Sizing and Survival

The Arithmetic of Drawdown

Why a 50% loss needs a 100% gain, and what that means for risk per trade.

intermediate · 3 min read · 20 XP

Losses and gains are not symmetric, and the asymmetry gets worse the deeper you go. This lesson shows you the numbers, because they are the strongest argument for small risk per trade that exists.

The recovery table

Lose a percentage and you must gain a larger percentage to get back, because the gain is calculated on a smaller base.

Drawdown Gain needed to recover
5% 5.3%
10% 11.1%
20% 25%
30% 42.9%
50% 100%
70% 233%
90% 900%

The curve is gentle at first and then vicious. Below about 30% it stops being a setback and becomes a different problem: you now need a performance you have never demonstrated just to return to where you started.

The practical conclusion

Keep drawdowns shallow and everything else becomes possible. This is the entire argument for small risk per trade — not caution for its own sake, but because the recovery maths punishes depth so severely.

What risk per trade does to a losing streak

Losing streaks are not bad luck; they are arithmetic. A strategy that wins 50% of the time will produce a run of 7 losses roughly once every 128 sequences. Over a year of trading, you will see it.

Here is the damage from 10 consecutive losses at different risk levels:

Risk per trade Account after 10 losses Gain needed to recover
1% 90.4% 10.6%
2% 81.7% 22.4%
5% 59.9% 67.0%
10% 34.9% 186%

At 1% risk a ten-loss streak is uncomfortable. At 10% it is close to fatal — and a ten-loss streak is a completely normal thing for a profitable strategy to produce.

"But 1% is so slow."

It is slower per trade and dramatically faster over a career, because you are still trading. The trader risking 10% will have a spectacular month at some point and will not survive the year. Compounding only works on an account that still exists — which is the entire game.

Expectancy: what actually makes money

Win rate on its own tells you nothing. What matters is expectancy:

expectancy = (win rate × average win) − (loss rate × average loss)

A strategy winning 40% of the time with a 1:3 risk-to-reward ratio:

(0.40 × 3) − (0.60 × 1) = 1.20 − 0.60 = +0.60R per trade

Positive, despite losing 60% of the time. Meanwhile a strategy winning 90% with a 1:0.1 ratio:

(0.90 × 0.1) − (0.10 × 1) = 0.09 − 0.10 = −0.01R per trade

Negative, despite winning nine times out of ten. High win rates paired with tiny targets and wide stops are the classic trap: it feels wonderful and loses money.

Read the ratio and its break-even

Interactive exercise — enable JavaScript to try it.

What to remember

  • Recovery is asymmetric and gets worse with depth: 50% down needs 100% up.
  • Losing streaks are normal arithmetic, not bad luck — size so a ten-loss run is survivable.
  • Expectancy, not win rate, determines whether a strategy makes money.
  • A 40% win rate at 1:3 is profitable; a 90% win rate at 1:0.1 is not.

Drawdown recovery is asymmetric and worsens with depth, which is the real argument for small risk per trade. Losing streaks are normal arithmetic rather than misfortune, and what determines profitability is expectancy — the combination of win rate and payoff — not the win rate alone.

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