Risk of Ruin Formula quantifies the exact probability that a trader will exhaust their capital — or breach a defined drawdown limit — before reaching a profit target. Formalized for trading by Ralph Vince in The Mathematics of Money Management (1992), it takes three inputs: win rate, average reward-to-risk ratio, and position size. The output is a single number that tells you whether your sizing is survivable.
Key Takeaways
- Position size — not win rate — is the primary lever. Cutting risk per trade from 10% to 1% can reduce ruin probability from 13.5% to near zero on the same strategy.
- A zero or negative edge makes ruin probability 100% regardless of how small your position size is — the formula only works when A is greater than 0.
- Ruin does not have to mean $0. Prop traders with a 10% drawdown limit have a much shorter survival horizon than their capital balance suggests.
How to Calculate Risk of Ruin
The standard formula is:
RoR = ((1 − A) / (1 + A))^N
A — Your per-trade edge, expressed as a decimal fraction of the unit risked:
A = (win_rate × avg_win_R) − (loss_rate × avg_loss_R)
N — Number of risk units in the account:
N = total_capital ÷ risk_per_trade
A trader needs at least 100 trades of journal data to estimate A reliably. Using fewer trades produces noisy inputs that make the output meaningless.
Edge case: If A is 0 or negative, ((1 − A) / (1 + A)) is 1 or greater, and raising it to any power yields 1 (100% ruin) or higher. The formula signals that no position sizing can rescue a losing system. Van Tharp documented that most retail traders risk 5–10% per trade, landing them in the 10–40% ruin probability range even when they believe they have a positive edge.
Quick Reference
| Aspect | Detail |
|---|---|
| Formula | RoR = ((1 − A) / (1 + A))^N |
| Edge A | (win rate × avg win R) − (loss rate × avg loss R) |
| Risk Units N | Total capital ÷ dollar risk per trade |
| Good Range | RoR below 1% |
| Warning Signs | RoR above 5%; any scenario where A is 0 or negative |
Practical Example
A trader has a $25,000 account and 100 trades of journal history: 50% win rate, average winner +$300 (1.2R), average loser −$250 (1.0R).
Step 1 — Calculate edge A:
A = (0.50 × 1.2) − (0.50 × 1.0) = 0.60 − 0.50 = 0.10
Step 2 — Apply three position size scenarios:
| Scenario | Risk Per Trade | N (units) | RoR Calculation | RoR |
|---|---|---|---|---|
| A — 1% risk | $250 | 100 | (0.90/1.10)^100 | ~0.000000019% |
| B — 5% risk | $1,250 | 20 | (0.8182)^20 | ~1.8% |
| C — 10% risk | $2,500 | 10 | (0.8182)^10 | ~13.5% |
Same trader, same edge, same $25,000. Scenario A is statistically safe. Scenario C means a roughly 1-in-7 chance of total ruin — before a single market condition changes.
Prop firm variation: If ruin is defined as a 10% drawdown ($2,500 loss limit rather than $25,000), N drops to 10 units at 1% risk per trade instead of 100. That shifts RoR from near-zero to ~13.5% even at conservative sizing. Prop traders must recalculate N using their drawdown ceiling, not their full balance.
The Risk of Ruin formula calculates the probability a trader loses their entire account before hitting a profit target. It uses win rate, average win-loss ratio, and position size. Smaller position sizes dramatically reduce ruin probability, even with an identical trading edge.
Common Mistakes
- Using too few trades to estimate edge. An A value derived from 20 trades has enormous variance. The formula requires 100 or more trades for the edge estimate to be statistically meaningful.
- Defining ruin as $0 when a drawdown limit applies. A prop trader with a $50,000 account and a 10% drawdown rule hits ruin at −$5,000, not −$50,000. Using the full balance as the ruin threshold understates risk by an order of magnitude.
- Assuming a positive backtest edge equals a positive live edge. Overfitted backtests inflate win rate and average win, shrinking A artificially. RoR calculated on backtest data can be orders of magnitude lower than live trading reality.
- Ignoring the Kelly Criterion relationship. Kelly gives the position size that maximizes long-run growth. Risking more than twice the Kelly fraction produces negative geometric growth in the long run, even if your edge is real. RoR and Kelly together define the survivable sizing range.
How JournalPlus Tracks Risk of Ruin Formula
JournalPlus automatically calculates your win rate, average R-multiple on winners, and average R-multiple on losers from your trade log, giving you the inputs to compute edge A from real data rather than estimates. The risk-per-trade report shows your actual historical sizing, so you can calculate N and plug both values directly into the RoR formula as your sample size grows past 100 trades.
