OptiNod Academy
Expectancy: Why a High Win Rate Can Still Lose Money
Win rate is only one input in expectancy. Evaluate a system by combining win rate with reward-to-risk, then check sample size and trade frequency as well.
> Win rate is only one part of *expectancy*. Until it is combined with reward-to-risk, a 90% win rate tells you nothing by itself.
This is the first article in our risk management series. It explains how to evaluate trades by expectancy. The next articles cover stop-loss placement and position sizing.
Expectancy is the average profit or loss per trade if you repeat the same type of trade many times. A coin toss makes the idea simple. If you win $1 when you are right and lose $1 when you are wrong, the game breaks even over time. Its expectancy is 0. But if you win $2 when you are right and lose only $1 when you are wrong, the same 50% win rate leaves an average profit of $0.50 per toss.
Trading works the same way. If the average result per trade is positive after hundreds of similar trades, the system makes money over time. If it is negative, the system loses money. That average result per trade is expectancy.
Van K. Tharp was one of the first to formalize this concept for traders. In *Trade Your Way to Financial Freedom*, he defines it in one line: expectancy is the win rate multiplied by average profit, minus the loss rate multiplied by average loss. That single formula combines both win rate and reward-to-risk.
Most traders look at only one part of the formula: win rate. Being right eight times out of ten sounds like a good system, and trade screenshots usually lead with win rate. But win rate alone cannot tell you whether a system makes money. You also need the size of the average win and the average loss.
In fact, a high win rate can be dangerous. A system that wins small often and occasionally loses big can have a high win rate but zero or negative expectancy. The table below shows the numbers clearly.
The Distance Between Entry and Stop Is 1R
To calculate expectancy, profits and losses need a common unit. That unit is R.
R is the amount you decide in advance to risk on one trade: the distance between your entry price and stop-loss price. If you buy at $100 and get stopped out at $90, 1R is $10. If you sell that trade at $120, you made 2R. If you sell at $95, you lost 0.5R.
When every trade result is recorded in R, trades can be compared on the same scale regardless of asset price or account size. A $100 trade and a $60,000 trade can both be measured by how many R they gained or lost. Expectancy is the average of those R results.
The Same Win Rate Can Produce Opposite Results
Win rate and reward-to-risk each show only one side of a system. You need to combine them into expectancy to see whether the system actually makes money. Here are three systems in one table.
| System | Win Rate | Average Win | Average Loss | Expectancy |
| :-- | :-- | :-- | :-- | :-- |
| A | 50% | 1R | 1R | 0R |
| B | 50% | 2R | 1R | +0.5R |
| C | 80% | 0.5R | 2R | 0R |
A and B both have a 50% win rate, but their outcomes are completely different. A breaks even. B earns an average of 0.5R per trade. The only difference is reward-to-risk.
C has the highest win rate at 80%, but its expectancy is 0. Eight wins of 0.5R build 4R in gains, but two losses of 2R take back the full 4R. Add fees and slippage, and expectancy turns negative. If you looked only at win rate, C would look like the obvious choice. By expectancy, it is the most dangerous system.
When a High-Win-Rate System Is More Dangerous
A structure that wins small often and loses big occasionally is the same as system C in the table. Examples include fading overbought moves inside a range, or shorting every new high against a strong trend.
In early February 2024, BTC started near $42,500 and climbed almost straight to $73,777 in five weeks. Imagine shorting each new high during that move because the market looked overextended. Around $48,000, $52,000, and $64,000, brief pullbacks could have produced small gains near 1R, keeping the win rate high.
The problem came next. When price ran straight from $64,000 to $73,777 without a real pullback, one short could turn into a 5R or 6R loss. That single loss would erase all the earlier small gains. The system may look fine in win-rate screenshots, but its expectancy curve collapses during a single strong trend.
Why Low-Win-Rate Trend Following Survives
BTC rose about 4.5x from near $16,600 in January 2023 to a weekly high of $73,777 on March 11, 2024. A system that followed that trend to the end would not have a high win rate. Trend following accepts many small losses during sideways periods, then earns one large win that covers all of them.
Consider a trend-following system with a 35% win rate, an average loss of 1R, and an average win of 4R. Its expectancy is 0.75R. Even if it is wrong more than six times out of ten, it still earns an average of 0.75R per trade.
This is why trend followers can keep trading through a string of small losses. They know, through expectancy, that those losses are recovered by one large win. If they looked only at win rate, they would have abandoned a 35% system long before that.
Expectancy Needs a Large Enough Sample
Even if expectancy is positive, a small number of trades cannot tell you whether the result came from skill or luck. A 0.5R expectancy after 20 trades may be random, and the same system could turn negative over the next 20 trades. You need at least 100 trades if possible, across different market regimes, to see whether the expectancy holds.
Positive expectancy does not eliminate losing streaks. A 40% win-rate system is right two times out of five on average, but it can still normally include stretches of seven or eight consecutive losses.
That is why you must track the maximum losing streak along with expectancy. Even with a 0.75R expectancy, if the maximum losing streak is 12R, a trader risking 1R per trade will lose 12% of the account during that stretch. Without knowing this number, you may abandon a system during a normal losing period.
Before taking a new strategy live, check three things in the backtest.
- [ ] Sample: At least 100 trades, including different market regimes.
- [ ] Expectancy: Still positive after fees and slippage.
- [ ] Maximum losing streak: Measured in R, then converted into account impact to confirm you can withstand it.
If any of these three conditions is not met, postpone live trading and collect more data.
Multiply Expectancy by Trade Count
Even with the same expectancy, annual results can differ depending on trade frequency. Expectancy is the average R per trade. Multiply it by the number of trades over a given period, and you get the expected return for that period.
A system with 0.2R expectancy traded 200 times per year has an expected return of 40R. A system with 0.8R expectancy traded only 10 times per year has an expected return of 8R. On trade quality alone, the second system looks four times better. Once the number of opportunities is included, the first is five times ahead.
So a system needs to be evaluated on two axes. A setup with modest expectancy can produce strong annual returns if it appears often. A setup with high expectancy but rare opportunities carries a large opportunity cost. But increasing trade count also increases fees and slippage. If trading costs consume a large part of expectancy, more trades can reduce net expectancy instead of improving it.
Two Ways to Track Expectancy
The first is a trading journal that records every trade in R. Write down the entry, stop, and exit, then convert the result into R. After dozens of trades, you can see the actual expectancy of your system. If you record only dollar profit and loss, your benchmark shifts whenever account size changes. R keeps the measurement consistent across time.
The second is to read backtest statistics through the lens of expectancy. Looking only at total profit in an optimization result is the same trap as looking only at win rate. Two systems can have the same total profit, but if their average reward-to-risk and maximum losing streak are different, they will feel completely different to trade live.
In the next article, we will look at where this 1R comes from and how to choose a stop-loss location. The stop distance defines R, and once R is defined, every calculation in this article can begin.