You found a bet with a real edge. Now what? Bet too little and the edge barely moves your bankroll. Bet too much and one cold week wipes out a month of good work. The Kelly criterion in sports betting is the standard answer to that question: a formula that turns your edge and the odds into a stake that grows your bankroll as fast as possible without betting it into the ground.
This guide explains what the Kelly criterion is, how the formula works, how to calculate a Kelly bet step by step, why almost nobody bets full Kelly, and how fractional Kelly keeps most of the growth with far less pain.
The short version: the Kelly criterion sizes each bet as a percentage of your bankroll based on your edge and the odds. The formula is (b × p - q) ÷ b, where b is your net payout per $1, p is your chance of winning and q is your chance of losing. If the result is zero or negative, you have no edge and should not bet. Because your win probability is only an estimate, most bettors stake a half or a quarter of the Kelly amount.
What Is the Kelly Criterion in Sports Betting?
The Kelly criterion is a bet sizing formula. It does not tell you which bets to make. It tells you how much to put on a bet once you believe it has positive expected value.
John L. Kelly Jr., a researcher at Bell Labs, published the idea in 1956 as part of a paper on information theory. Edward Thorp later applied it to blackjack and the stock market, and it has been the backbone of sizing for professional bettors ever since. You can read the background on Wikipedia.
The core idea is simple:
- Bigger edge, bigger bet. A bet with a 6% edge deserves more money than a bet with a 1% edge.
- Longer odds, smaller bet. At the same edge, a +300 longshot gets a smaller stake than a -110 side, because it loses more often.
- No edge, no bet. If the formula comes out at zero or below, the right stake is nothing.
Kelly sizes every bet as a percentage of your current bankroll, so your stakes grow as you win and shrink as you lose. That self-correcting feature is a big part of why it protects you from going broke.
The Kelly Criterion Formula
Here is the formula in the form most bettors use:
Kelly % = (b × p - q) ÷ b
- b is your net profit per $1 staked, which is decimal odds minus 1. At +120, b = 1.20. At -110, b = 100 ÷ 110 = 0.909.
- p is your estimated probability of winning.
- q is your probability of losing, which is 1 - p.
The top half of the formula, b × p - q, is your expected value per $1 bet. So there is an easier way to remember it:
Kelly % = edge ÷ net odds
That version makes the logic clear. Your edge pushes the stake up. The payout pushes it down, because longer odds mean more losing streaks between wins. If you want a refresher on expected value itself, see what EV means in betting.
One shortcut you may see is "double your win probability and subtract one." That only works at even money (+100). At any other price it gives the wrong answer, so use the full formula.
How to Calculate a Kelly Bet Step by Step
Say a sportsbook offers a team at +120, and after removing the vig from sharper markets you estimate the true chance of winning at 48%. Your bankroll is $5,000.
The full Kelly stake is 0.0467 × $5,000 = $233.33. Half of that is $116.67 and a quarter is $58.33. Most bettors would place the half or quarter amount, for reasons we cover below.
The fair odds for a 48% chance are about +108 (52 ÷ 48 = 1.083). The book is paying +120, so you are being paid more than the risk deserves. That gap is the whole reason the bet exists. Our guide on how to devig odds shows how to find that fair price yourself.
If you would rather not do this by hand, our free Kelly criterion calculator takes American odds, your win probability and your bankroll and returns the full, half and quarter Kelly stakes.
Kelly Criterion Examples at Different Odds
The same formula behaves differently across prices. Here are four bets, each sized on a $5,000 bankroll:
- -110 with a 55% chance. b = 0.909. Edge = (0.909 × 0.55) - 0.45 = 0.50 - 0.45 = 5.0%. Kelly = 0.05 ÷ 0.909 = 5.50%, or $275 full Kelly.
- +120 with a 48% chance. Edge = 5.6%. Kelly = 4.67%, or $233.
- +300 with a 27% chance. b = 3.00. Edge = (3 × 0.27) - 0.73 = 0.81 - 0.73 = 8.0%. Kelly = 0.08 ÷ 3 = 2.67%, or $133.
- -110 with a 52% chance. Edge = (0.909 × 0.52) - 0.48 = 0.4727 - 0.48 = -0.73%. Kelly is negative, so you pass.
Notice the +300 bet. It has the biggest edge of the group, yet it gets the smallest stake. A 27% shot loses nearly three times out of four, so Kelly keeps the bet small enough that a long run of losses cannot sink you.
The last example matters too. At -110 you need to win 52.38% of the time just to break even. A 52% estimate looks close, but it is still a losing bet, and Kelly correctly says to skip it.
Why Full Kelly Is Too Aggressive
Full Kelly gives you the fastest long-run growth only if your win probability is exactly right. In sports betting, it never is. Your 48% might really be 46%, and that small miss changes everything.
Using the +120 example, here is what happens to your long-run growth rate when you bet different multiples of the Kelly stake (full Kelly = 100%):
Two things stand out:
- Half Kelly keeps about 75% of the growth while betting half as much. You give up a quarter of the upside and cut your swings roughly in half.
- Overbetting is punished hard. At twice the Kelly stake, long-run growth falls to almost zero even though every bet is +EV. Past that point, your bankroll shrinks over time.
Now look at what an estimation error does. If the true win chance on our +120 bet is 46% instead of 48%, the real edge drops from 5.6% to 1.2%. Betting the 4.67% full Kelly stake on that bet produces a negative long-run growth rate. You are making +EV bets and still losing money, purely because of bet size. Quarter Kelly on the same bet still grows, just slowly.
The swings are rough even when your numbers are perfect. Under the standard model, a full Kelly bettor has about a 50% chance of seeing the bankroll fall to half of its starting value at some point. At half Kelly, that drops to about 12.5%, and at quarter Kelly to under 1%.
Fractional Kelly: Half Kelly and Quarter Kelly
Fractional Kelly means betting a fixed share of the Kelly stake. It is what most serious +EV bettors actually use.
| Kelly fraction | Stake on the +120 example ($5,000) | Best for |
|---|---|---|
| Full Kelly (4.67%) | $233 | Almost no one. Only if your probabilities are proven and you can stomach big drawdowns |
| Half Kelly (2.33%) | $117 | Experienced bettors with a tested, sharp source of fair odds |
| Quarter Kelly (1.17%) | $58 | Most +EV bettors, newer bettors, props and thinner markets |
A good rule of thumb: the less confident you are in your fair price, the smaller your fraction. Main-market sides with deep, sharp lines can handle half Kelly. Player props, small markets and anything priced off a single source deserve a quarter or less. Our player prop betting strategy guide explains why prop estimates carry more uncertainty.
Many bettors also set a hard cap, such as never more than 2% to 3% of the bankroll on any single bet, no matter what the formula says. That protects you from the occasional bad data point that makes an edge look far bigger than it is. Our sports betting bankroll management guide covers how to set those limits and split money across books.
Where Your Win Probability Comes From
Kelly is only as good as the p you feed it. Guessing "I think this team wins 60% of the time" and plugging that in is the fastest way to overbet.
The most reliable source of p for most bettors is the market itself. Sharp books and exchanges post prices that are hard to beat, and when you remove their margin you get a solid estimate of each side's true chance. If a softer book is offering a better price than that fair line, you have a measurable edge. This is the heart of positive EV betting.
A few habits keep your inputs honest:
- Use devigged sharp prices, not opinions. Strip the vig from the sharpest market you can find, ideally more than one.
- Compare devig methods. Multiplicative, additive and power methods can give slightly different fair odds. If they disagree, use the more conservative number.
- Check your results against the closing line. If your bets beat the closing price over time, your edge estimates are probably real. Our guide to closing line value shows how to track it.
- Shrink edges that look too good. A 15% edge on a main market is usually a stale line or a data error, not a gift.
Kelly in Practice: Multiple Bets, Parlays and Arbitrage
The simple formula assumes one bet at a time. Real betting rarely works that way.
Several bets at once. If you have five bets running on the same Sunday, sizing each one at full Kelly as if it were alone puts too much of your bankroll at risk at the same time. The simplest fix is to use fractional Kelly on each and cap your total open exposure, for example at 10% to 15% of the bankroll.
Correlated bets. Two bets on the same game, like a side and a total that tend to move together, are not independent. Treat them as one bigger position and size them down.
Parlays. You can run Kelly on a parlay using its combined odds and combined win chance. Because a parlay wins rarely, Kelly will always recommend a small stake, and any error in each leg's probability compounds across the ticket. Size them very conservatively.
Arbitrage. Kelly does not apply to a true arbitrage. When you cover every outcome across books, there is no losing scenario to size against, so your stake is set by book limits and how much capital you want tied up, not by a growth formula. Our guide to what arbitrage betting is explains how those stakes are split.
Common Kelly criterion mistakes
Most problems with Kelly come from the inputs, not the math.
- Using decimal odds as b. b is the net profit per $1, so at decimal odds of 2.20 it is 1.20, not 2.20. Using the full decimal odds roughly doubles your stake.
- Betting full Kelly on estimated edges. As shown above, a 2-point error in p can turn full Kelly into a losing strategy.
- Sizing off your starting bankroll forever. Kelly is a percentage of your current bankroll. After a downswing, your stakes should shrink.
- Ignoring simultaneous exposure. Ten "small" bets at once can add up to one very large bet.
- Topping up after losses. Adding money every time you dip below your starting balance defeats the protection Kelly gives you. Decide on your bankroll and stick to it.
How AVO Sizes Bets With Kelly
Running Kelly by hand works for one bet. Doing it for every opportunity across every book, with odds that move every few seconds, is what software is for.
AVO's positive EV betting tool pulls prices from 70+ sportsbooks, exchanges and prediction markets, devigs the sharpest markets with several methods and flags bets where a book's price beats the fair line. Each opportunity shows the edge, the fair odds and a Kelly-based stake using the Kelly fraction and bankroll you set, so the sizing step happens automatically. Before you place it, you can see whether the devig methods agree, which is a quick check on how much to trust the edge.
For one-off checks, the Kelly calculator gives you full, half and quarter Kelly stakes in seconds.
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Frequently Asked Questions
What is the Kelly criterion in sports betting? It is a formula that tells you what percentage of your bankroll to bet based on your edge and the odds. Bigger edges get bigger bets, longer odds get smaller bets, and bets with no edge get nothing.
What is the Kelly criterion formula? Kelly % = (b × p - q) ÷ b, where b is your net profit per $1, p is your win probability and q is 1 - p. At +120 with a 48% win chance, that is (1.20 × 0.48 - 0.52) ÷ 1.20 = 4.67% of your bankroll.
Should I use full Kelly or half Kelly? Half Kelly or less for almost everyone. Half Kelly keeps about 75% of full Kelly's long-run growth with much smaller swings, and it protects you when your win probability estimate is a little too high.
What does a negative Kelly number mean? It means the bet has negative expected value at that price. The correct stake is zero. Look for a better price at another book or skip the bet.
Does the Kelly criterion work for parlays? You can apply it using the parlay's combined odds and win chance, but the result will be small, and errors in each leg multiply. Most bettors keep parlays to a tiny slice of the bankroll, if they bet them at all.
Is there a Kelly criterion calculator? Yes. AVO's free Kelly criterion calculator takes American odds, your win probability and your bankroll and returns full, half and quarter Kelly stakes.
AVO is an entertainment tool for adults and an analytics platform, not a sportsbook. AVO does not accept wagers and does not hold funds. You must be of legal age to bet in your jurisdiction (21+ in most states). Examples are illustrative, and betting involves real risk of loss. If you or someone you know has a gambling problem, call 1-800-GAMBLER. Please bet responsibly.
