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Expected Value
Quick Summary
Expected value (EV) tells you what a bet is worth over the long term. By comparing the odds to your estimated probability of an outcome, EV reveals whether a wager is likely to generate profit or loss if repeated many times.
What Is Expected Value?
Expected Value is a statistical measure of a bet’s average result over many repetitions. It combines:
- Your estimated probability of success
- The payout if the bet wins
- The cost if the bet loses
EV helps you quantify whether the odds are in your favor or not.
Two Types of EV
- Positive EV: The bet is profitable in the long run
- Negative EV: The bet loses money over time—even if it wins occasionally
Why EV Matters
- Replaces guesswork with math
- Shifts focus from short-term outcomes to long-term value
- Helps avoid bets where the odds don’t match the true probability
- Reinforces disciplined bankroll decisions
- Is foundational to identifying value bets and tracking edge
How to Calculate Expected Value
Step 1: Estimate the True Probability
This is your best estimate (based on data, modeling, or analysis) of how likely the outcome is.
Example: You believe a team has a 45% chance to win.
Step 2: Determine the Odds and Payout
Example: The team is listed at +150. That means:
- A $100 bet returns $150 in profit if it wins
- If it loses, you lose your $100 stake
Step 3: Use the EV Formula
EV=(Probability of Win×Profit)–(Probability of Loss×Stake)\text{EV} = (\text{Probability of Win} × \text{Profit}) – (\text{Probability of Loss} × \text{Stake})
EV=(Probability of Win×Profit)–(Probability of Loss×Stake)
In this case:
- Probability of win = 0.45
- Probability of loss = 0.55
- Profit = $150
- Stake = $100
EV=(0.45×150)–(0.55×100)=67.50–55.00=+12.50\text{EV} = (0.45 × 150) – (0.55 × 100) = 67.50 – 55.00 = \text{+}12.50
EV=(0.45×150)–(0.55×100)=67.50–55.00=+12.50
Step 4: Interpret the Result
A positive EV (e.g., +$12.50) means the bet is profitable on average over time. A negative EV means the math is against you—even if you win occasionally.
Step 5: Repeat This Process
EV is not about one bet. It’s about repeating the process over time and trusting the math to work in your favor if you continue placing +EV bets.
FAQs
How do I identify EV bets?
Look for cases where your win probability is higher than what the odds imply. Comparing your projection to the market price is the first step.
What is the expected value of a fair bet?
Zero. In a fair gamble, the risk equals the reward.
Does EV guarantee profit?
No. EV operates on long-term averages. You may still lose any single bet.
How does EV differ from win probability?
Probability only shows how likely the event is. EV combines that with the payout to show whether the odds are worth the risk.
Can a bet win but still have negative EV?
Yes. Negative EV bets can win sometimes, but they lose money over time.
How accurate does my probability estimate need to be?
Very. EV relies on having a realistic, data-supported estimate of probability. Otherwise, the calculation is meaningless.
Is EV useful for live betting?
Yes—especially if odds shift faster than probability. Real-time alerts can help identify pricing inefficiencies.
What is CLV and how does it relate to EV?
CLV (Closing Line Value) tracks how your odds compare to the final market price. Beating the closing line suggests you’re placing +EV bets.
Should I always bet if I find a +EV opportunity?
Only if it aligns with your bankroll and risk profile. Not all +EV bets are worth taking—consider your staking plan and variance.
Can software help calculate EV automatically?
Yes. Odds tracking tools like Pinnacle Odds Dropper highlight movements that may indicate value. You still need to apply judgment.
Learn More
To understand the numbers behind your bets and monitor line movement in real time, visit The Advantage—your home for data-driven sports betting education.