Mathematical expectation
Definition
Mathematical expectation (Expected Value, EV) is the average result of one trade over a long stretch. Computed by the formula (Win Rate × profit) − ((1 − Win Rate) × loss): positive EV means the approach makes money over many trades, negative means it is still losing.
What mathematical expectation shows
Mathematical expectation answers a strategy's main question: does it make or lose money over the long run. A single trade can close any way, but average the result over hundreds of trades and it tends toward EV. Positive EV — the approach is in profit; negative — in the red, and no streak of luck changes that over distance.
The formula combines two numbers that are misleading on their own — the win rate and the payout: (Win Rate × profit) − ((1 − Win Rate) × loss). In binary options the loss equals the whole trade amount and the profit only the payout percent, so EV is sensitive to both numbers at once.
A worked example
Take a 57% win rate and an 80% payout. Compute EV per $1 of stake:
| Component | Calculation | Result |
|---|---|---|
| Contribution of wins | 0.57 × 0.80 | +0.456 |
| Contribution of losses | 0.43 × 1.00 | −0.430 |
| EV per trade | 0.456 − 0.430 | +0.026 |
Each trade returns +2.6 cents on the dollar on average — the approach is in profit. Drop the win rate to 55% and EV becomes 0.55 × 0.80 − 0.45 = −0.01: the same approach now loses. Two percentage points of win rate flipped the sign — which is why EV is computed precisely, not by eye.
Mathematical expectation in the terminal
EV is not printed directly in the terminal, but it is assembled from the statistics: BinoView Supercharts shows the win rate and the series result, and the payout is visible per asset. Plug them into the formula and you get an honest answer on whether to continue. The closest ready-made proxy is the profit factor (earned over lost): above 1 roughly corresponds to positive EV.
How it differs from win rate
Win rate and mathematical expectation are often confused, but they answer different questions. Win rate is "how often do I guess right"; EV is "how much does that bring on average". A strategy with a 65% win rate and a 60% payout loses to one with a 56% win rate and a 90% payout, even though the first looks better on win rate. What you want to keep positive is EV — it is the final verdict, and win rate is just one of its components.
Frequently asked questions
How does expected value differ from win rate?
Win rate tells you how often you win; mathematical expectation tells you how much one trade returns on average, given the payout. A high win rate at a low payout can still be negative EV. The final verdict on profitability is EV — win rate is just one input to its calculation.
How do you compute your strategy's EV?
You need three numbers: the win rate, the profit on a win and the loss on a loss. In binary options the loss is the whole trade amount and the profit is the payout percent. Plug them into (Win Rate × payout) − ((1 − Win Rate) × 1) per unit of stake and read the sign of the result.
Can EV be negative during a profitable streak?
Yes. Over a short stretch a lucky streak wins even with negative EV — that is just sampling luck. But the more trades you take, the closer the result moves to the expectation. Over distance, negative EV always beats luck.