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The Kelly Criterion for Prediction Markets: How Big Should Your Position Be?

You found a price you think is wrong. The next decision, how much, will matter more to your account over a year than whether you were right tonight. There is an actual formula for it, it simplifies beautifully for binary contracts, and it comes with one commandment: use less than it says.

Most losing accounts do not lose because their opinions were bad. They lose because they sized a good process badly, too big on shaky edges, too small on real ones, and catastrophically big exactly once. Picking is the fun problem. Sizing is the profitable one.

The classic answer is the Kelly Criterion, a 1950s formula that tells you what fraction of your bankroll to commit given your edge, derived to maximize long-run compound growth. In most settings Kelly is awkward to apply. Prediction markets are the exception: binary contracts make it collapse into arithmetic you can do at the kitchen table.

The formula, for $1-settlement contracts

You believe an outcome has probability p. Its contract trades at price c (in dollars, so 40¢ is 0.40). Kelly says the fraction of your bankroll to put into the position is:

f = (p − c) / (1 − c)

That is the whole thing. Your edge over the market price, divided by the price's distance from certainty.

Worked example: you think a team trading at 40¢ is really a 50% proposition. f = (0.50 − 0.40) / (1 − 0.40) = 0.10 / 0.60 = about 17% of your bankroll. A $600 bankroll puts $100 on it.

Second example, same 10-point edge at a higher price: contract at 80¢ you believe is 90%. f = 0.10 / 0.20 = 50% of your bankroll. Same edge, triple the size? Yes, and the formula is being logical: the 80¢ contract loses its whole stake less often, so Kelly tolerates more of your bankroll in it. Notice what this implies in reverse: cheap longshot positions deserve to be small even when your edge is real, because at c = 0.10, even p = 0.20, a doubled probability, gives f = 0.10 / 0.90, about 11%, not the plunge your gut wants.

And one number worth memorizing: if p = c, f = 0. No edge, no position. Kelly is the only voice in your head that ever says that sentence.

The commandment: cut it in half

Full Kelly assumes the one thing you do not have: that your p is correct. Your p is an estimate, and Kelly is brutally sensitive to estimate error in one specific direction. Sizing at what you think is full Kelly, when your true edge is smaller than you believe, does not just reduce returns; overshooting Kelly actively destroys compound growth, and going past double-Kelly turns a winning process into a losing one. The penalty for oversizing is bigger than the penalty for undersizing. It is not symmetric.

So the standard professional practice is fractional Kelly: half, sometimes a quarter, of the formula's output. Half-Kelly keeps most of the growth (about three quarters of it, under standard assumptions) at half the volatility, and it converts "my probability estimate was a little optimistic" from fatal to annoying. Our two examples become 8% and 25% of bankroll. Still assertive. No longer staking the house on your own calibration.

Three more honest adjustments before the formula touches money:

Fees and spread shrink p − c. Your real entry is the ask plus fees, not the midpoint (the round-trip math). An edge that dies when you add 2¢ of friction was never an edge.

Correlated positions share one bankroll fraction. Five positions that all die if the favorite wins are one position wearing five hats. Kelly's fraction applies to the scenario, not to each ticket.

Your bankroll is your trading bankroll. The formula's aggression is only survivable when the account is money you can genuinely lose without your life changing.

Where p comes from (the part Kelly cannot do)

Kelly is a converter: it turns a probability estimate into a size. Garbage estimate, confidently-sized garbage. So the real work lives upstream, in having a p worth trusting, and the honest hierarchy goes:

The market price itself is the best free estimate on earth for most games, most of the time; that is the whole premise of these markets. When your p differs from c, the first question is never "how much do I buy?" It is "what do I know that the market does not?" Sometimes there is a real answer: you watched the game state change before the price finished moving, you have a live read the crowd is slow on, the situation matches a pattern you have genuinely studied. Live game-state math is exactly the terrain where prices lag reality by seconds (price scenarios exist to make that arithmetic visible). Sometimes the answer is "I like the team," in which case p = c, f = 0, and Kelly just saved you money (the fandom tax).

A practical calibration habit: write down your p before every trade for a month, then check whether your 60% calls actually hit around 60%. Most people discover their 60% means 52%, and that discovery is worth more than any formula. Adjust, then let Kelly size the adjusted number.

So how big should it be?

Position sizing has an actual answer: your edge over the price, divided by the price's distance from a dollar, then cut in half because you are human. It puts real numbers on instincts that are usually vibes, forces the "what do I know that the market doesn't" question that kills bad trades before they are sized, and, on the nights you have nothing, tells you the most profitable position size in trading: zero.

Educational information, not financial advice. The Kelly Criterion is a mathematical framework, not a guarantee; results depend entirely on the accuracy of your probability estimates. Prediction markets involve risk of loss, and their legal status varies by location and changes over time.