Crypto trade returns: mean vs median

The mean crypto trade return is the arithmetic average of the chosen trade returns; the median is the middle value after sorting them. The mean reflects every outcome's magnitude, so a few large wins or losses can dominate it while the median describes the center by rank. Report both with the same trade definition, costs and return denominator, then show which trades drive the gap.

A positive average and a negative median are compatible. The useful question is which observations create that difference, whether their execution records are credible, and how much capital actually earned those returns.

Give both numbers the same input

Define one observation as a completed position, combining its entry fills, additions, exits and attributable costs. A partial exit is not automatically another independent trade. Keep open positions visible elsewhere in marked equity; excluding them from this table does not eliminate their risk.

For this article, each trade return is 100 × net P&L / entry notional. The examples use fully closed, unlevered spot positions with one entry each. Net P&L already includes every assumed cost. This denominator is a declared reporting choice, not margin return or a universal convention for positions with additions.

The mean is sum of trade returns / number of trades. For an odd count, the median is the sorted middle value; for an even count, use the arithmetic average of the two middle values. Python's official mean definition and median convention specify these calculations. Another median convention should be labeled before comparing exports.

The trade expectancy guide explains how win frequency and payoff size combine in an average outcome. Here the focus is the gap between that average and the middle-ranked trade.

Nine trades, opposite signs

This original hypothetical ledger contains nine completed positions, each with $1,000 entry notional. The returns are invented net outcomes, not historical market data or KLINEO results. Trade identifiers preserve the connection to the source ledger; the rows below are sorted by return.

The returns sum to +6 percentage points, giving a mean of 6 / 9 = +0.6667%. The fifth sorted observation is −0.5%, so that is the median. Six positions lose money, yet total net P&L is +$60 because the large winner outweighs the other outcomes.

These are two useful descriptions of the same ledger. The median says where its center sits by rank. The mean incorporates the magnitude of the large winner. Neither establishes the frequency or size of future opportunities.

The sum of trade percentages is not an account return. We have not specified starting account equity, idle cash or overlapping exposure. For actual sequential compounding, follow the simple versus log returns guide using the appropriate portfolio return series.

Attribute the gap before judging it

Each observation contributes trade return / 9 percentage points to this sample mean. Trade I contributes +1.3333 percentage points. The other eight together contribute −0.6667 percentage points. Adding them gives +0.6667%.

That decomposition answers “what carried the average?” without replacing the full sample.

Excluding I is a sensitivity diagnostic, not a corrected estimate. If a strategy deliberately accepts repeated small losses to capture occasional large moves, removing its biggest winner removes part of its intended mechanism. Conversely, a large loss cannot be discarded merely because it disrupts a reassuring median.

Increasing I from +12% to +20%, with everything else fixed, raises the mean by 8 / 9 = 0.8889 percentage points. The median stays −0.5% because the middle rank does not change. This particular replacement illustrates resistance to an extreme magnitude; it does not mean the median can never change when observations are added or replaced.

Contribution percentages also need care. I supplies 200% of the net dollar total, because 120 / 60 = 2; the remainder supplies −100%. That is valid arithmetic but can be confusing. If total P&L is zero, these shares are undefined. Prefer the actual dollars and percentage-point contributions when the net total is small.

Equal trade weights can hide unequal money

Now keep every percentage outcome unchanged, but reduce I's entry notional to $100. All other trades still use $1,000. I earns $12, while the other eight still lose $60 together. The actual total becomes −$48.

The unweighted mean remains +0.6667% and the median remains −0.5%. Both still describe the nine percentage observations correctly. Neither by itself tells you the account's dollar result.

A notional-weighted mean instead equals:

sum(net P&L) / sum(entry notional) = −48 / 8,100 = −0.5926%.

This weights a dollar committed to an entry equally across the listed positions. Reused capital and different holding periods mean the $8,100 denominator is not necessarily starting account capital. Do not label this ratio portfolio growth.

For capital tied up over different durations, exposure-adjusted returns addresses the time-in-market denominator. That is a separate question from whether the middle trade resembles the average trade.

Investigate an extreme without erasing it

Suppose I's +12% originated from a bad exit-price decimal, duplicated proceeds or an impossible fill. Reconcile quantity, timestamps, price, fees and the matching position identifier. Correct a demonstrated error and retain a record of the original and corrected calculations.

If the fill is real, retain it in the full ledger even if it is unusual. NIST's outlier guidance distinguishes erroneous observations from legitimate extremes and warns against simply deleting an unexplained point. Its discussion also notes that an inappropriate distribution assumption can create misleading outlier labels. A large crypto trade outcome does not become invalid merely because a normal-model rule flags it.

A quieter failure is an export with missing returns replaced by zero. Those rows can move the median and dilute the mean. Missing is not breakeven. Verify the cause, report the missing count and apply a declared eligibility rule. Python's statistics input guidance also warns that NaN values can produce surprising sorting-based results. For an empty eligible sample, report both statistics as undefined; a zero entry denominator makes that trade's chosen return undefined.

Keep a rank-and-contribution review card

Use the following worksheet alongside the full ledger, preserving both favorable and unfavorable extremes.

Mean and median do not describe the entire payoff distribution. For a question about gains and losses relative to a chosen target, the Omega ratio threshold guide changes the analysis to a threshold-dependent measure. It should not be inferred from the mean–median gap alone.

These summaries are descriptive. The backtest trade-count discussion explains why many related trades may contain little independent evidence. A transparent report can therefore say: “The average was positive, the middle trade was negative, and one verified position carried the net gain.” That is more useful than selecting whichever headline sounds strongest.

Method and limits

This article is AI-assisted educational synthesis of primary statistical documentation, with an original hypothetical ledger and review worksheet. The arithmetic and alternative sizing were recomputed. No market dataset, future-return estimate or KLINEO reporting feature was tested. The example demonstrates how summaries differ under stated conventions; it does not validate a trading strategy.