The Kelly Criterion: A Mathematician’s Approach to Sports Betting
Does it seem like the most successful bettors have some sort of knack for consistently increasing their profits? It does, doesn’t it? What you may not know is that there is a method they use—and it’s not a secret! It mostly comes down to smart money management and their strategy? The Kelly Criterion. It’s a mathematical formula that is designed to help bettors determine the best amount to wager based on the odds, which maximizes returns over the long term—and doesn’t risk too much money—or too little.
It was first introduced by John Kelly in 1956, and the Kelly Criterion has become a super popular tool in both the financial and betting circles. Want to know how it can work for you? We are gonna unpack how the formula works, its origins, and why some bettors absolutely swear by it. We’ll also go over the pros and cons so you can determine whether it’s that missing puzzle piece you’ve been searching for in your sports betting strategy!
What Is the Kelly Criterion?
The Kelly Criterion is basically a tool that helps bettors figure out how much to wager to get the most out of a bet without risking too much. It’s designed to hit a good balance between maximizing potential profit and minimizing the chances of going broke. By weighing the odds of winning against the possible payouts, you know how much of your bankroll you should bet safely.
Historical Background
It was first introduced by John L. Kelly Jr., a scientist at Bell Labs, in 1956. Kelly originally devised the formula to improve telecommunications signals, but it didn’t take long for people in finance to realize it also worked well for managing investments.
Transition
Eventually, the Kelly Criterion made its way into the sports betting world, where it became a really helpful and handy tool for bettors who want to make smarter, more calculated decisions when placing their bets!
The Formula Explained
Ok, don’t be nervous if you failed HS Algebra or hate all things math. The Kelly Criterion does look like a mouthful, but if you break it down, it’s not that scary. It just explains how much of your bankroll you should bet based on the odds and how confident you are in winning.
Breaking Down The Formula
The following is the formula:
f = (bp – q) / b*
Don’t let it intimidate you! It’s just a complicated-looking way of saying this:
- f*: How much of your bankroll to bet.
- b: The net odds (that’s the odds minus 1).
- p: Your estimated chance of winning.
- q: Your chance of losing (which is just 1 minus your chance of winning).
And below is what it means and how it’s applied to sports betting:
- f* is the percentage of your total bankroll the formula says you should bet. This is what we’re calculating.
- b is the net odds. For example, if the odds are 3.0, then the net odds are 2 (just subtract 1 from the odds).
- p is how sure you are that your bet will win, like saying, “I think there’s a 60% chance my team will win.”
- q is just the other side of that, your chance of losing, which is always 1 minus your chance of winning.
Next up? An example of the Kelly Criterion at work:
Say you’re betting on a game with odds of 2.5, and you think your team has a 60% chance of winning (so p = 0.60).
- The net odds (b) = 2.5 – 1 = 1.5
- p = 0.60 (your chance of winning)
- q = 1 – 0.60 = 0.40 (your chance of losing)
Then, you plug the numbers into the formula:
- f = (1.5 * 0.60 – 0.40) / 1.5*
- f = (0.90 – 0.40) / 1.5*
- f = 0.50 / 1.5 = 0.33*
What does it all mean? That you should bet 33% of your bankroll on this bet. The Kelly Criterion is saying, “You’re pretty confident, but don’t bet it all, just a healthy portion.” It helps you make sure you’re making the right-sized bet based on your confidence and the odds!
How the Kelly Criterion Applies to Sports Betting
The Kelly Criterion isn’t just some abstract formula—it’s a practical tool that can change the way you approach sports betting. By helping you decide exactly how much to bet and how to manage your bankroll, it brings a more calculated, less risky approach to placing bets. Here’s how it fits into the world of sports betting.
Figuring out how much to bet can feel like a guessing game. You don’t want to go all in and lose it all, but betting too small can feel like you’re not making the most of a good opportunity. That’s where the Kelly Criterion comes in. It gives you a specific percentage of your bankroll to bet, based on your confidence in the outcome and the odds. No more second-guessing yourself—it takes the emotion out of the decision and helps you make a smarter, more calculated wager. For example, if you’re really confident in a bet, the Kelly Criterion suggests you bet more, but never so much that a loss would hurt you too badly.
One of the hardest parts of betting is managing your bankroll. Bet too much, and a losing streak can wipe you out. Bet too little, and you might miss out on big opportunities. The Kelly Criterion helps you strike a balance by optimizing how much you should risk on each bet. It prevents you from betting too aggressively when the odds aren’t in your favor while also encouraging you to bet more when the odds look good. The idea is to grow your bankroll steadily over time without risking it all in one go. It’s a great way to protect yourself from bad runs while still making the most of your good picks.
The concept of Expected Value (EV) is at the heart of the Kelly Criterion. In sports betting, EV is all about making wagers where the odds are in your favor over the long run. The Kelly Criterion works best when you’re making positive EV bets, meaning the odds and your own analysis show that the bet should, over time, turn a profit. The formula pushes you to bet more when there’s a higher EV and less when the EV is lower. So even if you don’t win every bet (which nobody does), the long-term strategy is to come out ahead if you keep placing smart, positive EV wagers.
Advantages of Using the Kelly Criterion
The Kelly Criterion has become a trusted strategy for bettors looking to take a more calculated approach to their wagers. It comes with several key advantages that can help improve both profitability and long-term betting success.
Profit Maximization
The Kelly Criterion focuses on helping you grow your bankroll over time. Using the formula, you can determine exactly how much to bet on each wager to aim for steady growth without taking on unnecessary risks. It’s not about placing huge bets but rather making sure your money works for you smartly and consistently.
Risk Management
One of the most important benefits is how it helps manage risk. The Kelly Criterion prevents you from betting too much on any one outcome, reducing the chance of wiping out your entire bankroll. By betting only a calculated portion of your funds, you can weather losses without derailing your overall betting strategy. This approach creates a buffer, allowing you to continue betting even if things don’t go your way.
Disciplined Betting Approach
The Kelly Criterion promotes a more structured approach to betting, encouraging careful, well-thought-out wagers rather than impulsive decisions. This method helps you stay consistent in how you manage your bets, keeping emotions in check and maintaining focus on long-term success rather than chasing short-term wins. It brings a sense of control and reliability to the betting process.
Limitations and Considerations
The Kelly Criterion is globally regarded as a good betting strategy, but that doesn’t mean it doesn’t have limitations. While the formula helps bettors manage risk and maximize long-term growth, there are a few important factors to keep in mind when using this approach. Let’s look at the key limitations and considerations involved in applying the Kelly Criterion to sports betting.
Accurate Probability Estimation
One of the biggest challenges with the Kelly Criterion is that it depends on accurately estimating the probability of winning. The formula relies on you having a strong grasp of the likelihood of an event occurring, which can be tough to nail down, especially in sports betting, where unexpected outcomes are common. If your probability estimates are off, the formula will guide you to make bets that may be too risky or not aggressive enough, ultimately hurting your bankroll.
Misjudging probabilities can lead to over-betting on outcomes that aren’t as likely as you think or under-betting on ones that offer a good chance of success. This is why it’s so important to base your probability estimates on thorough research and analysis. Without that, even the best formula won’t protect your bankroll from poor decisions.
Overconfidence Risk
Another possible hazard of the Kelly Criterion is overconfidence. The formula is designed to help you maximize profit over time, but it assumes you’re making accurate predictions. If you overestimate your knowledge or how well you can predict outcomes, you could end up making overly aggressive bets. This is especially dangerous because, in the Kelly Criterion, larger bets are made when you’re more confident, which can lead to big losses if those predictions are wrong.
This overconfidence can also come into play if you’re on a winning streak. Bettors may start to feel like they have a handle on predicting outcomes, leading them to rely too heavily on their own judgment. It’s important to stay grounded and avoid letting emotions or streaks dictate your confidence level, as the Kelly Criterion won’t shield you from the risks of overconfidence.
Variance and Short-Term Volatility
Sure, the Kelly Criterion is great for long-term success, it doesn’t shield you from the ups and downs that come with short-term betting. Even when you’re following the formula perfectly, variance can lead to temporary losses. Sports betting is unpredictable; sometimes, the best odds and careful calculations won’t save you from an unexpected result.
This is why the Kelly Criterion is considered a long-term strategy—it aims to grow your bankroll over time, but there will be periods where variance works against you. Short-term volatility can be frustrating, especially if you experience a string of losses, but sticking to the strategy is key to success in the long run. Bettors need to be patient and prepared to handle these fluctuations without panicking or abandoning the plan.
Comparison with Fixed-Stake Betting
The differences are clear when you compare the Kelly Criterion to fixed-stake betting. In fixed-stake betting, you wager the same amount on every bet, regardless of the odds or the likelihood of the event. This approach is simpler and doesn’t require the same calculation level, making it appealing to bettors who prefer a more straightforward strategy.
However, fixed-stake betting doesn’t allow you to adjust your bet size based on the value of the bet. When a bet presents a high probability of success, the Kelly Criterion will suggest betting more, while fixed-stake betting remains constant.
On the flip side, fixed-stake betting won’t expose you to the risk of betting too much on a low-probability event. It’s undoubtedly a safer, simpler approach but doesn’t provide the same potential for long-term growth as the Kelly Criterion does.
Fixed stake betting can be more suitable for those who prefer stability over time, while the Kelly Criterion offers a more dynamic and flexible strategy aimed at maximizing growth. However, the latter requires more effort and accurate estimations to work effectively.
Practical Tips for Using the Kelly Criterion in Sports Betting
The Kelly Criterion can be a super useful tool for sports bettors looking to make more calculated, strategic bets. But as with any betting strategy, it’s important to approach it in a careful manner. Below are a few practical tips to help you get the most out of the system while minimizing the risks!
Start Small
When you first begin using the Kelly Criterion, it can sometimes suggest bet sizes that feel a bit large, especially if you’re not used to placing calculated bets. One way to ease into the system is by starting with the Half Kelly or Quarter Kelly approach. Instead of betting the full amount recommended by the formula, you can bet half or even just a quarter. This helps smooth out the volatility and lessens the impact of potential short-term losses, which can be particularly useful for beginners or those with smaller bankrolls. Many experienced bettors favor these modified versions as they reduce risk while still allowing for gradual bankroll growth.
Track Your Bets
Keeping a detailed log of your bets is really important when you are using the Kelly Criterion! Since the formula relies on your ability to estimate the probability of winning, tracking your results can help you refine your predictions over time. The more data you have on your past bets, the better you’ll get at understanding the nuances of probability and how your own estimations line up with actual outcomes. This feedback loop will improve your accuracy in future wagers, which is critical to making the Kelly Criterion work for you.
Stay Disciplined
One of the biggest challenges in betting, regardless of the system you use, is staying disciplined. The Kelly Criterion works best when you stick to the calculated bet sizes without letting emotions take over. Whether you’re on a winning streak or going through a rough patch, the key is to avoid increasing or decreasing your bets based on emotion or a “gut feeling.” The formula is designed to help you avoid impulsive decisions, which are often the downfall of many bettors. If you find yourself tempted to stray from the plan, remember that discipline is what makes long-term success possible with the Kelly system.
Use Betting Calculators
For those who find the math behind the Kelly Criterion intimidating or downright terrifying, there are a lot of online tools and calculators that are available to help simplify the process! These calculators allow you to plug in the odds, your estimated probability of winning, and your bankroll size, and they’ll do the rest. This saves time and lessens the likelihood of making any errors in your calculations. Using a calculator will almost guarantee that you’re applying the formula correctly and consistently (unless you have a slip of the finger, so double-check your work!).
If you start out small, track your bets, maintain discipline, and use calculators for the highest accuracy, you can make the Kelly Criterion a really effective part of your sports betting strategy!
Applying the Kelly Criterion in Sports Betting
The Kelly Criterion is a useful formula to calculate how much of your bankroll you should wager on a bet based on your perceived edge. Let’s take a look at how this would work with a bet during the NFL season!
Using It to Bet on an NFL Game
You’re thinking about placing a bet on a matchup between the Dallas Cowboys and the Green Bay Packers. The odds offered by the sportsbook are +200 for the Cowboys to win. In decimal odds, that translates to 3.0. Based on your own analysis of the game, you believe the Cowboys have a 35% chance of winning (p = 0.35). To figure out how much of your bankroll to bet, you can apply the Kelly Criterion formula:
- Kelly Fraction = (bp – q) / b
Where:
- b represents the net odds, which are the decimal odds minus 1. In this case, b = 3.0 – 1 = 2.0.
- p is your probability of winning, which is 0.35.
- q is the probability of losing, which is 1 – p, so q = 0.65.
Then, plug the numbers into the formula:
- Kelly Fraction = (2.0 * 0.35 – 0.65) / 2.0
- Kelly Fraction = (0.70 – 0.65) / 2.0 = 0.05 / 2.0 = 0.025
According to the Kelly Criterion, you should bet 2.5% of your bankroll on the Cowboys. It’s a relatively small bet that shows both the long odds and your moderate confidence in the Cowboys’ chance of winning.
Outcome Analysis
In this particular scenario, the Kelly Criterion helps you make a calculated bet to optimize your potential bankroll growth. The formula balances both the risk and reward, meaning you aren’t betting too much on a long shot but are still allocating enough to take advantage of the favorable odds if your confidence in the Cowboys is accurate.
If your prediction is correct and the Cowboys win, you’ll see a solid return, only having risked a small portion of your bankroll. If you’re wrong, you’ve limited your exposure to just 2.5% of your bankroll, thereby protecting yourself from big monetary losses.
This approach is particularly effective for bettors who are in it for the long term. Why? Because it decreases the likelihood of going bust while still letting you capitalize on the positive expected value bets.
Keep in mind that the accuracy of the Kelly Criterion relies on how well you estimate your probabilities. Overestimating your edge, for example, could cause you to bet too much, and underestimating might mean you will bet too conservatively!
When you apply the Kelly Criterion, you are able to make the most informed, data-driven decisions that will optimize your betting strategy and manage your bankroll effectively.
When to Ditch the Kelly Criterion
The Kelly Criterion isn’t always the best tool for every betting situation! Below are a couple of instances when it would be smart to reconsider using it.
The Kelly Criterion works best when you have a solid, confident estimate of your chances of winning a bet. If you’re unsure about your probability estimations or your data isn’t very reliable, this strategy could backfire. The formula relies entirely on how accurately you can assess the odds of a particular outcome. If your estimates are way off, you might bet too aggressively or cautiously, causing an unnecessary risk or missed opportunities. In the situations where you don’t have reliable data, or you’re not sure about your odds, sticking to a flat-betting strategy or using a smaller, more conservative fraction of Kelly might be safer.
In high-variance sports like horse racing or betting on long-shot underdogs, the Kelly Criterion can lead to more risk than it’s worth. The formula might suggest you bet a larger chunk of your bankroll on a high-risk, high-reward bet, which can cause big swings in your bankroll, especially in the short term. This is because sports with lots of volatility are harder to predict accurately, and even a well-researched bet can turn into a losing streak. In these cases, reducing your stake (using a Half Kelly or Quarter Kelly approach) or using a fixed-stake system can help protect your bankroll from the potential of massive, sudden losses.
Conclusion
The Kelly Criterion is a really smart way to manage your bets! It helps to figure out how much of your bankroll to wager based on your confidence in a certain outcome. It’s a method that is designed to maximize growth and minimize risk, but it hinges on you getting those probabilities right.
Read on for a brief recap of what the Kelly Criterion is and how it can benefit your sports betting game:
- Benefits: Maximizes long-term bankroll growth and balances risk and reward.
- Requirements: Relies on accurate estimates of winning probabilities.
- Considerations: It might not be the best choice for sports with a high variance or when you’re unsure about the odds.
All in all, the Kelly Criterion can be a great tool for serious bettors, but it’s far from a one-size-fits-all solution. It takes discipline, careful calculation, and a strong knowledge of the probabilities to make it work for you. If you’re thinking about giving it a go, start small and always bet responsibly!
If you want to learn more about managing your funds, check out our guide on Bankroll Management in Sports Betting to find out everything you need to know.
FAQs
Do you still have questions about the Kelly Criterion in relation to sports betting? Don’t worry—we have answers! Below is a list of common FAQs that our readers have asked about it!
What Is the Kelly Criterion, and How Does It Work?
The Kelly Criterion is a formula that calculates the ideal amount of your bankroll to bet, depending on the odds and how confident you are in your chances. The formula looks like this:
Kelly Fraction = (bp – q) / b, where b is the net odds, p is the probability of winning, and q is the probability of losing. Basically, it helps you decide how much to bet without taking any unnecessary risks so you can maximize long-term gains and keep your bankroll safe.
Is the Kelly Criterion Good for Beginners?
The Kelly Criterion can be harder for beginners because it relies on you having a really solid understanding of the probabilities. If you’re new to betting, starting with easier strategies like flat betting (which is where you wager the same amount on each bet) will be simpler until you have a better grasp of estimating probabilities. And once you’re comfortable, you can start to play with the Kelly Criterion!
Can the Kelly Criterion Guarantee Profits?
Nope, it can’t guarantee profits—nothing can. Yes, it’s designed to optimize your bankroll over time, but it still depends on your ability to make accurate predictions. The formula manages risk, but like any betting strategy, there’s always a chance of losing, especially in the short term. The Kelly Criterion is more about the long game—not quick wins.
How Does the Kelly Criterion Compare to Fixed Stake Betting?
The biggest difference is that the Kelly Criterion adjusts your bet size based on the perceived value of the bet, and fixed stake betting means you bet the same amount no matter the odds. Fixed stake betting is much easier and more stable, but the Kelly Criterion has the possibility to make your bankroll grow faster—but it does come with a side of extra volatility.
Why Is Accurate Probability Estimation Important for the Kelly Criterion?
The Kelly Criterion all boils down to your ability to estimate the probability of winning. The formula could result in bad choices if you overestimate or underestimate your chances. Say you think you’re more likely to win than you actually are—the formula will suggest that you bet too much, which obviously increases your risk. Accurate estimates guarantee that the strategy will work as intended and keep your bets proportionate to the real risk and reward.
