# Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football

By Wayne Winston | Go to book overview

44
OPTIMAL MONEY MANAGEMENT

The Kelly Growth Criteria
Suppose we believe we have an almost sure bet on Colts — 12. We believe the Colts have a 90% chance of covering the spread. This would probably never happen, but let's assume that such a bet really exists. What fraction of our capital should we allocate to this bet? If we bet all our money many times on bets with a 90% chance of winning, eventually we will be wiped out when we first lose a bet. Therefore, no matter how good the odds, we must be fairly conservative in determining the optimal fraction of our capital to bet.Edward Kelly determined the optimal fraction of capital to bet on any one gamble.1 Kelly assumes our goal is to maximize the expected long- run percentage growth of our portfolio measured on a per gamble basis. We will soon see, for example, that if we can pick 60% winners against the spread, on each bet we should bet 14.55% of our bankroll and in the long run our capital will grow by an average of 1.8% per bet. Kelly's solution to determining the optimal bet fraction is as follows. Assume we start with \$1. Simply choose the fraction to invest that maximizes the expected value of the natural logarithm of your bankroll after the bet. The file Kellyxls contains an Excel Solver model to solve for the optimal bet fraction given the following parameters:
 • WINMULT = the profit we make per \$1 bet on a winning bet. • LOSEMULT = our loss per \$1 bet on a losing bet. • PROBWIN = probability we win bet. • PROBLOSE = probability we lose bet.

For a typical football point spread bet, WINMULT = 1 and LOSEMULT = 1.1. For a Super Bowl money line bet on Colts —240,

1 The story of Kelly's work is wonderfully told in Poundstone, Fortune's Formula.

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