What Expected Value Actually Means
Expected value (EV) is the average outcome of a decision if you made it many times. If a coin flip pays $3 when heads and costs $1 when tails, the expected value is (0.5 times $3) minus (0.5 times $1) = $1.00 per flip. Over 100 flips, you would expect to be ahead approximately $100.
Every market decision has an expected value, even though the calculations are more complex than a coin flip. When you buy a prediction market contract at 45 cents, you are implicitly saying: the probability of this event is higher than 45%, therefore the expected value of this purchase is positive. The question is how much higher, and how confident you are in that estimate.
Why Intuitive EV Calculation Fails
Humans are systematically bad at intuitive probability estimation. We overweight vivid, recent, or emotionally salient information. We anchor to the first number we hear. We confuse confidence with accuracy. We are loss-averse, weighting potential losses about 2x as much as equivalent gains. And we suffer from the availability heuristic, estimating probabilities based on how easily examples come to mind rather than their actual frequency.
These biases compound. A trader who overestimates the probability of an event by 10 percentage points (thinking 65% when the true probability is 55%) and then sizes their position based on that inflated estimate will systematically lose money even though they have a genuine informational advantage. The advantage exists, but the position sizing based on the biased probability wipes it out.
Making EV Calculations Explicit
The fix is deceptively simple: write it down. Before entering any trade, explicitly estimate the probability of each outcome, the payoff for each outcome, and calculate the expected value. For a binary prediction market contract priced at 45 cents:
If your probability estimate is 55%: EV = (0.55 times $0.55) minus (0.45 times $0.45) = $0.10 per dollar risked. Positive EV, worth considering.
If your probability estimate is 48%: EV = (0.48 times $0.55) minus (0.52 times $0.45) = $0.03 per dollar risked. Barely positive, probably not worth the transaction costs and capital lockup.
If your probability estimate is 43%: EV = (0.43 times $0.55) minus (0.57 times $0.45) = -$0.02 per dollar risked. Negative EV. Pass.
EV Is Necessary But Not Sufficient
A positive expected value does not automatically make a trade worth taking. You also need to consider the variance of outcomes (how much can you lose on a single trade), the opportunity cost (are there better EV trades available), the liquidity (can you actually get the size you want at the quoted price), and the time horizon (how long is your capital locked up).
A trade with +$0.10 EV per dollar that locks your capital for six months is very different from the same EV on a trade that resolves in a week. Annualizing the expected return and comparing it to your cost of capital (or alternative uses of that capital) is part of a complete decision framework.
EV Across a Portfolio
The real power of EV thinking shows up at the portfolio level. If you have 20 positive-EV positions, some will lose and some will win, but the portfolio's aggregate expected value is the sum of the individual EVs. Over time, as long as your probability estimates are reasonably calibrated and your positions are appropriately sized, the portfolio converges toward its expected value.
This is why professional traders and prediction market participants focus on process rather than individual outcomes. Any single trade can go wrong. But a portfolio of positive-EV trades, sized according to the Kelly criterion or a fractional variant, trends toward profitability over a sufficient number of resolved positions.
Explore these tools on Blockcircle: Prediction Markets Mispricing Engine