Law of Large Numbers: Streaks and Reality

In the short run, anything can happen. In the long run, only your expectancy matters.

New traders abandon winning strategies after a few losses and chase losing strategies after a few wins. Both reactions ignore the single most important statistical law in trading: the Law of Large Numbers (LLN).

The law

The LLN states that as sample size grows, the sample mean converges to the true expected value:

lim(n→∞) (1/n) Σxi = μ

If your strategy has a true win rate of 55%, then:

• 10 trades → actual wins can easily be 3 or 8
• 100 trades → usually between 45 and 65
• 10,000 trades → almost exactly 55%

The average only settles onto the true mean as n grows. Small samples are dominated by variance.

What this means for your edge

A positive expected value (EV) strategy will make money — but only across enough trades. With a thin edge (say, EV of +0.2R per trade), you may need thousands of trades before the variance washes out and the edge becomes visible.

Trades	Likely range for a 55% win rate
10	27%–79%
100	45%–65%
1,000	52%–58%

Notice how the band shrinks with √n. This is why backtests with only 20 trades are nearly useless, and why live trading a new strategy for a month tells you almost nothing about its true edge.

Streaks are normal — not signals

A 55% win-rate strategy will, by pure chance, produce 6-, 7-, even 8-loss streaks. Traders interpret these as "the strategy broke" and abandon it. In reality, streaks are statistically expected. Use the binomial distribution:

P(k losses in a row) = (1 − p)^k

With p = 0.55, an 8-loss streak happens with probability ~0.008 — rare per sequence, but near-certain over a long enough career. Expect them; don't overreact.

The flip side: gambler's fallacy

Just as a streak doesn't mean the strategy is broken, it also doesn't mean a win is "due." Each independent trade still has a 55% chance. Past losses don't increase future win probability.

Practical rules

1. Judge strategies on hundreds of trades, not dozens
2. Pre-compute expected worst-case streaks so a normal drawdown doesn't panic you
3. Size positions so that LLN has time to work before you blow up — over-sizing kills the strategy before the long run arrives
4. Don't abandon a strategy for streak reasons alone; abandon it only when the long-run statistics shift

Summary

The Law of Large Numbers is the trader's faith: it says that if your edge is real, the long run will pay you. It also says the short run will be wild, frustrating, and full of meaningless streaks. Plan your capital and your psychology so that you survive to reach the long run where the math actually wins.