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Although I'm not trying to get so deeply into a mathematical discussion as to confuse anyone, I thought that I would also offer up a useful formula for all of those who enjoy modeling and are eternally unsure if their race sample size is large enough to base future expectation with confidence...namely, to wager, or not to wager.
The following formula will approximate the minimum number of races necessary to accomplish the above stated goal with a 90% confidence level:
WIN % x LOSS % x 1.645 x 1.645 / E / E
where E = WIN % - (2 x ROI) / AVERAGE MUTUEL
If you require a more stringent confidence level, then replace 1.645 with 1.96 (for 95% confidence), or with 2.575 (for 99% confidence).
As an example, a 20% win rate, coupled with a 1.20 ROI and an average mutuel of $15 would result in the following:
E = .2 - (2 x 1.2) / 15 = .04
.2 x .8 x 1.645 x 1.645 / .04 / .04 = 270.6
Therefore, after modeling, this can be used as a tool to determine which models can be expected to produce long term results, and which models need further testing before such assumptions can be made.
Have fun!
THE GENERAL
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