Chapter 9 · Win rate and payoff ratio
Why can a strategy with 90% wins still keep losing money?
- Skills to practice
- Probabilistic decisionsResearch Edge
- Read first
- Chapter 8 · Expected value
- 3D simulation
- None
Market scene
Lin compares two simulations. A has 90% chance to win $100, otherwise losing 1,000. B has 40% chance to win 2,000, otherwise losing 1,000. Neither includes costs yet.
A's frequent profitable notices feel safer. But its fixed-rule average is −$10 while B's is +$200.
Why may frequently being right still fail to make money?
Your decision
Assuming probabilities are credible, how will you compare?
Observe the result
| Teaching rule | Win chance | Mean win / mean loss | Mean per loss unit |
|---|---|---|---|
| A | 90% | 0.1 | −0.01 |
| B | 40% | 2 | +0.2 |
Comfortable winning frequency is not favorable payoff structure. One big win also cannot replace full records.
The mechanism
A wins 100 with 90% chance or loses 1,000; B wins 2,000 with 40% or loses 1,000. All are teaching assumptions, not historical performance. Normalize losses of 1,000 to one unit.
With average win b and loss one, break-even requires win probability × b = loss probability. Minimum probability is 1 ÷ (1 + b).
| Win relative to loss | Break-even probability before costs |
|---|---|
| 0.1× | About 90.9% |
| 1× | 50% |
| 2× | About 33.3% |
- Record every trade under one rule
- Measure win/loss amounts separately
- Combine them with probabilities
- Deduct costs
- Inspect different regimes
Actual estimates include early exits and abnormal losses. Planned target divided by stop is not realized average payoff. Chapter 6's card is the plan; journals record what materialized.
What it is called
Real markets
Chapter 15 combines frequent spreads with inventory losses. Positive-spread counts are not total-portfolio win probability.
Chapter 4 shows exits changing retained profits. Truncating large winners while retaining original payoff assumptions is inconsistent.
Chapter 13 separates quotes/fills. Target touches do not prove entire positions sold. Use executable rules for realized ratios.
Hands-on
Assume independent outcomes. A win earns the reward-to-risk amount in R; a loss costs 1R. The same cost is deducted on each trade. R is the stop-loss amount planned in advance.
Seed1; changing payoffs or costs leaves this outcome sequence unchanged. A sample win rate does not promise the next outcome, and the same sample cannot validate the probability you entered.
Course versionV1-docs; sourcelab:probability；Chapter 9 / TRD-PROB-003
Records parameters and results at the click only; does not mean the experiment passed.View snapshot to save
- Set wins 90%, payoff 0.1, costs 0; inspect mean.
- Switch to 40%, payoff 2; compare break-even probability and one sample.
- Hold win rate and lower payoff to find zero, then add costs.
- Write probabilities, realized payoffs, costs, sources, and omitted outcomes. Simulation only; no orders.
Change one variable
Three depths
- FoundationWhy can a strategy with a 90% win rate keep losing money?Chapter 9
- AdvancedWhat win-rate and reward/risk structures typify trend, mean-reversion, and Carry strategies?Advanced B · Strategy research
- InstitutionalHow can low-win-rate, high-reward/risk strategies complement high-win-rate strategies?Institutional
Write win rate and payoff together, then costs/extreme losses. Winning streaks must not set next size.
Estimate conditional win rates, tails, and payoffs for trend, reversion, and Carry. Categories do not determine fixed win rates; samples, exits, and costs change shapes. See Advanced B.
Continue the project: compare eight return shapes and tails.
Combining high/low win rates is not sufficient. Inspect shared losing regimes, simultaneous tails, and capital needed while waiting for rare winners. Strategy counts prove no diversification.
Continue the project: allocate different win-rate strategies by common risk.
Questions to take away
Chapter self-test
0.9 × 0.1 − 0.1 = −0.01R. The more frequent amounts remain too small.
1 ÷ 3, about 33.3%, before costs. Costs raise it.
Not automatically. Fill probability, horizon, and exits may change; reestimate.
0.4 × 2 − 0.6 = 0.2R becomes 0.4 − 0.6 = −0.2R.
One idea to take away
Combine win rate and reward/risk: expected return = win rate × average gain − loss rate × average loss.
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