Expectancy Calculation Guide

Expectancy is one of the most fundamental and important performance metrics in quantitative trading. In a single number, it tells you: on average, how much do you expect to earn or lose per trade over the long run?

What is Expectancy?

The definition of Expectancy:

Expectancy = (Win Rate × Average Profit) - (Loss Rate × Average Loss)

Or expressed equivalently:

Expectancy = Win Rate × Average Win-Loss Ratio - Loss Rate
(in units of average loss amount)

A Concrete Example

Suppose your strategy historical data:

• Total Trades: 100
• Profitable Trades: 55 (Win Rate 55%)
• Losing Trades: 45 (Loss Rate 45%)
• Average Profit: $500
• Average Loss: $300

Calculation:

Expectancy = (0.55 × $500) - (0.45 × $300)
           = $275 - $135
           = $140

This means: on average, each trade expects to earn $140.

Intuitive Understanding

Imagine you have a strategy with an Expectancy of $140:

• If you execute 10 trades, expected total profit ≈ $1,400
• If you execute 100 trades, expected total profit ≈ $14,000
• If you execute 1,000 trades, expected total profit ≈ $140,000

Key Insight: Expectancy tells you the long-term average result. In the short term, you may experience consecutive losses, but as the number of trades increases, actual results converge toward the Expectancy.

Relationship Between Expectancy and Other Metrics

Expectancy vs. Win Rate

Expectancy vs. Profit Factor

Relationship between the two:

• If Expectancy is positive, Profit Factor is usually > 1
• If Expectancy is negative, Profit Factor is usually < 1
• But they may rank strategies differently (different scales)

Steps to Calculate Expectancy

Step 1: Collect Trade Data

Collect all historical trade records:

Step 2: Calculate Win Rate and Loss Rate

Win Rate = Profitable Trades / Total Trades
Loss Rate = Losing Trades / Total Trades

Step 3: Calculate Average Profit and Average Loss

Average Profit = Sum of all profitable trades / Number of profitable trades
Average Loss = |Sum of all losing trades| / Number of losing trades

Step 4: Calculate Expectancy

Expectancy = (Win Rate × Average Profit) - (Loss Rate × Average Loss)

Applying Expectancy in Strategy Development

1. Strategy Screening

When developing new strategies, Expectancy is the first evaluation metric:

• Expectancy < 0: Strategy lacks long-term profitability — abandon
• Expectancy 0-50: Strategy is sustainable but thin margins
• Expectancy 50-200: Strategy has good profitability
• Expectancy > 200: Strategy has strong profitability

2. Strategy Comparison

When choosing among multiple candidate strategies:

• Prioritize strategies with higher Expectancy
• But also consider capital requirements, risk tolerance, etc.

3. Capital Management

Expectancy is used to calculate optimal position sizing:

Suggested Position Size = (Expectancy / Average Loss Amount) × Kelly Factor

How Algo Lab Uses Expectancy

Every Algo Lab strategy is evaluated with Expectancy before publication:

1. Minimum Threshold: Expectancy must be ≥ $30 (per trade)
2. Rolling Monitoring: Monthly rolling Expectancy calculated for early decay signals
3. Strategy Scoring: Expectancy accounts for 20% of strategy score weight

Limitations of Expectancy

1. Short-Term Volatility

Expectancy is a long-term average; short-term results may deviate significantly:

• Even with positive expectancy, you may experience 10 consecutive losses
• Sufficient number of trades needed to converge toward Expectancy

2. Assumes Independent Trades

Expectancy calculation assumes trades are independent, but real trades may be correlated:

• Market regime changes may cause correlated trade outcomes
• Losses may cluster during periods of market turbulence

3. Ignores Capital Management

Expectancy does not tell you:

• How much capital to allocate
• How to control maximum drawdown
• What the risk-adjusted return is

Recommendation: Use Expectancy alongside Profit Factor, Sharpe Ratio, Maximum Drawdown, and other metrics.

Conclusion: Expectancy is the Soul of a Strategy

Expectancy summarizes a strategy's long-term profitability in a single, simple number. It is the starting point of strategy development and the endpoint of strategy evaluation — if a strategy's Expectancy is negative, no amount of beautiful secondary metrics can make it worth using.

Every Algo Lab strategy undergoes rigorous Expectancy calculation and validation, ensuring you face strategies with genuine long-term profitability.

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Frequently Asked Questions

What is Expectancy?

Expectancy is the average amount you expect to earn or lose per trade over many repetitions. It combines win rate and risk-reward ratio, making it the core metric for determining whether a strategy has long-term profitability.

How is Expectancy calculated?

Expectancy = (Win Rate × Average Profit) - (Loss Rate × Average Loss). Example: Win rate 55%, average profit $500, average loss $300. Expectancy = (0.55 × 500) - (0.45 × 300) = $130. This means each trade expects to earn $130 on average.

Does a positive Expectancy guarantee profit?

No. Positive expectancy means you will profit on average over many repeated trades, but short-term losses are still possible. It also does not reflect maximum drawdown or capital management needs. Positive expectancy strategies still require strict risk management.