Edge or luck? How many trades before a win rate means anything
hypothesess.com, AI-assisted writing ยท
How many trades before a win rate means anything? Short answer: far more than feels natural. Fifty trades at 60% happens to a coin-flipper with no edge at all about one time in ten [1]. To tell a real 55% edge from luck you need roughly 800 trades [1]. This notebook entry shows why, with every number computed in the open.
What does luck alone look like?
Picture 1,000 traders with no edge at all. Every trade is a fair coin. Give each of them 50 trades and look at how their win rates spread out. About a hundred of the thousand land at 60% or better [1]. Any of them would swear the strategy works, and would have a 50-trade record to show for it.
Stretch the same thousand to 200 trades each and the lucky crowd shrinks to about three [1]. At 500 trades there is nobody left: a coin reaches 60% of 500 about four times in a million [1]. Luck does not disappear with more trades; it stops being able to impersonate a 60% edge.
The middle 95% of those thousand coin-flippers sits between roughly 36% and 64% at 50 trades, and between 43% and 57% at 200 [1]. That band is the noise. A win rate inside it is a win rate the noise can explain.
So what does Maya's 60% actually tell her?
Two numbers answer it, and both come from the same 30 wins in 50 trades.
The first is the one from the guess: the chance that a coin does at least this well is 10.13%, about 1 in 10 [1]. That is not rare. In any room of ten coin-flippers, one has Maya's record.
The second is the range her true win rate could be in. Thirty of fifty gives a 95% interval from 46.2% to 72.4% [1], computed with the Wilson method, which behaves properly at small samples where "rate plus or minus two standard errors" does not [2]. The range includes 50%. Maya may be a 70% trader or a coin, and 50 trades cannot say which.
Put in your own numbers: the box below recomputes both.
How many trades would she need?
It depends on how big her edge really is. A big edge shows quickly; a small one hides in the noise for a long time.
With the usual test (5% significance, 80% power), a trader whose true win rate is 65% needs about 85 trades before the record stands clearly apart from a coin [1]. A true 60% needs about 194. A true 55% needs about 783, which at three trades a week is five years of patient logging. A true 52%, a real but thin edge of the kind many systematic strategies actually have, needs about 4,900 trades [1].
Small edges are real. They are also slow to prove, and that gap is where most backtests go wrong: the strategy is judged on the number of trades the data happened to contain, not on the number the edge would need.
The arithmetic, in the open
| Figure | Value | Where it comes from |
|---|---|---|
| Chance a coin wins 30 or more of 50 | 10.13% | binomial tail, p = 0.5, summed exactly [1] |
| Chance a coin wins 120 or more of 200 | 0.28% | binomial tail [1] |
| 95% range for 30 of 50 | 46.2% to 72.4% | Wilson interval [1] |
| Trades to tell a true 55% from a coin | 783 | one-proportion sample size, 5% significance, 80% power [1] |
| Trades to tell a true 52% from a coin | 4,904 | the same formula [1] |
The chance a fair coin wins at least k of n is the binomial tail, the sum of C(n, i) × 0.5^n from i = k to n. The trades needed come from the sample-size formula for one proportion, n ≈ ((1.96 × √0.25 + 0.84 × √(p(1 − p))) / (p − 0.5))² [2]. None of this allows for testing many strategies and keeping the best one; each extra strategy you try is another coin-flipper in the room, and the best of twenty of them shows 60% or better at 50 trades about 88% of the time [1].
Check yourself
A strategy wins 12 of 20 trades. Is that stronger or weaker evidence than 120 of 200? Much weaker. The win rate is the same 60%, but a coin does it about 25% of the time at 20 trades and about 0.3% of the time at 200 [1].
You test 20 strategies on the same data and keep the best. Why should its win rate impress you less? Twenty coin-flippers make it likely that one of them looks good by luck: at 50 trades each, the best of twenty reaches 60% about 88% of the time [1].
Your true edge is 52%. Roughly how many trades before a test can tell? About 4,900 [1]. Small edges are real but slow to prove.
Maya is an illustration, not a real trader. This is a lab notebook entry for hypothesess.com, written with AI and checked by hand; every figure in it was computed, not estimated, and the box above recomputes the ones that depend on your numbers.