Understanding Expected Value: The Math Behind Prop Firm Profitability

When evaluating whether to take a prop firm challenge, most traders focus on one question: "Can I pass?" But the better question is: "What's my expected return per attempt?" This is where expected value (EV) changes everything.

What Is Expected Value?

Expected value is a statistical concept that calculates the average outcome of an event if it were repeated many times. For prop firm challenges, the formula is:

EV = (Pass Rate × Net Profit After Fees) − (Fail Rate × Challenge Cost)

A positive EV means the challenge is profitable over many attempts. A negative EV means you're expected to lose money over time — even if you occasionally pass.

A Real-World Example

Let's say you're considering an FTMO $100K challenge that costs $540:

• Your simulated pass rate: 45%
• Average gross profit when you pass: $8,200
• Profit share: 80% → net profit = $6,560
• Net after fee: $6,560 − $540 = $6,020

Your EV per attempt:

EV = (0.45 × $6,020) − (0.55 × $540) = $2,709 − $297 = $2,412

This is a highly positive EV. On average, each challenge attempt is worth $2,412 to you — even accounting for the 55% of times you'll fail and lose the fee.

Why Pass Rate Alone Is Misleading

A 30% pass rate sounds bad, but if your average profit when passing is very high, the EV can still be strongly positive. Conversely, an 80% pass rate with tiny profits might yield a worse EV than a 30% pass rate with large profits. Always look at the complete picture.

The Break-Even Pass Rate

Another useful metric is your break-even pass rate — the minimum pass rate needed for EV to equal zero:

Break-Even Rate = Challenge Cost ÷ (Net Profit When Passing + Challenge Cost)

If your actual pass rate exceeds this threshold, the challenge has positive expected value for you.

Optimising Your EV

There are several ways to improve your expected value:

• Risk sizing: Finding the optimal risk level that maximises EV (not pass rate)
• Firm selection: Different firms' rules suit different strategies
• Strategy filtering: Some of your strategies may hurt your pass rate
• Cost comparison: Lower fees directly improve EV

PropFirmSim's Risk Sweep and Compare tabs are designed specifically to help you optimise these variables using your actual trade data.