How do I calculate expected value on a prediction market?

Multiply your probability of winning by the $1 payout and subtract what you pay per contract, fees included: EV = q − (price + fee).

How do you calculate expected profit?

Multiply the profit if you win by your probability of winning, and subtract the loss if you lose times its probability. For 100 contracts at 60¢ plus a 1¢ fee on a 70% event: 0.70 × $39 − 0.30 × $61 = $9.00 of expected profit.

What is the break-even probability?

The probability at which expected value is zero — the price plus fee. If you believe the event is more likely than that, the trade has positive expected value.

Tools

Expected value calculator: expected profit on a trade

Is a contract worth buying at this price? Enter the price, your probability, the number of contracts and the fee. The calculator shows your expected profit, the return on what you pay, and the probability at which the trade breaks even.

Expected value calculator

SideYES price (¢)Your probability of YES (%)ContractsFee per contract (¢)

Expected profit: $9.00 ($0.09 per contract)
Expected return: 14.8%
Break-even probability: 61.0%

The formula

EV per contract = p(win) × $1 − (price + fee)

What expected value tells you

Expected value is what a trade earns on average if you could repeat it many times at your probability. A contract that costs c and pays $1 has an expected value of q − c, where q is your probability of winning. Positive means the price is below your estimate; negative means you are paying more than you think it is worth.

Worked example: YES at 60¢, you think 70%, 1¢ fee. Each contract is expected to earn 0.70 − 0.61 = 9¢, a 14.8% expected return, and the trade breaks even at 61%.

Expected profit, worked through

Expected profit is the average of what you win and what you lose, each weighted by its chance: expected profit = P(win) × profit if it wins − P(lose) × amount lost.

Take 100 contracts bought at 60¢ with a 1¢ fee, so $61 in all, on an event you put at 70%. If it happens they pay $100, a profit of $39; if not, you lose the $61. Expected profit = 0.70 × $39 − 0.30 × $61 = $27.30 − $18.30 = $9.00 — the same 9¢ a contract the formula above gives, and a 14.8% expected return on the $61.

The same arithmetic works for a sportsbook bet: replace the contract price with the stake and the $1 payout with what the bet returns at the quoted odds.

What it does not tell you

A positive expected value is not a likely profit on one trade: a 70% event still loses three times in ten. It also assumes you can buy at the price you entered — on a thin order book a large order moves the price against you, which our guide to liquidity and spreads explains.

Frequently asked questions

How do I calculate expected value on a prediction market?: Multiply your probability of winning by the $1 payout and subtract what you pay per contract, fees included: EV = q − (price + fee).
How do you calculate expected profit?: Multiply the profit if you win by your probability of winning, and subtract the loss if you lose times its probability. For 100 contracts at 60¢ plus a 1¢ fee on a 70% event: 0.70 × $39 − 0.30 × $61 = $9.00 of expected profit.
What is the break-even probability?: The probability at which expected value is zero — the price plus fee. If you believe the event is more likely than that, the trade has positive expected value.

Not financial advice. These calculators do arithmetic on the numbers you enter; they do not know a platform’s current prices or whether it is open to you. Check both in the platform reviews.