Money Management in Sports Betting: Staking plans
One of the pilars of profitable systematic long term sports betting is Money Management. But, how should I do it? How much does it impact profit?
In this article we detail our approach to money management, what the available research shows and our backtest results.
Before delving into money management you need to decide which is more important
- Minimizing default risk, reducing the probability of bankruptcy
- Maximizing profit, increase the expected payoff
Depending on your decision and your risk profile (how short term you expect big gains) you can choose a staking plan. The plan will define how you will manage your money.
Staking plans
Assuming gains will be reinvested there are three common staking plans:
- Fixed percentage staking, you bet a fixed percentage of your equity
- Kelly staking, the amount of the bet is calculated with the Kelly criterion
- Progressive staking, increase the amount you bet after each loss
Fixed percentage staking fixes the stake size(the amount you bet) before each bet depending on the bank. The size of your stake should change with the quantity of available money. The larger the percentage you choose for each bet the bigger the risk of default and expected payoff. Depending on your Win/Loss ratio you can select a percentage that balances maximizing profit and minimizing default risk.
For example, in one of our Handball betting strategies the probability of picking a winning bet is estimated in 73%. Using a monte carlo simulation we estimated that the optimal percentage to bet was 10% of the available money on each bet. In real life betting the optimal percentage is re-calculated periodicly to take into account the current market, previous gains, changes in risk profile, etc.
Kelly staking is similar to fixed percentage staking, where the stake is calculated using the Kelly criterion. Kelly (1956) determined that a gambler should not aim to maximize the expected profit for each bet and instead should seek to maximize the expected log of the payoff. This approach makes a lot of sense because it is equivalent to maximizing the rate of growth of profit.
p is the probability of winning, q is the probability of losing and b is the odd.
A common choice is the “Half Kelly” staking plan, where the optimal Kelly fraction is multiplied by 0.5. Half Kelly has 3/4 the growth rate of the full Kelly but has a much less chance of a big loss or default.
The progressive staking plan comes from casino gambling, and in particular from roulette betting where the payoff is the same as the amount staked (odds of 2.00). The initial goal is to win a small profit with the first bet. However, if this bet is lost, the goal of every subsequent bet is to gain back the money that has been lost up to that point, plus the original target profit, returning to the original stake size once a bet is won. At odds of 2.00 the progressive staking strategy calls for doubling the staked amount after a losing bet. This type of staking has a large default risk although being the best when trying to maximize profit short term.
TL;DR Summary
In our experiments we actually use a mix of the three staking plans depending on the betting strategy. For the strategies with the worst and average Win/Loss ratio we use a capped Half Kelly plan. Strategies with the very best Win/Loss ratio we use a mix of progressive and fixed percentage plan.
We create our own custom staking plans depending on how much risk we are willing to take, the performance of the betting strategies being considered (sharpe ratio and average return estimated via backtesting, using historical data), liquidity of the market, number of arbitrage opportunities and more.
The Kelly staking has been shown to maximize long-term growth. However, this criterion demands for exact estimation of the true probabilities of the events. Be aware that the estimation error can have big impact on profit.
References:
- Thorp, E. O. (2008). The kelly criterion in blackjack sports betting, and the stock market
- Moya, Fabián Enrique (2001). Statistical Methodology for Profitable Sports Gambling
- Barge-Gil, Andrés and García-Hiernaux, Alfredo (2019). Staking plans in sports betting under unknown true probabilities of the event
- Snowberg, E. and Wolfers, J. (2010). Explaining the favorite–long shot bias: Is it risk-love or misperceptions?
- Baker, R. D. and McHale, I. G. (2013). Optimal betting under parameter uncertainty: improving the kelly criterion.
