Bayes Theorem in short is a method of analysing data.
Horse Racing is a very good model for using Bayes Theorem because it deals with degrees of belief. A purely systematic approach is far too rigid whilst frequency models are not a good fit either.
Thomas Bayes came up with the formula P(H\E) which is simply the conditional probability of an hypothesis H given some evidence E.
What we want to do is sort out which evidence is important and the formula above enables us to do just that.
The first step is to gather data for analysis; this is where a system comes in very handy. A system is a set of rules (few the better) which provide a selection for a race.
As an example lets say you have researched a system and have gathered 500 results. You want to find out how winners last time out fared against the system as a whole. Of the 500 selections, 100 were winners and 400 were losers, sifting through the data you record that 100 selections had won last time out and 40 were system winners.
We can see from these basic figures that its looking pretty good for last time out winners but rarely does it look this obvious, what we need is a way to calculate pieces of data to clear an otherwise muddy picture, this is where Likelihood Ratios come in.
The best way is to show you using a simple table.
Filter Winners |
Total Losers |
40 |
400 |
100 |
60 |
Total Winners |
Filter Losers |
(Filter Winners x Total Losers) Divided by (Total Winners x Filter Losers) (40 x 100)/(100 x 60) = 2.666
2.666 is then our Likelihood Ratio for last time out winners in our system under review. The Posterior odds are system winners divided by systems losers, in this case its 0.666 (40/60)
We then calculate 0.666 x 2.666 = 1.778, we now add 1 to this figure giving 2.778.
To bring us back to a workable percentage we divide 1.778 by 2.778 = 64% The system running normally with its rules has a strike rate of 20%
This particular way of using Bayes theorem has increased the strength of the system selection to 64% using just one piece of information.
Sample size is very important and given enough test results from a researched set of system rules, Filtering can reveal strength and weakness which may otherwise lay undetected.
We are looking at a small Filter sample so caution must be maintained. But using this example shows that pieces of information can be filtered and assessed for its effectiveness, whether improving a plan or filtering out non production material.
It’s easier done on a spreadsheet but can be done on a calculator; it’s a very interesting past time in its own right if you like number crunching but also if you like hunting for as of yet uncovered angles which may turn your system into a nice little earner.
The more filtering you do,the smaller the sample size, so less reliable, build up a good sized set of Data on a system and then let Thomas Bayes help you on your way!
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