The Kelly Criterion in Sports Betting

The Kelly Criterion, a mathematical formula derived by John L. Kelly Jr. in 1956, is a pivotal concept in sports betting that determines the optimal bet size to maximize the long-term geometric growth rate of a bankroll [1]. This concept is grounded in the principle that to maximize wealth, one must wager a fraction of the bankroll proportional to the edge divided by the odds, as expressed by the formula $f^* = \frac{bp - q}{b}$ [2].

Theoretical Foundation and Historical Developments

The Kelly Criterion's theoretical foundation is based on information theory, where the goal is to maximize the rate at which wealth grows [1]. Historically, the criterion was first applied to Blackjack by mathematician Edward Thorp in the 1960s, demonstrating its practical utility in gambling [3]. Later, in the 1980s, sports betting syndicates like The Computer Group adopted the Kelly Criterion to manage variance and optimize betting strategies [4].

Mitigating Volatility: Fractional Kelly Strategies

To address the extreme volatility and risk of overbetting associated with the full Kelly formula, professional bettors have employed Fractional Kelly strategies. This approach, such as the Half-Kelly method, sacrifices a small amount of theoretical growth for a significant reduction in variance and protection against model error [5]. The use of Fractional Kelly strategies underscores the importance of balancing growth with risk management in sports betting.

Conclusion

In conclusion, the Kelly Criterion has had a profound impact on the development of sports betting strategies. By understanding the theoretical foundation and practical applications of this concept, bettors can make more informed decisions to maximize their long-term growth rate. The evolution of the Kelly Criterion, from its initial formulation to the adaptation of Fractional Kelly strategies, highlights the ongoing quest for optimal betting approaches in the sports betting community.