 years later – for Bayes’ work to really be appreciated and gain widespread acceptance. Since then Bayesian analysis has been interpreted and applied in many different spheres such as artificial intelligence. In its simple form the Bayesian approach is arguably the most sensible way to use probability and reasoning to make decisions in the face of uncertainty, and that includes gambling.
It applies an iterative process of assessing what you know about the probability of a future event, and then testing the impact of new evidence as it becomes available.
Bayesian statistics is a particular approach to applying probability to statistical problems. It provides us with mathematical tools to update our beliefs about random events in light of seeing new data or evidence about those events.
In particular Bayesian inference interprets probability as a measure of believably or confidence that an individual may possess about the occurrence of a particular event.
Bayesian statistics provides us with mathematical tools to rationally update our subjective beliefs in light of new data or evidence.
This is in contrast to another form of statistical inference, known as classical or frequentest statistics, which assumes that probabilities are the frequency of particular random events occurring in a long run of repeated trials.
Bayesian inference has its simple formula P(A|B)= P(A)*P(B|A)/P(B) which can be used even in the needs of betting, predicting weather, catching athletes who were using doping, election of candidate, etc…
Now, let’s transpose this to a sports betting example. Suppose you are interested in a Bayern Munich match, where you believe they have a 50% chance to win outright. You also know that
when they win, it rains 11% of the time, compared to the usual likelihood of rain in a Bayern Munich Match of 10%.
- P(A)= Probability Bayern Munich wins= 50%
- P(B)= Probability of rain in a Bayern Munich match= 10%
- P(B |A)= Probability of rain in a football game when Bayern Munich Wins= 11%.
Now, if you receive information about the weather, there is no need to scramble to consider how it will affect the odds. You can, as do many professionals in many fields (including sports betting), perform a Bayesian Update. If there is rain, you know that P(A|B)=P(A)*P(B|A) P(B)= 50%* 11%/10%= 55%.Notice that P(B|A) P(B) is the same as asking “how much More likely is B happening, given A?”- In this case. 11/10 (11%10%).Once you know that B is a given, your new estimation of A can change accordingly by simply multiplying them.
Another good example are scouts who start with pre-conceived notions of players from watching their game, and then look at their stats to further analyze and learn about the player. Finally, they make an opinion on the player based on the combination of these two things. Consider a scout who is analyzing two players, Stewart Downing or Adel Taarabt. From prior analysis, these two players were determined to have had poor seasons, and thus were negatively rated by scouts. However, when analyzing these players, a far more appealing assessment was made. They found that Downing averaged 2.6 shots and two key passes per 90 mins while Taarabt averaged 3.9 shots and 2.2 key passes per 90 mins. These statistics are usually highly indicative of future performances and thus scouts became more interested in these players. With these stats in mind, the outlook of these players are updated. Then, scouts look to next season to determine a final judgment regarding these players. In the next season, Downing’s performances with Liverpool begin to look a little better. However, Taarabt still gave the ball away far too often and showed that he was a poor decision maker. With these two years of information, scouts were able to update their original opinion of these players by analyzing the statistics and watching them play another season. As a result, the scouts would have probably suggested to his club that they should buy Downing. In fact, Downing was signed to a new team and is now on pace for a career season while Taarabt has continued to struggle. If the scout had not accessed these player’s statistics he probably wouldn’t have suggested buying either one. However, had he only based his judgment on only these stats, he probably would have suggested signing Taarabt. Thus, by using a combination of both looking at their statistics and watching how they perform at their games, it was clear that Downing was the better option.
There are many statistics in use, many of them provoke a debate whether Bayesian statistics is the best access to the problem, but in the wide range in which Bayesian statistics can be used. There is certainly a dazzling future, as far as statistic in sports frames. If you have actual prior-information, then there is just one way to go, and that is Bayesian statistics.