How to calculate risk of ruin from win rate, payoff and risk per trade

Contents

1. How do you calculate the risk of ruin for a trading strategy?
2. How do win rate and payoff ratio change the probability of ruin?
3. What risk of ruin is safe?
4. 1% vs 2% risk per trade: how much does it change the odds?
5. Where does the simple risk of ruin formula break down?
6. Why is Monte Carlo on your real trades a better estimate of ruin?
7. Frequently asked questions
8. References

How do you calculate the risk of ruin for a trading strategy?

A risk of ruin calculator takes four numbers from your backtest report: win rate, payoff ratio, risk per trade as a share of capital, and the ruin level you choose. It returns the probability that a run of losses pulls the account down to that level. Feed it after-cost figures and read the output as a percent.

Risk of ruin is the probability that your equity falls to a preset level before the edge of the strategy has time to work. Think of a staircase. Each losing trade is one step down. The ruin level is the basement floor. The question is how likely it is that you take enough steps down in a row, or nearly in a row, to reach that floor. The free risk of ruin calculator does the arithmetic from the four inputs below, so this article is about what to put in and how to read what comes out.

Input	What it is	Where you get it
Win rate	Share of closed trades that ended with a profit, after commission and slippage	Trade summary of the backtest report
Payoff ratio	Average winning trade divided by average losing trade, both after costs	Average win and average loss in the report
Risk per trade	Share of capital you lose when the stop is hit, for example 1%	Your position-sizing rule: stop distance × point value × contracts ÷ capital
Ruin level	The equity level at which you would stop trading the strategy, as a share of starting capital	Your own decision, written down before you trade

The ruin level does not have to be zero. Most traders stop long before the account is empty, so set it where you would really stop: 50% of starting capital is a common choice, 30% is a stricter one. Risk per trade is fixed by the stop, so the choice of stop described in stop loss types for systematic futures strategies decides this input as much as the contract count does.

The one formula worth knowing is the textbook case where a win and a loss are the same size (payoff ratio 1):

probability of ruin = ((1 − A) ÷ (1 + A))^U

Here A is the edge per trade, which is the win rate minus the loss rate (55% wins and 45% losses give A = 0.10), and U is the number of risk units the account can lose before it touches the ruin level (risking 1% per trade with a ruin level 50% below the start gives U = 50). The calculator extends this to payoff ratios other than 1, which have no short closed form.

How do win rate and payoff ratio change the probability of ruin?

Win rate and payoff ratio together set the edge per trade, and only a positive edge can push the probability of ruin toward zero. A high win rate with a small payoff and a low win rate with a large payoff can carry the same edge, so neither number means anything on its own. Read them as a pair.

The edge per unit risked is the expectancy, and expectancy is the average amount you gain per trade for every one unit you risk: win rate × payoff ratio − loss rate. The free win rate and expectancy calculator returns this number from the win rate, average win and average loss in your report, so you can check its sign before you think about size. When this is zero or negative, no position size is small enough to make the probability of ruin zero; you only slow the walk to the basement. When it is positive, the probability of ruin falls as the edge grows and as the size per trade shrinks. The trade-off between the two inputs, and the break-even payoff for each win rate, is covered in detail in how to calculate the risk reward ratio and why win rate decides it.

The last point in the example matters for breakout and trend systems, which usually win less than half the time. Their long losing streaks are normal, not a fault, but they need a smaller risk per trade than a high-win-rate system with the same expectancy to reach the same probability of ruin.

What risk of ruin is safe?

A probability of ruin that rounds to zero at your chosen ruin level is the only comfortable result. A result of a few percent means the position size is too large for the edge. A result in double digits means the strategy is being traded on luck. In every case the fix is size, because the entry rule does not change the arithmetic.

A working rule many systematic traders use has three zones. The thresholds are a judgment, not a law, but the logic behind them is simple: if you plan to trade a strategy for years, a probability of ruin of even 5% per strategy adds up quickly across several strategies and several years.

Result	What it means	What to change
Under 1%	Normal losing streaks do not reach the ruin level at this size	Nothing; trade at this size
1% to 5%	The edge is real but the size is too large for it	Cut risk per trade until the result drops under 1%
Above 5%	The edge is too small for this size, or there is no edge	Cut size sharply, or go back to the strategy and check that the edge survives costs

Notice what is not on the list: a better entry signal. A trader who sees 8% risk of ruin and goes looking for a filter to raise the win rate is solving the wrong problem. Halving the risk per trade changes the result far more than a few points of win rate, as the next section shows.

1% vs 2% risk per trade: how much does it change the odds?

Doubling the risk per trade from 1% to 2% does not double the probability of ruin; it multiplies it many times over. The reason is in the exponent of the formula: the account at 2% can absorb only half as many losing units before it touches the ruin level, and the probability of a streak that long falls off steeply with each extra unit of room.

The same effect shows up when real trades are resized. AlphaPrime (Valynox) ran a search on NQ daily bars and kept one candidate out of 1,024 it tried, chosen for its return against its drawdown. The rule is a stand-in built from standard indicators, not a sizing rule itself. The box below takes that candidate's closed trades and applies nine money-management methods to them with $100,000 of starting capital and at most 10 contracts. The entries and exits stay the same in every row; only the size changes, so any difference between rows comes from sizing. Because the candidate was picked after the fact as the best of many tries, every row is flattered by that selection.

Read the max drawdown column against the average contracts column. Fixed dollar risk averaged 2.62 contracts and reached a max drawdown of $120,065. Fixed fractional risk averaged 7.83 contracts on the same trades and reached $626,980. The drawdown grew by more than the contract count did, and it was survivable in this run only because it arrived after equity had already grown far above the $100,000 start. A trader who began trading just before that stretch would have met it from a much lower peak. That is the risk of ruin question in real money: the order of the trades decides whether the same drawdown is a bad year or the end. Kelly (1956) derived the fraction that maximizes long-run growth, and sizing above that fraction lowers growth while deepening drawdowns, which is why the high-size rows here are not simply "more of a good thing".

Where does the simple risk of ruin formula break down?

The textbook formula gives a floor, not a full estimate, because each of its four assumptions is broken by real futures trading in a direction that makes ruin more likely. Knowing which assumption fails for your strategy tells you how much to distrust a result that looks comfortable.

1. Same amount risked on every trade. The formula assumes the stop always fills at the stop price. In futures, a stop order becomes a market order when touched, so a fast move or an overnight gap fills it further away, and the "1% loss" becomes 1.5% or 3%. Leverage makes the gap worse in account terms, as how futures leverage changes backtest drawdown works through with numbers. A margin increase during a volatile period can also force a smaller position or a forced exit at a bad price, which is one more way the amount lost on a single trade departs from the planned 1%.
2. Only two outcomes, win or lose a fixed amount. Real trade results spread from tiny to very large. A list with a few huge winners and many small losers has the same average as a tidy two-value list, but its equity path swings more, and more swing means a higher chance of touching the ruin level.
3. Each trade independent of the last. Losses cluster. A trend system loses in sideways markets, and sideways markets last weeks. A mean-reversion system loses in strong trends, which also last. The formula treats ten losses in a row as a rare coin-flip event; for a strategy in the wrong regime, it is a normal month.
4. Costs already inside the win rate. If the win rate and payoff ratio come from a backtest without commission and slippage, both inputs are too kind, and the result inherits the error. Every input should come from a report that charged fees and slippage on each trade.

Each break moves the true probability upward. The formula result is therefore the lowest the probability of ruin can be, given your inputs. The honest estimate needs the real trade list, which is the subject of the last section.

Why is Monte Carlo on your real trades a better estimate of ruin?

Monte Carlo on the real trade list gives a better estimate of ruin because it keeps the actual spread of wins and losses instead of a two-value approximation, and it tests many possible orders of the same trades. Monte Carlo simulation is a method that answers a question by running the same random experiment thousands of times and counting the outcomes, first described by Metropolis and Ulam (1949). For a trader, the experiment is: shuffle the closed trades like a deck of cards, deal them out again, and see whether this ordering touches the ruin level.

1. Take the closed trade list from the backtest, each trade with its net result after commission and slippage.
2. Reshuffle or resample the order thousands of times. Reshuffling keeps every trade exactly once in a new order; resampling draws trades with replacement, the bootstrap idea of Efron (1979), so some trades appear twice and some not at all, which also tests a somewhat different mix of outcomes.
3. Draw each ordering as an equity path from your starting capital, with the ruin level as a horizontal line.
4. Count the share of paths that cross the line. That share is the estimated probability of ruin at this size. Read the distribution of max drawdown at the same time; its tail tells you how bad a normal unlucky ordering can get.

The box below is the trade list such a test would use. It is the same NQ run as the sizing table above: daily bars from 2019-01-02 to 2025-06-30, long and short, one contract, $20 commission and $10 slippage per trade. The rule is a stand-in built from standard indicators that enters and exits on one signal, with no stop or target; it is not a sizing or ruin rule itself. The search tried 1,024 candidates and kept this one for its return against its drawdown, so the numbers are flattered by that choice, and they describe one past path, not what the rule earns or what a reader can expect.

Two things in this box matter for ruin. First, 151 trades is enough to reshuffle but not many; with a sample this size the tail of the drawdown distribution is itself uncertain, and a run with a few hundred trades would give a steadier answer. Second, the single backtest shows one max drawdown of $62,950, but that figure belongs to one ordering of the trades. The Monte Carlo view below shows how wide the range of drawdowns becomes when the order changes. The closed-trade list that feeds this view, with each trade's result after costs, is the trade table in AlphaPrime's Performance Report, and the free Monte Carlo simulator accepts a pasted list of trade results and draws the drawdown distribution from it.

Bailey, Borwein, López de Prado and Zhu (2014) show that the best result of many tries is almost always inflated, which applies to this box as much as to any other: a kept candidate's trade list is kinder than the list a fresh strategy would produce, so treat its Monte Carlo result as the gentle case. Reading the drawdown tail, and why the single backtest drawdown is usually the optimistic one, is the subject of why your real max drawdown is probably worse than the backtest.

Next step: export the closed trade list of one strategy you are considering, with commission and slippage charged on every trade. Write down the ruin level where you would really stop. Run the trades through the calculator with your planned risk per trade, then reshuffle the same list and count how many paths cross your line. If the two answers differ, trust the larger one and cut size until it rounds to zero.

Frequently asked questions

What risk of ruin is considered safe?

A result that rounds to zero at the ruin level you set is the comfortable one. Results between 1% and 5% mean the edge is real but the position is too large for it; cut risk per trade until the result falls under 1%. Above 5%, the size is far too large for the edge, or the edge does not survive costs, so reduce size sharply and recheck the strategy with fees and slippage included.

How much difference does 1% vs 2% risk per trade make?

Far more than double. At 2% the account can absorb only half as many losing units before the ruin level, and the probability of a streak that long falls steeply with each unit of extra room. In the worked example in this article, moving from 1% to 2% took the probability of ruin from about 0.004% to about 0.7%, roughly 150 times higher, with the same win rate and payoff.

How do win rate and payoff ratio affect the probability of ruin?

Together they set the edge per trade: win rate × payoff ratio − loss rate. If that number is zero or negative, no position size brings the probability of ruin to zero. If it is positive, a higher payoff lets a lower win rate reach a near-zero result, and a higher win rate lets a lower payoff do the same. Two strategies with the same edge but different win rates do not have the same risk of ruin; the one with fewer, larger winners swings more and needs a smaller size.

Is risk of ruin the same as maximum drawdown?

No. Maximum drawdown is the largest fall from a peak that one specific equity path actually had. Risk of ruin is the probability that some path of the same trades falls to a level you chose in advance. A backtest gives one drawdown; a Monte Carlo reshuffle of the same trades gives the range of drawdowns and the share of paths that reach the ruin level.

References

• Kelly, J. L. (1956). A New Interpretation of Information Rate. Bell System Technical Journal, 35(4), 917–926.
• Metropolis, N., & Ulam, S. (1949). The Monte Carlo Method. Journal of the American Statistical Association, 44(247), 335–341.
• Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics, 7(1), 1–26.
• Bailey, D. H., Borwein, J., López de Prado, M., & Zhu, Q. J. (2014). Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance. Notices of the American Mathematical Society, 61(5), 458–471.