Expected Value in Prediction Markets: How to Calculate It

Expected value is the core math behind smart decisions in prediction markets. It tells you, on average, what a bet is worth before you place it.

If you can estimate a probability better than the market price, expected value helps you see whether a trade is favorable. This article walks through the formula and several worked examples.

What Expected Value Means

Expected value (EV) is the average outcome of a bet if you could repeat it many times. On Polymarket, prices for YES shares range from 1 to 99 cents, and a winning share pays $1.00. That price can be read as the market's implied probability.

If you believe the true probability differs from the price, you can calculate expected value to check whether buying is worthwhile in the long run. This does not guarantee any single outcome, since a single trade can still lose.

The Expected Value Formula

For a binary YES share bought at price price (in dollars, between 0 and 1), with your estimated probability p that YES happens, the per-share expected value is:

EV = p × (1 − price) − (1 − p) × price

• The first term is your probability of winning times the profit per share if you win.
• The second term is your probability of losing times the price you paid (your loss).

A positive EV means the trade is favorable given your estimate of p. A negative EV means the price is too high relative to your belief.

Worked Example 1: A Favorable Trade

Suppose a YES share trades at 40 cents (price = 0.40), and you estimate the true probability at 55% (p = 0.55).

EV = 0.55 × (1 − 0.40) − 0.45 × 0.40
EV = 0.55 × 0.60 − 0.45 × 0.40
EV = 0.33 − 0.18 = 0.15

Expected value is 15 cents per share. If your probability estimate is accurate, this trade is favorable on average.

Worked Example 2: An Unfavorable Trade

Now suppose the same share trades at 70 cents, but you still believe p = 0.55.

EV = 0.55 × 0.30 − 0.45 × 0.70
EV = 0.165 − 0.315 = −0.15

Expected value is negative 15 cents. Even if you like the outcome, the price already exceeds your estimated probability, so buying is unfavorable.

Why Your Probability Estimate Matters

The formula only works as well as your input for p. Expected value calculations are sensitive to small changes in your belief about probability. Two traders looking at the same price can reach opposite conclusions if their estimates differ.

Some practical habits when estimating p:

• Base estimates on evidence, not hope for a specific outcome.
• Compare your number against related markets or public information.
• Write down your reasoning before checking the price, to avoid anchoring.

Expected Value Is Not a Guarantee

A positive expected value describes an average across many similar bets, not a promise for one trade. Prediction markets involve real uncertainty, and any single position can lose money even with sound math.

Understanding how prediction markets work helps put this formula in context. Expected value is also central to Kelly position sizing, which uses your EV edge to size a bet responsibly.

Putting Expected Value Into Practice

Start small. Track a handful of trades where you wrote down your probability estimate beforehand. Compare your estimate to the eventual outcome and market price.

Over time, this record shows whether your estimates are calibrated. Traders who are well calibrated tend to have positive average expected value, even though individual trades vary.

Expected value also helps you compare markets. If two markets offer similar edges, you might prefer the one with better liquidity or lower fees, since both affect your realized return.

Quick Reference Table

To skip manual math, use the expected value calculator. You can also check the profit calculator to see potential payouts, and review Polymarket fees since fees reduce realized EV.

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