Expected value and edge: the math behind every profitable trade

Every trade is a bet on a distribution of outcomes. Expected value tells you whether that bet is worth making on average. If you remember one formula from systematic trading, make it this one.

#What expected value means

Expected value is the probability-weighted average of all possible outcomes:

EV = Σ (probability of outcome × profit in that outcome)

It is the average result you would get if you could repeat the same trade, under the same conditions, many times. A single trade will never pay exactly its EV. It either wins or loses. EV describes the long run.

#EV of a binary event contract

Binary contracts make the math unusually clean. A YES contract bought at price c pays $1 if the event happens.

EV = p × (1 − c) + (1 − p) × (−c)
   = p − c

The expected profit per contract is your probability minus the price. If you believe an event has a 70% chance and the contract costs 62¢, your EV is 8¢ per contract before costs. If the market is right and the probability really is 62%, your EV is zero.

That is why calibration matters so much. The whole question of edge reduces to: is p really different from c? See Market calibration for how to measure it.

#Adding costs

Two costs apply to almost every trade.

Fees. Exchanges charge a fee per contract or per trade. Prediction-market fees often vary with price, so look up the venue's current schedule and model it exactly.

Spread. You buy at the ask and sell at the bid, not at the mid. If you plan to exit before settlement, you pay the spread twice: once to get in, and again to get out.

Including a fee f per contract when holding to settlement:

EV = p − c − f
Breakeven probability = c + f

In a spreadsheet:

B2  Your probability   0.70
C2  Ask price          0.64
D2  Fee per contract   0.02
E2  EV per contract    =B2 - C2 - D2        → 0.04
F2  Breakeven prob.    =C2 + D2             → 0.66
G2  Return on cost     =E2 / (C2 + D2)      → 6.1%

Notice how fast costs eat edge. The mid might be 62¢, but buying at a 64¢ ask with a 2¢ fee means you need 66% just to break even.

#Edge vs. variance

A positive EV does not mean you will make money soon. Each binary contract has a standard deviation of profit of:

SD = SQRT(p × (1 − p))   per $1 contract

At p = 0.70, that is about 46¢. Compare that with an edge of 4¢: the noise on each trade is more than ten times the signal. Over n independent trades, the total edge grows with n while the noise grows only with √n, so it takes many trades for the edge to dominate.

A useful rule of thumb: the number of independent trades needed before your edge is about two standard errors above zero is roughly:

n ≈ 4 × p × (1 − p) / edge²

With p = 0.70 and a 4¢ edge, that is 4 × 0.21 / 0.0016 ≈ 525 trades. Until then, a run of losses is entirely consistent with a real edge, and a run of wins is entirely consistent with no edge at all.

#Where edge comes from

Edge in event contracts usually comes from one of four places:

1. Better information. You process public information faster or more completely than the market. (Trading on material non-public information can be illegal; this means public data used better.)
2. Better models. Your probability estimate is systematically more accurate, for example because you account for a factor most traders ignore.
3. Systematic biases. The market as a whole misprices a category, such as longshots. These edges are measurable with calibration studies.
4. Liquidity provision. You earn the spread by posting orders others trade against, and accept the risk of adverse selection.

Each of these can be tested historically before you trade.

#Common mistakes

• Confusing win rate with EV. Buying 90¢ contracts that win 88% of the time has a high win rate and negative EV (0.88 − 0.90 = −0.02).
• Using the mid as your price. You cannot buy at the mid. Use the ask.
• Forgetting fees on both legs when you plan to sell before settlement.
• Overstating your probability. If your p comes from a backtest, it carries the backtest's errors. Shrink it toward the market price when uncertain.
• Judging a strategy on ten trades. See the variance math above.

#Frequently asked questions

#What is expected value in trading?

Expected value is the average profit or loss per trade that you would get over many repetitions, computed by weighting each possible outcome's profit by its probability. A strategy with positive expected value after all costs makes money on average in the long run.

#How do I calculate the expected value of a Kalshi contract?

For a YES contract that pays $1, expected value per contract equals your probability that the event happens minus the price you pay, minus fees. For example, with a 70% probability, a 64¢ ask and a 2¢ fee, EV is 0.70 − 0.64 − 0.02 = 4¢ per contract.

#What is a breakeven probability?

It is the probability at which a trade's expected value is exactly zero. For a binary contract held to settlement, it equals the price paid plus fees per contract, expressed as a fraction of the $1 payout.

#Can a positive expected value strategy lose money?

Yes, over any finite number of trades. Each trade's outcome is noisy, so a real edge can still produce long losing streaks. The more trades you make and the larger your edge relative to the noise, the more likely the long-run result reflects the edge.