Debunking the Kelly Criterion
By: JV Miller | Professional Sports Bettor and Publisher
The Formula Isn't the Problem. The Input Is.
The Kelly Criterion is a legitimate probability formula. Let’s establish that right away.
We are not arguing that John L. Kelly Jr. got the mathematics wrong. Kelly has perfectly valid applications when the probabilities and payoffs involved can be estimated with sufficient accuracy. Our objection is narrower:
The Kelly Criterion requires sports bettors to know something they do not know.
To calculate an optimal wager, Kelly needs an estimate of the probability that a specific bet will win. That is where the problem begins.
Tell Me the Probability That This Bet Wins
Suppose you handicap an NFL game and decide the underdog at +3 is worth betting at -110.
Now answer this:
What is the exact probability that your wager wins?
53.2%?
54.7%?
56.1%?
58.4%?
You don't know. Neither do we.
You may have an excellent handicapping process. You may have decades of results showing that your methods produce a long-term edge. Your model may identify genuine value. But none of that tells you that this particular wager has precisely a 56.1% probability of winning.
You can estimate it. You cannot know it. And Kelly uses that estimate to decide how much of your bankroll should be at risk.
Kelly Turns an Estimate Into a Precise Wager
For a simple wager, the Kelly fraction can be written as:
f = (bp − q) ÷ b
where:
b = net odds received on the wager
p = estimated probability of winning
q = probability of losing, or 1 − p
At standard -110 pricing, a bettor risks $110 to win $100, so the net odds are approximately:
b = 100 ÷ 110 = 0.9091
Now watch what happens when we change only the bettor's estimated probability of winning.
At 53%, full Kelly calls for risking approximately 1.3% of bankroll.
At 55%, approximately 5.5%.
At 57%, approximately 9.7%.
At 60%, approximately 16%.
Same -110 wager.
Wildly different recommended bet sizes. Why? Not because the formula changed. Because your estimate changed.
And that estimate is the one number in the equation we cannot know with anything approaching that degree of precision.
False Precision Is Still False
This is where Kelly becomes dangerous in sports betting. The formula can be exact. The bankroll can be exact. The sportsbook price can be exact. The payout can be exact. But the bettor's true probability of winning is still an estimate.
A spreadsheet can calculate twelve decimal places. That does not make the underlying assumption twelve-decimal-place accurate.
For a professional bettor operating on relatively thin margins, this is not a minor weakness. It is the central weakness.
The formula isn't the problem. The input is.
Your Historical Winning Percentage Is Not the Missing Input
A common response to the Kelly problem is: “I already know my probability. I win 55% of my bets.”
No, you don't. If you have won 55% over a sufficiently large sample, you have valuable evidence about the historical performance of your handicapping process. But that is not the same thing as knowing the probability that tonight's wager will win.
Suppose you have gone 550–450 over your last 1,000 wagers. That's a 55% historical winning percentage. But those 1,000 wagers were not identical events. They involved different teams, different prices, different markets and different circumstances. Some undoubtedly had larger edges than others. Some may have had virtually no edge at all.
Kelly doesn't need to know what percentage of your previous 1,000 bets won. It needs an estimate of the probability that this particular bet wins. Those are two very different numbers.
A 55% Bettor Does Not Make 55% Bets
A bettor capable of sustaining approximately 55% winners against -110 over a meaningful sample is doing exceptionally well. But that does not mean every wager he makes has a 55% probability of winning.
One selection might genuinely have a 53% chance. Another might be 57%. Another might be a mistake that has no positive expectation whatsoever. The problem is that we don't get to observe those true probabilities.
After the game, we observe only the result: win or lose.
Even a long and successful betting record cannot tell us precisely what the probability was before an individual game was played.
“Fine. Then Use Half Kelly.”
This is another common response. If Full Kelly is too aggressive, use Half Kelly. Or Quarter Kelly. Or some other fractional version of the formula.
Fractional Kelly certainly reduces the amount of capital exposed to an inaccurate estimate.
But reducing the consequence of estimation error is not the same thing as eliminating the estimation error.
If your estimate says a wager has a 57% probability of winning when its true probability is substantially lower, dividing the resulting Kelly wager by two doesn't suddenly make the original estimate correct.
You're simply risking less money on the same uncertain assumption.
Think of it this way:
If your compass is pointing in the wrong direction, walking half as fast doesn't make the compass accurate.
Fractional Kelly may reduce the damage caused by being wrong.
It does not solve the fundamental problem:
You still don't know the input.
The Most Dangerous Number Is the One You Supplied Yourself
Sports betting is already filled with uncertainty:
Injuries. Weather. Matchups. Market movement. Human performance. Model error. Incomplete information. Incorrect assumptions. Randomness.
A model assigning an NFL side a 56.4% probability of winning can look impressively scientific.
But adding a decimal point does not create knowledge.
Sometimes it merely creates false precision.
And when that false precision determines whether you risk 2%, 5%, 10% or more of your bankroll, the distinction stops being academic.
Real money is now attached to the estimation error.
Even If Your Probability Estimate Were Perfect, We Would Still Reject Kelly
Suppose, for the sake of argument, that we eliminate our first objection entirely. Imagine that somehow you do know the true probability that your next wager will win.
We would still not recommend the Kelly Criterion for sports betting. Why?
Because Kelly requires you to continually change the size of your wager.
That creates an entirely separate problem.
Variable Bet Sizing Is Not a Side Effect of Kelly. It's the Point.
Kelly determines how much of your bankroll to wager based on the size of your perceived advantage and the odds being offered. Change the estimated probability and Kelly changes the wager. Change the odds and Kelly changes the wager. Change the bankroll and Kelly changes the wager. In other words, Kelly is designed to do precisely what our money-management strategy is designed not to do: Jiggle the bet size.
Changing the Bet Size Changes the Break-Even Math
At standard -110 odds, sports bettors are commonly told they must win 52.38% of their wagers to break even. That statement assumes something important that is almost never mentioned:
The wagers are the same dollar amount.
Once wager sizes vary, winning 52.38% of the bets no longer necessarily means breaking even.
Two bettors can make the exact same selections at the exact same odds, win and lose the exact same bets, and finish with different amounts of money simply because one bettor changed wager sizes while the other flat bet.
We demonstrate the mathematics separately in: Flat Betting Bombshell: Changing Bet Size Raises Break-Even Percentage
That's where the simulation and proof belong, so we won't duplicate them here. The implication for Kelly, however, belongs squarely on this page:
Kelly cannot preserve fixed-dollar flat betting because changing wager size is built into the system itself.
Kelly Therefore Has Two Problems, Not One
Our objection to Kelly is not simply that the bettor must estimate an unknowable probability. Even if we granted Kelly the perfect probability input, we would still be left with its variable-staking mechanism.
So there are two independent objections:
1. Kelly requires an estimate of the probability that an individual wager will win—an input sports bettors cannot know with precision.
2. Kelly uses that estimate to continually alter wager size, sacrificing the break-even advantage of fixed-dollar flat betting.
The first problem concerns what you know.
The second concerns what Kelly tells you to do with your money.
Solving the first would not eliminate the second.
And that is why our disagreement with the Kelly Criterion goes considerably deeper than whether a bettor should use Full Kelly, Half Kelly or Quarter Kelly.
We disagree with the underlying staking mechanism itself.
We Separate Handicapping From Money Management
We believe the handicapper's job is to determine whether a wager is worth making.
Money management has a different job: Keep the bettor adequately capitalized, protect against normal variance and preserve the mathematical advantages of fixed-dollar wagering.
That's why the Miller Flat Betting System begins with a maximum standard wager of 2% of bankroll, giving the bettor 50 betting units.
Once established, that wager remains the same dollar amount. We don't increase it because one selection appears stronger than another. We don't recalculate it after every win or loss. We don't reduce it during a drawdown.
Only after the bankroll reaches a new 25% plateau do we establish a new 2% wager.
The system isn't trying to determine the theoretically perfect amount to risk on tonight's game.
We don't believe that number can be known.
Two Different Philosophies
Kelly attempts to optimize wager size by asking:
How large is my edge on this particular opportunity?
Our approach asks a different question:
How much can I consistently risk while remaining adequately capitalized through the inevitable variance of sports betting?
That distinction is at the heart of our disagreement with Kelly.
For the complete staking method, see our Miller Flat Betting System.
For the mathematical demonstration of what happens when wager sizes are changed, see Flat Betting Bombshell: Changing Bet Size Raises Break-Even Percentage.
And for the broader framework tying bankroll size, unit sizing, variance, drawdowns and staking together, see Sports Betting Money Management: Professional Bankroll & Staking Strategies.
Our Verdict on the Kelly Criterion
The Kelly Criterion is legitimate mathematics. Our argument has never been that Kelly's formula is mathematically defective.
Our argument is that its application to sports betting depends upon an uncertain input and produces a form of variable staking that we independently reject. Kelly asks you to estimate a number you cannot know precisely—and then allows that estimate to determine how much of your bankroll you risk.
Even if we somehow solved the first problem, we would still have the second. That's why we don't use Kelly.
The formula isn't the problem. The input is.
And in sports betting, we don't believe an uncertain input should be jiggling the size of your bet.