What does an 18th century English minister and sports betting have in common?

by , 25 April 2019
What does an 18th century English minister and sports betting have in common?
It took over 200 years for Thomas Bayes' work to be recognised.

With the invention of the personal computer Thomas Bayes' Bayesian analysis has gained wide spread acceptance in many different spheres.

Such as predictive models and artificial intelligence to name a few.

In its simple form the Bayesian analysis uses probability and reasoning to make a decision in the face of uncertainty, and this includes sports betting and gambling in general.

That's why today I want to delve deep into what the Bayesian analysis is and how you can use it to predict your next winning outcome.

Let's get started…
 
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What exactly is the Bayesian analysis formula?
 
The Bayesian analysis goes by many names. Inverse probability, Bayesian Updating and Bayesian Inference to name a few.
 
But it comes down to this formula:
 
P (B|A) = P (A) *P (B|A)/P (B)
 
If you want to know the probability of A when you know that B is also present (given), you can get the answer by multiplying you prior estimation of A (Probability of A) by how much more likely B is when A is present.
 
This may seem confusing to most, but let me explain using an example.
 
Using Bayesian analysis to predict the weather
 
Suppose you estimate that there is a 30% chance it will rain tomorrow.
 
And you know that on an average day there is a 50% chance of clouds in the sky.
 
You also know that the likelihood of clouds is 100% given that rain is 100% (there will always be clouds if there is rain).
 
You have the following information:
 
Formula =
 
P (B|A) = P (A) *P (B|A)/P (B)
 
P (A) = Probability of rain= 30%
P (B) = Probability of clouds= 50%
P (B|A) = Probability of clouds given rain= 100%
 
You wake up in the morning and are blessed with a new piece of information: there are clouds in the sky. You should now perform a Bayesian update on the probability of it raining, Given that there are clouds in the sky.
 
So, as we recall, P (A|B) = P (A)*P (B|A)/P (B) = chance of rain * chance of clouds given rain/chance of clouds = 30%*100%/50% = 60%
 
You can now update your belief about it raining to 60%.
 
So with a new piece of information your estimate of rain went from 30% to 60%.
 
But how does this work with sports betting?
 
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Bayesian analysis and sports betting
 
Suppose you’ve worked out that Liverpool have a 50% chance to win the match.
 
You also know that when they win, it rains 11% of the time, compared to the usual likelihood of rain at a Liverpool game of 10%.
 
Formula =
  
P (B|A) = P (A) *P (B|A)/P (B)
 
P (A) = Probability of Liverpool winning = 50%
P (B) = Probability of rain in a Liverpool match = 10%
P (B|A) = Probability of rain in a match when Liverpool wins = 11%
 
So, if there is rain, you know that P (A|B) = P (A)*P (B|A)/P (B) = 50%*11%/10% = 55%
 
There is a 55% chance that Liverpool will win.
 
So in summary the Bayesian analysis encourages the consistent testing of NEW evidence against your position.
 
Allowing you to refine your estimates of a likelihood of an event occurring.
 
This formula isn’t a crystal ball, but if you are confident in your evaluation of the evidence you have at your disposal, then the Bayesian analysis is a great tool to add to your sports betting strategy.
 
And you’ve got an 18th century English Presbyterian to thank. 
 
Until next time,
Christopher Ammon,
Head Tipster, The Winning Streak Team


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