What Is Expected Value?
Expected value tells you how much you will win or lose on average for each bet placed, assuming the same scenario repeated thousands of times. It does not predict the outcome of individual bets. Instead, it measures whether a bet is mathematically profitable.
The core idea:
If your estimated probability of winning is higher than the probability implied by the odds, the bet has positive EV.
Positive EV (+EV) bets grow your bankroll over the long term. Negative EV (-EV) bets shrink it, no matter how lucky you get in the short term.
The Expected Value Formula
For decimal odds, EV is:
EV = (p × profitWhenWin) − (q × stake)Where:
- p = your estimated chance of winning
- q = 1 − p (your chance of losing)
- profitWhenWin = stake × (decimalOdds − 1)
If EV is positive, the bet is profitable in theory. If EV is negative, the bet should be avoided.
Worked Example: Finding EV on a Betfair Market
Suppose you believe a football team has a 55% chance of winning, but the exchange is offering odds of 2.20.
- p = 0.55
- q = 0.45
- profitIfWin = stake × (2.20 − 1) = stake × 1.20
EV = (0.55 × 1.20 × stake) − (0.45 × stake) EV = (0.66 × stake) − (0.45 × stake) EV = 0.21 × stake
A 21% expected return is strongly positive. Even though the bet might lose on any given day, placing many bets at this edge would grow your bankroll over time.
Understanding Implied Probability
Decimal odds express probability in a different form. To convert odds to probability:
impliedProbability = 1 / decimalOddsSome examples:
- 2.00 implies a 50% chance
- 3.00 implies a 33.33% chance
- 5.00 implies a 20% chance
If you believe the real probability is higher than the implied probability, you have a +EV bet.
Using the Smarter Trades Expected Value Calculator
To make EV even easier, the Smarter Trades calculator lets you plug in:
- Your decimal odds
- Your stake
- Your estimated chance of winning
- Your exchange commission
The calculator returns full EV, break-even probability, net win after commission, and the EV over 100 theoretical bets. Try it here: Smarter Trades EV Calculator
Why EV Matters More Than “Picking Winners”
The goal of betting is not to win the most bets — it is to win the most money. A trader with a 40% strike rate can earn more than someone with a 60% strike rate if the first trader consistently takes +EV odds.
EV teaches you to:
- Stop taking short prices “for safety”
- Recognise when the market undervalues an outcome
- Ignore emotion and focus on long-term edges
- Develop strategies that actually scale
Common Mistakes Traders Make with EV
1. Overconfidence in Win Probability
The biggest danger in EV calculations is misjudging your edge. If you think a horse wins 35% of the time but the real number is closer to 25%, your EV is wrong — and you may be staking too much.
2. Forgetting Exchange Commission
Betfair charges commission only on winning bets. This reduces your net gain and must be included in your EV calculations. The Smarter Trades EV calculator includes this automatically.
3. Evaluating Bets in Isolation
EV works best across large samples. A single bet can win or lose regardless of EV. Over hundreds of bets, positive EV compounds and negative EV drains your bankroll.
How EV Connects to Kelly Staking
Kelly staking uses expected value as part of its formula. Without understanding EV, Kelly cannot be applied correctly. EV tells you whether a bet is profitable; Kelly tells you how much to stake.
You can learn more in our Kelly Staking Guide: Read the Kelly Guide
Frequently Asked Questions
Does EV guarantee long-term profit?
No. EV assumes your win probability estimates are accurate. If those estimates are wrong, your EV will also be wrong. But if your estimates are sound, EV is the only reliable way to guide long-term profitability.
What is break-even probability?
Break-even probability tells you how often you must win at certain odds to avoid losing money.
It is calculated as 1 / decimalOdds.
If you believe your chance of winning is higher than this number, the bet is +EV.
Can EV apply to lay betting?
Yes — EV works for both back and lay bets, as long as the correct formulas and commissions are used. The Smarter Trades calculator supports EV on both sides of the market.
Is EV useful for in-play betting?
EV can be used in any market, but estimating true win probability in-play is much harder due to jumps in odds and rapidly changing conditions. In-play EV requires strong models or deep market experience.
Where is the EV calculator?
You can find it here: Smarter Trades EV Calculator.