3 Mar

Betting with the Kelly Criterion Formula

How to Use Kelly Criterion in Sports Betting

How to Use Kelly Criterion in Sports BettingThe Kelly Criterion is a unique betting system that combines the science of probability theory with the fundamental responsibility of bankroll management. Universally recognized as the most statistically effective scientific gambling method, the Kelly Criterion lays out a specific formula for bet sizing. It takes its name from Bell Labs’ scientist and researcher John L. Kelly, Jr., who co-developed the formula alongside associate research partner Claude Shannon, the world famous mathematician known as “the father of information theory”.

Does the Kelly Criterion Work?

Yes, in terms of sports betting strategies, the Kelly Criterion is recognized as the most effective scientific gambling method for long-term use. That is not to say that anyone who uses the criterion will make money. As the old adage goes, “There is no such thing as a sure thing.” And there are certainly no guarantees in gambling. Las Vegas would have become a ghost town years ago, were that the case. But to reiterate, compared to all other bet-sizing formulas, the Kelly Criterion is hands-down the most successful.

The purpose of the formula is to achieve the same goal of every betting system – to minimize the risk of loss, while maximizing the potential for profit. The Kelly Criterion is all about creating a balance between risk and reward; increasing value while reducing volatility.

What is Kelly Percentage?

Kelly Percentage refers to the result of the equation. When all variables are injected into the formula – which I’ll explain in greater detail shortly – the result of the calculation represents the exact amount of money you should theoretically risk on the wager, relative to the size of your bankroll.

For example, if the answer is 3, it indicates a wager of 3% of your bankroll. Thus, if your bankroll is $1,000, you would wager $30. This is considered the “correct” amount of money to wager, based on your bankroll size, and the probability of the bet being won.

How to Use Kelly Criterion in Sports Betting

You’re probably thinking this sounds way too easy. You want to jump ahead, grab the formula, and start using it. But before you do, you need to understand how much is involved. In order to calculate the criterion, you need to know a few important numbers – not just the lines, but the probability of the bet actually winning.

The Criterion must take this into account so that you can place higher bets when the probability of winning is elevated. And therein lies the uncertainty. There is no way to know the exact probability of any sports bet winning or losing. We can make an educated guess. We can research every facet of an event, from the individual athletes, to past performance records and power rankings, right down to the weather forecast or field conditions (where applicable). There are a multitude of factors to be considered, but in the end, every evaluation comes down, in part, to personal opinion.

If you consider yourself highly knowledgeable, it could be your own personal opinion. Or, you can purchase picks from a professional handicapper who computes this knowledge for a living – which still means you’re relying on the handicapper’s opinion. Better yet, you could use the opening lines (prior to any shifts) presented by the almighty oddsmakers. They are considered to be the most accurate “implied odds” of all, statistically and theoretically speaking, of course.

If you don’t already have a method in mind, I suggest using implied probability from the opening lines, if for no other reason than these odds are set by people, and sophisticated computer algorithms, that know exactly what they’re doing. You can learn more about it here:

However you choose to produce win probability, once you’ve got a figure down, you’re ready to begin using the Kelly Criterion formula.

How is Kelly Criterion Calculated?

Every time you prepare to place a wager, gather the right information and inject it into this formula:

(bp – q) / b = f

  • b – This factor represents the multiple of your bet that you stand to win. You can figure this out by looking at the odds. Using the US Odds format:

    • With positive odds, such as +150, divide the odds by 100. [150 / 100 = 1.5]. So the multiple would be 1.5.

    • For negative odds, like -150, the calculation is reversed. You divide 100 by the odds. [100 / 150 = 0.66]. Here, the multiplier is 0.66.

  • p – This factor represents the probability of winning the wager. Remember, probability is subject to interpretation. If you decide the probability of winning is 44%, you convert this to a whole number by inserting a decimal two spaces to the left. Thus, 44% = 0.44.

  • q – The easiest of all, this factor represents the probability of losing the wager. It’s simple, because it is the opposite of “p”. In other words, 1 – p = q. If p is 0.44, then [1 – 0.44 = 0.56], so q = 0.56 (i.e. a 56% chance of losing).

  • f – This last factor represents the solution to the equation, which determines the Kelly Percentage, or the percentage of your bankroll worthy of staking on the wager.

Example 1

Let’s see the formula in action. We’ll assume you’re looking to bet on odds of +150, with a 44% probability of winning; 56% probability of losing.

b = 1.5
p = 0.44
q = 0.56

[(1.5 * 0.44) – 0.56] / 1.5 = .05

After injecting the integers into the formula, we find that f = 0.05, or 5%, meaning this bet is worthy of 5% of your total bankroll.

Example 2

Let’s try another example, this time where the odds are lower, because the probability is higher, as is often the case with moneylines on an odds-on favorite. We’ll say the odds are -150, with a win probability of 60%; loss probability 40%.

b = 0.66
p = 0.65
q = 0.35

[(0.66 * 0.65) – 0.35] / 0.66 = .119

Due to the high probability of winning, in combination with relatively favorable odds, the Kelly Criterion formula suggests wagering 11.9% of your bankroll on this wager. For the record, that’s an incredibly high percentage, and one you’re not likely to find in a realistic situation unless you’re calculating line movements (instead of opening lines). I would never suggest betting anywhere near 12% of your bankroll on any one bet. See the Pros/ Cons section below for additional information.

Example 3

Let’s try one more example. This time, the odds are -110 with a probability of 40% to win, 60% to lose.

b = 0.909
p = 0.40
q = 0.60

[(0.909 * 0.40) – 0.60] / 0.909 = -.394

This time, f = -0.394, a negative number. When the solution to the formula is negative, it simply means this is a bad bet. You should not be making this wager at all. There is no expected value in it; or rather, the expected value is negative, meaning you can expect to lose money.

Expected Value in Kelly’s Scientific Gambling Method

Expected value is a term used to delineate the value of a bet. It can either be positive or negative. If the expected value is positive, the probability of winning is higher than the implied probability of the odds. In this case, the bet is worth making. If the expected value is negative, then the probability of winning is lower then the implied odds, thus the bet is not worth making. The ability to quickly and effectively determine a positive or negative expected value is perhaps the greatest advantage of the Kelly Criterion. Knowing exactly how much of your bankroll to invest when the value is positive – that’s more like the cherry on top.

Pros & Cons in Using Kelly Criterion System

Like most gambling systems, there are some distinct advantages and disadvantages in using the Kelly Criterion. Let’s start with the good stuff.

  1. It’s a simple, straight-forward way to size your bets. Inject the numbers into the formula, calculate the results, follow the advice.

  2. Once you get the hang of it, it’s really easy to calculate the formula. Over time, you’ll be able to recognize positive and negative expected values without doing all the math. In positive situations, you do the math to determine the bet size.

  3. It takes into account bankroll size by suggesting bet units in percentages. In this way, absolutely anyone, with any amount of money in their bankroll, can use it.

  4. Kelly Criterion applies theoretical values to each wager, which is the prime catalyst for its ability to correctly balance the growth and security of your bankroll (i.e. risk vs. reward).

  5. It eliminates the all-too-common mistake of placing bets that have a negative expected value. This is especially common when a bettor finds an opportunity to bet on something with an above 50% win probability. They don’t take into account the impact the odds have on the value, which often leads to placing bets with a negative expected return. Without this formula, such situations are virtually impossible to recognize.

  1. It only works when you’re able to accurately pin down the probability of a bet winning or losing. Without this element, the system cannot possibly be correct.

  2. The system can be very aggressive in certain situations. In our Example 2 above, the criterion suggested wagering nearly 12% of your bankroll. Most strategies consider 10% to be too high for a single wager, so 12% seems outrageous. Yes, it’s a good opportunity, but let’s remember the probability of winning was 65%. About one in three times, this bet will lose. You don’t bet the house on those kind of figures. It is for this reason that some bettors use what’s called a Fractional Kelly Strategy. Everyone has their own idea of what fraction is appropriate, but the most common is half. Thus, whatever percentage the formula suggests betting, you only bet half. However, for this method to work, you have to follow the half-bet rule on every single wager, without exception.

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