Expected value: judge the decision across a sample, not one outcome

The short answer

Expected value is the probability-weighted average of all modeled net outcomes: multiply each outcome by its estimated probability and add the results. A positive estimate means the assumptions imply an average gain across repeated comparable decisions. It does not promise that this trade will win or that the estimate is correct.

The useful work is not the final number. It is defining mutually exclusive outcomes, including costs and failed exits, exposing the probabilities you are assuming, and checking those forecasts against a timestamped sample.

Build an outcome tree before using a win rate

Binary win/loss math is convenient but often incomplete. A token trade can fill at the planned price, fill worse, partially fill, fail, become temporarily unsellable, exit through another route, pay a changing transfer fee, or suffer a security event. Define the branches that materially change capital.

Make outcomes mutually exclusive and collectively useful for the decision. For each branch, record gross proceeds, entry and exit price impact, pool and platform fees, network and priority costs, token-level fees, failed-attempt costs, and any residual position. Use net wallet change rather than a chart percentage.

Start with the break-even probability

In a two-outcome model with a net gain of G and an absolute net loss of L, the break-even win probability is L ÷ (G + L). If the average net gain is 2R and the average net loss is 1R, break-even is one third before any omitted failure state. Add costs to the appropriate outcomes before calculating.

Compare the break-even requirement with a range of plausible win probabilities, not a single confident guess. If a small change in costs, fill quality, or exit probability turns the estimate negative, the decision has little margin for model error.

Probabilities need provenance

Label each probability as a base rate from a defined sample, a model output, a market-implied estimate, a judgment, or unknown. Preserve the sample dates, inclusion rules, strategy version, chain, venue, liquidity range, and market regime. A number without that context is not reusable evidence.

Do not convert conviction words directly into precision. “High confidence” is not 80% until forecasts using that label have been scored. Record an honest range and show EV under the low, central, and high cases.

The denominator can manufacture an edge

Include every opportunity that met the setup definition, not only remembered winners, public calls, or trades that filled cleanly. Preserve failed transactions, partial fills, unsold residuals, abandoned exits, and delisted or dead tokens. Excluding adverse operational outcomes inflates both win rate and payoff.

Separate live, simulated, reconstructed, and backtested observations. A backtest using final holder labels, later liquidity, or tokens selected because they survived contains information unavailable at the original decision time.

Score forecasts separately from trade P&L

For repeated binary forecasts, group probability ranges and compare the stated probability with the observed frequency. A proper scoring rule such as the Brier score can reward honest probabilistic forecasts rather than only counting correct directional calls. Keep probability calibration separate from payoff quality.

A well-calibrated 60% thesis can still be a bad trade when the loss is much larger than the gain or execution costs consume the edge. A profitable sample can still contain poor forecasts if one rare winner dominates. Review probability, payoff, execution, and sizing as different layers.

Classify process and outcome independently

• Valid process, favorable outcome: the trade met the plan and the realized branch produced a gain.
• Valid process, unfavorable outcome: the thesis lost within its modeled distribution and the rules were followed.
• Invalid process, favorable outcome: a rule break or unsupported thesis won; the capital outcome does not repair the decision record.
• Invalid process, unfavorable outcome: the loss combines market variance with an avoidable decision or execution failure.

Update the strategy from the sample, not from whichever quadrant feels most memorable. The trading journal preserves the plan before the outcome is known.

Positive EV is not sufficient permission to trade

Expected value is an average, not a survival rule. Two opportunities can have the same EV and radically different drawdowns, tail losses, liquidity needs, custody risk, outcome timing, and estimation uncertainty. An attractive average does not make an account able to withstand the path.

Apply the loss-limit hierarchy, total open-risk cap, liquidity constraint, and security gates independently. If a catastrophic branch cannot be bounded or its probability is unknowable, model it explicitly instead of hiding it inside the average.

An expected-value workflow

1. Fix the decision. Save the setup, strategy version, size, route, timestamp, and information available before entry.
2. Build the branches. Define material win, loss, partial, failure, and residual-position outcomes without overlap.
3. Net the payoffs. Include every execution cost and value outcomes in one consistent unit.
4. Source the probabilities. Preserve base rate, sample, judgment, model, ranges, and unknowns.
5. Stress the estimate. Recalculate with worse fills, higher costs, reduced exit probability, and the low end of the probability range.
6. Review by cohort. Score forecasts, payoffs, execution, and process across comparable trades before changing the strategy.

What belongs in the journal

Record strategy version and setup, decision timestamp, information set, every outcome branch, net payoff calculation, probability estimate and provenance, low/central/high EV, break-even probability, omitted or unknown risks, stress cases, loss and liquidity constraints, actual branch, forecast score, process classification, execution variance, and the cohort used for later review.

Primary and official sources