Analytical (Kelly) And Numerical (Solver) Solutions

Many sports trading problems yield to both an analytical and a numerical solution.



In the above example, the numerical solution (using Solver in Excel) to minimizing the difference between expected value and volatility drag over a sequence of similar bets equals the analytical solution (using Kelly) for the same sequence!

Equivalent Single Bet

With multiple bets (illustration only) in a single win market, what is the equivalent single bet that best summarizes the overall position?

As the worst win-loss outcomes are to either win only the minimum profit or lose the total stake, then the most informative summary position is a combination of both scenarios.

Volatility Drag

Aaron Brown, author of The Poker Face Of Wall Street, makes a strong case for the negative impact of volatility drag on expected value with respect to the Kelly Criterion in the following posts:
  * Short-Term Variance
  * Risk Of Ruin And Kelly Betting
  * Bankroll Performance Simulator
  * Betting Strategy.

The above before and after illustrations show a worked example of setting stakes to match a zero difference between expected value and volatility drag.