Bayes Stake Calculator

Kelly staking is a function of win probability (p = wins /events) but not of the magnitude of wins and events. So, in Kelly terms, $(p = \frac {26}{52})$ is equivalent to $(p = \frac {260}{520})$ but to the SportsTrader these historical records represent qualitatively different pieces of information. We have more confidence in the second proportion than in the first.

You can use our online Bayes Stake Calculator to evaluate your own betting strategies.

Canadian statistics professor - David Beaudoin - suggests a potentially profitable trading strategy for the NBA Playoffs based on a historical record of $271$ wins from $484$ events at decimal odds of $1.90909$ $(-110)$. Kelly recommends a stake of $7.58\%$ to capitalize on this edge. However, using the no-vig odds of $2.00$ to generate a prior and using the historical record to create a likelihood, we can calculate a Bayes stake of $5.36\%$.

This new Bayes stake reflects both the magnitude of the historical record and the probability of winning. By contrast, the Kelly stake only reflects the probability of winning.

In his excellent book, A Mathematician Plays The Stock Market, John Allen Paulos outlines a potentially disastrous trading strategy that on the surface suggests riches but in reality is likely to lead to poverty.

Once again, using our Bayesian approach, we calculate a stake of $4.49\%$ in constrast to a Kelly stake of $12.50\%$. If, however, Paulos had 10 years of data $(\frac {260}{520})$ then we would recommend a stake of $10.50\%$ whereas the Kelly recommendation would remain unchanged.

We strongly advise that you read both Market Efficiency and Bayesian Probability Estimation via the Beta Distribution and Modified Kelly Criteria - both of which publications inspired this post.

Note, the Confidence option represents how confident you are in the quality of the historical record. Selecting a low confidence level will reduce the calculated stake. As ever, there is limited error handling - Enjoy!