You know whom to bet on, at what odds to bet on them, and why to bet on them, but not how much? The optimal stake for your tip can be determined using the Kelly Criterion.
Kelly Criterion
John Larry Kelly, Jr.
The essence of the Kelly criterion (also Kelly equation or Kelly formula) in sports betting lies in finding the optimal portion of the bankroll that you should bet on a given odds. The basis of the calculation is the Kelly equation, which, using the most accurately expressed probabilities of winning, leads to the exact portion of the bankroll that must be bet to maximize profit and minimize loss. It is a very advanced method that we recommend only to experienced bettors who fully understand the principle of value betting.
Kelly equation
The equation is named after the American scientist John Larry Kelly Jr., who was a colleague of the prominent American mathematician Claude Shannon at Bell Labs. Kelly himself based his research on Shannon’s earlier work on information theory and in 1956 published his own work in which he presented his formula for estimating what portion of the bankroll to risk in a sequence of bets with a positive expected value to maximize the rate of return. There are reports online that Shannon, together with his wife and mathematician Ed Thorp, successfully applied Kelly’s theory to blackjack and roulette in Las Vegas casinos and later celebrated successes on the stock market. Among the most famous investors who reportedly practiced the Kelly criterion in their investment activities is the legendary Warren Buffett. However, we have not verified any of this information.
Kelly equation formula
The Kelly criterion in probability theory denotes a formula for determining the optimal bet size to maximize profits. For the formula to work in practice, it is necessary to accurately determine the probability of the outcome we are investing in. If this assumption is met, the Kelly equation leads to higher long-term profits than any other strategy.
F = (B*P) – Q / B or
- F = percentage of bankroll to bet
- B = odds as a decimal (e.g., 2.50 – 1 = 1.50)
- P = probability of winning (e.g., 55% probability = 0.55)
- Q = probability of losing (e.g., 45% probability = 0.45)
Coin toss example
As a simple example to demonstrate the Kelly criterion, let’s use a coin toss. We know the coin is biased and heads will come up 55% of the time, while tails will come up 45%. However, the odds do not reflect this fact, so we bet on heads at odds of 2.00. In this case, the equation looks like this:
- (1.00 * 0.55) – 0.45 / 1.00 = 0.1 / 1.00 = 0.1
According to the Kelly equation, we should bet 10% of the bankroll. A positive percentage indicates an advantage in favor of your balance, so it will grow exponentially. See how the situation would change if we got odds of 1.80 for heads:
- (0.80 * 0.55) – 0.45 / 0.80 = -0.01 / 0.80 = -0.0125
In this case, the equation would result in a negative number. With a negative number, avoid the bet as it is unprofitable.
Advantages and disadvantages of the Kelly equation
Advantages
- The best method for determining the amount of stake to invest in a given bet. The Kelly equation maximizes your profits while minimizing your losses.
- Unlike flat staking and unit staking, it takes more variables into account, especially the value of the odds.
- The Kelly criterion works with the current value of the bankroll.
Disadvantages
- To use the Kelly equation, you must accurately determine the probabilities of winning and losing your bet, which is very difficult, in many cases impossible.
- Compared to other methods, it is more difficult to understand.
Frequently asked questions
1️⃣ How to use the Kelly equation in sports betting?
Using the Kelly equation, you will calculate the optimal amount of bankroll to invest in a bet to maximize profit.2️⃣ Is the Kelly equation optimal for every bettor?
There is no more optimal staking strategy in sports betting for maximizing profits. Given that its effectiveness depends on the ability to predict accurate probability distributions of chances, we would not recommend it to anyone who does not know about value betting and the expected value of a bet.
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