EV Betting Formula: How to Calculate Expected Value

Expected value is one of the most important calculations in value betting.

It tells you whether a sportsbook price is theoretically favorable or unfavorable based on the probability of the outcome and the payout available.

The basic EV betting formula is:

EV = (Probability of Winning × Profit if You Win) - (Probability of Losing × Stake)

If the result is:

Above $0 = +EV

Exactly $0 = break-even EV

Below $0 = -EV

The formula itself is straightforward.

The difficult part is making sure the true probability you put into it is realistic.

Quick Answer: What Is the EV Betting Formula?

The standard expected value formula for a sports bet is:

EV = (Win Probability × Profit if Win) - (Loss Probability × Stake)

For example:

• Stake: $100
• Potential profit: $200
• True win probability: 40%
• Loss probability: 60%

The calculation is:

(0.40 × $200) - (0.60 × $100)

= $80 - $60

= +$20 EV

That means the wager has an expected value of +$20 per $100 staked under those probability assumptions.

ProfitDuel's Expected Value Calculator performs the same calculation automatically.

What Is Expected Value in Betting?

Expected value, or EV, estimates the average financial result you would expect if you could repeat the same type of wager many times under identical conditions.

A bet can have:

• Positive expected value.
• Zero expected value.
• Negative expected value.

The key word is expected.

EV does not predict the result of one individual wager.

A +EV bet can lose.

A -EV bet can win.

The calculation tells you whether the price and probability combination is mathematically favorable over repeated bets.

What Information Do You Need to Calculate EV?

You need four things:

1. Your stake.
2. The sportsbook odds.
3. Your estimated true probability of winning.
4. Your probability of losing.

The losing probability is:

1 - win probability

So if your estimated chance of winning is:

48%

your losing probability is:

52%

Once you know your potential profit, those inputs are enough to calculate expected value.

EV Formula Example

Suppose you're considering:

$100 bet

at:

+200

and you estimate the true probability of winning at:

40%

At +200, a $100 winning bet produces:

$200 profit

Your probability of losing is:

60%

Apply the formula:

EV = (0.40 × $200) - (0.60 × $100)

= $80 - $60

= +$20

So:

EV = +$20

That means the theoretical expected return is:

+$20 per $100 wagered

if your 40% probability estimate is accurate.

Expert Insight: EV Does Not Mean You Make the Expected Amount on That Bet

A +$20 EV wager does not mean the sportsbook pays you $20.

The actual result is still binary:

• You win the sportsbook payout.
• Or you lose your stake.

The +$20 figure describes the average mathematical value of repeatedly taking that same opportunity.

Think of EV as the quality of the wager, not the result of the next game.

How to Calculate EV Step by Step

Here's the full process.

Step 1: Find the Sportsbook Odds

Suppose the sportsbook offers:

+150

Step 2: Calculate Your Profit if You Win

At +150:

A $100 winning stake produces:

$150 profit

Step 3: Estimate the True Probability

Suppose your fair estimate is:

48%

Step 4: Calculate the Loss Probability

100% - 48% =

52%

Step 5: Apply the EV Formula

EV = (0.48 × $150) - (0.52 × $100)

= $72 - $52

= +$20

Under those assumptions, the bet has:

+$20 expected value

or:

+20% EV on a $100 stake.

EV Betting Formula at a Glance

This is the basic calculation regardless of sport.

How to Calculate EV With Positive American Odds

Positive American odds tell you the profit from a $100 winning stake.

For example:

+150

means:

$100 stake → $150 profit

If your stake is $50:

$50 × 1.50 = $75 profit

You then use $75 as the profit figure in the EV formula.

Positive Odds EV Example

Suppose:

• Stake: $50
• Odds: +150
• True win probability: 45%
• Loss probability: 55%

Profit if win:

$75

EV:

(0.45 × $75) - (0.55 × $50)

= $33.75 - $27.50

= +$6.25

So the expected value is:

+$6.25

EV percentage:

$6.25 ÷ $50 × 100 = +12.5% EV

How to Calculate EV With Negative American Odds

Negative American odds tell you how much you would normally need to risk to make $100 profit.

For example:

-150

means:

Risk $150 to make $100 profit

But you don't need to stake exactly $150.

If you're staking $100:

Potential profit = $100 × (100 ÷ 150)

= $66.67

You can then use that figure in the EV formula.

Negative Odds EV Example

Suppose:

• Stake: $100
• Odds: -150
• True probability: 65%
• Loss probability: 35%

Potential profit:

$66.67

EV:

(0.65 × $66.67) - (0.35 × $100)

≈ $43.34 - $35

= +$8.34

So the wager has:

+$8.34 expected value

or approximately:

+8.34% EV

under your probability assumptions.

American Odds Profit Formulas

If you want to calculate the potential profit before applying the EV formula:

Positive Odds

Profit = Stake × (American Odds ÷ 100)

Example:

$50 at +200

= $50 × 2

= $100 profit

Negative Odds

Profit = Stake × (100 ÷ Absolute American Odds)

Example:

$100 at -200

= $100 × 0.5

= $50 profit

Once you know the profit figure, plug it into:

EV = (Win Probability × Profit) - (Loss Probability × Stake)

How to Convert American Odds Into Implied Probability

Before calculating EV, it helps to understand the probability implied by the sportsbook price.

For positive American odds:

Implied Probability = 100 ÷ (Odds + 100) × 100

For negative American odds:

Implied Probability = |Odds| ÷ (|Odds| + 100) × 100

Positive Odds Example

At:

+150

100 ÷ (150 + 100)

= 100 ÷ 250

= 40%

So +150 implies approximately a:

40% probability

Negative Odds Example

At:

-150

150 ÷ (150 + 100)

= 150 ÷ 250

= 60%

So -150 implies approximately a:

60% probability

ProfitDuel's current Betting Odds Calculator also shows implied probability alongside potential payout and odds conversion.

Implied Probability vs True Probability

This is one of the most important distinctions in EV betting.

Implied probability comes directly from the sportsbook price.

True probability is your best estimate of how likely the event actually is.

EV appears when those two differ.

For example:

Sportsbook implied probability:

40%

Estimated true probability:

48%

If that 48% estimate is reliable, the sportsbook may be offering a favorable price.

Expert Insight: Never Automatically Use the Sportsbook's Own Probability as “True Probability”

If you simply convert one sportsbook's odds into implied probability and feed that same number back into the EV formula, you haven't identified an edge.

You're effectively asking the sportsbook whether its own price is fair.

EV betting requires an independent fair-probability estimate.

That may come from:

• No-vig market prices.
• Sharper sportsbook markets.
• Wider market consensus.
• Statistical models.
• Prediction markets.
• Historical data.

The maths is easy.

The probability input is the hard part.

Why Sportsbook Vig Matters

Sportsbooks build a margin into their prices.

This is commonly called:

• Vig.
• Juice.
• Hold.
• Overround.

Consider:

Team A -110

Team B -110

Each side implies:

52.38%

Combined:

104.76%

But the actual event can only represent:

100% total probability

The additional percentage reflects sportsbook margin.

That means raw implied probability is not necessarily fair probability.

What Are No-Vig Odds?

No-vig odds remove the sportsbook margin to estimate a fairer underlying probability.

Using the previous example:

Team A implied probability:

52.38%

Team B implied probability:

52.38%

Total:

104.76%

After normalizing those probabilities back to 100%, you get approximately:

50% / 50%

Those no-vig probabilities can provide a more useful starting point for EV analysis.

ProfitDuel's EV Matcher currently uses wider market pricing and removes vig to estimate fair odds when identifying potential +EV bets.

Why True Probability Is the Hardest Part of the EV Formula

Anyone can calculate:

0.55 × payout

minus:

0.45 × stake

The difficult question is:

Why do you believe the wager actually wins 55% of the time?

A calculation is only as good as the probability used.

Possible probability sources include:

• Sharp sportsbook prices.
• No-vig odds.
• Statistical models.
• Prediction markets.
• Wider market consensus.
• Historical data.

If your probability estimate is wrong, your EV result can also be wrong.

EV Percentage Formula

You can express expected value as a percentage of the amount staked.

The formula is:

EV% = EV ÷ Stake × 100

Example:

Stake:

$100

Expected value:

+$5

EV%:

5 ÷ 100 × 100

= +5% EV

That means the theoretical expected return is:

5% of the amount wagered

over repeated equivalent bets.

EV Percentage Example

Suppose:

• Stake: $50
• EV: +$3

EV%:

3 ÷ 50 × 100

= +6%

So the wager has:

+6% expected value

under your assumptions.

EV vs ROI

Expected value and return on investment are related, but they are not the same thing.

For example:

Your bets may average:

+4% calculated EV

while your actual short-term ROI is:

-8%

That can happen because individual results vary.

Over a larger sample, a genuine edge would theoretically have more opportunity to appear in realized results.

What Does Zero EV Mean?

If:

EV = $0

the wager is theoretically break-even.

Under your assumptions:

• Expected winning value equals expected losing value.
• Neither side has a mathematical advantage.

For example:

$100 at +100

with:

50% true probability

gives:

(0.50 × $100) - (0.50 × $100)

= $0 EV

What Does Negative EV Mean?

If the answer is below zero, the wager is expected to lose money over repeated bets.

Suppose:

• Stake: $100
• Odds: +100
• True win probability: 45%
• Loss probability: 55%

EV:

(0.45 × $100) - (0.55 × $100)

= $45 - $55

= -$10

The wager therefore has:

-$10 EV

or:

-10% EV

under those assumptions.

What Does Positive EV Mean?

Positive EV simply means:

EV > $0

For example:

• Stake: $100
• Odds: +100
• True win probability: 55%

EV:

(0.55 × $100) - (0.45 × $100)

= $55 - $45

= +$10

So:

EV = +$10

and:

EV% = +10%

If you want a deeper explanation of the concept itself rather than the formula, read ProfitDuel's guide to what +EV means in sports betting.

Break-Even Probability and EV

Another useful calculation is the break-even probability.

This tells you the win rate required at a particular sportsbook price to achieve:

0 EV

Examples:

If your fair probability is higher than the break-even probability, the wager may have positive EV.

Break-Even Probability Example

Suppose a sportsbook offers:

+200

Break-even probability:

100 ÷ (200 + 100)

= 33.33%

If your fair probability estimate is:

40%

the bet may have positive expected value.

If your estimate is:

25%

the bet is likely negative EV.

This is often the quickest conceptual way to think about EV:

Does the outcome happen more often than the sportsbook price requires me to break even?

EV Formula Using Decimal Odds

Decimal odds provide a compact EV formula:

EV% = (Decimal Odds × True Probability) - 1

Multiply by 100 to express the answer as a percentage.

Suppose:

• Decimal odds: 2.50
• True probability: 45%

Calculation:

2.50 × 0.45

= 1.125

1.125 - 1

= 0.125

= +12.5% EV

Converting American Odds to Decimal Odds

For positive American odds:

Decimal Odds = (American Odds ÷ 100) + 1

Example:

+150

= 1.50 + 1

= 2.50

For negative American odds:

Decimal Odds = (100 ÷ |American Odds|) + 1

Example:

-200

= 100 ÷ 200 + 1

= 1.50

You can then use the decimal-odds EV shortcut.

EV Formula Using Total Return

You may also see EV written as:

EV = (Probability of Win × Total Return) - Stake

This produces the same result when used correctly.

For example:

• Stake: $100
• Odds: +200
• Total winning return: $300
• True probability: 40%

EV:

(0.40 × $300) - $100

= $120 - $100

= +$20

Same result.

Why Do EV Formulas Sometimes Look Different?

Different sources may use:

• Profit.
• Payout.
• Total return.

These formulas can all work.

The important thing is to stay consistent.

If you use profit if you win, use:

(Win Probability × Profit) - (Loss Probability × Stake)

If you use total return, make sure the original stake is subtracted correctly.

For most beginners, the easiest version is:

EV = (Win Probability × Profit) - (Loss Probability × Stake)

because the winning and losing outcomes are clearly separated.

Full EV Betting Calculation Example

Suppose you're considering an NBA bet.

Sportsbook odds:

+140

Stake:

$100

Estimated true probability:

48%

Step 1: Calculate Potential Profit

At +140:

$140

Step 2: Calculate Loss Probability

100% - 48%

= 52%

Step 3: Calculate Expected Winning Value

0.48 × $140

= $67.20

Step 4: Calculate Expected Losing Value

0.52 × $100

= $52

Step 5: Calculate EV

$67.20 - $52

= +$15.20

Step 6: Convert to EV%

$15.20 ÷ $100 × 100

= +15.2% EV

So under those assumptions:

EV = +$15.20

EV% = +15.2%

Does +15.2% EV Mean You Make 15.2% on That Bet?

No.

If the wager wins, you receive the actual sportsbook payout.

If it loses, you lose the stake.

The +15.2% figure means:

theoretical average return over repeated wagers with the same pricing and probability

It is not a guaranteed return on that specific bet.

How Sensitive Is EV to Your Probability Estimate?

Very.

Small probability changes can completely change your conclusion.

Suppose the sportsbook odds are:

+150

Break-even probability:

40%

Now compare:

A difference of just a few percentage points can turn an apparent value bet into a losing proposition.

That's why probability quality matters more than simply knowing the formula.

Data Insight: The Same Formula Can Produce Completely Different Answers From Small Input Changes

EV looks precise because the result might say:

+4.8%

or:

-2.1%

But the calculation is only precise relative to the inputs.

If your fair probability changes from:

44%

to:

41%

your EV can shift dramatically even though the sportsbook odds haven't moved.

This is why serious EV analysis focuses as much on how the fair probability was generated as on the final percentage displayed.

Can You Calculate EV Without Knowing True Probability?

Not accurately.

This is the fundamental limitation of the formula.

You can always determine:

• Sportsbook price.
• Implied probability.
• Potential payout.

But none of those tells you whether the price is actually good.

You need an independent fair-probability estimate.

Without one, you can calculate the sportsbook's economics — but not whether the bet has genuine expected value.

How to Get a Better True-Probability Estimate

One common method is to use a sharper or more efficient market as your reference.

For example:

Sportsbook A:

+150

Reference market suggests fair odds closer to:

+120

You can:

1. Take the reference prices.
2. Remove the vig.
3. Calculate no-vig fair probabilities.
4. Compare those with +150.
5. Calculate the resulting EV.

This is broadly how automated EV tools approach the problem at scale.

ProfitDuel's EV Matcher scans sportsbook prices, compares them against wider market prices and calculates the potential expected-value edge automatically.

EV Formula vs Closing Line Value

Expected value and Closing Line Value measure different things.

EV compares your available price with your estimated fair probability.

CLV compares the price you took with the later closing market.

For example:

You bet:

+150

The market closes:

+120

You beat the closing price.

That doesn't guarantee the bet wins.

But consistently getting better prices than a reliable closing market can provide useful evidence that your fair-price process is identifying value.

Common EV Formula Mistakes

Using Implied Probability as True Probability

The sportsbook price contains margin and does not automatically represent fair probability.

Forgetting the Vig

Where possible, use no-vig probabilities or another reliable fair-price source.

Confusing Profit With Total Return

A $100 bet at +150 produces:

$150 profit

and:

$250 total return

Do not use $250 as the profit figure in the standard EV formula.

Entering +150 and -150 the Same Way

They produce very different payouts.

Always calculate potential profit correctly first.

Using 55 Instead of 0.55

In the formula:

55% = 0.55

Forgetting Loss Probability

If your win probability is:

55%

your loss probability is:

45%

for a two-outcome market.

Trusting an Unrealistic Probability Estimate

A calculator can verify your arithmetic.

It cannot verify whether your probability model is sensible.

Using Stale Sportsbook Odds

If the sportsbook price moves, recalculate EV using the current odds.

Comparing Different Markets

An Over 25.5 player prop is not the same wager as Over 26.5.

Different lines can create a false EV signal.

Is a Positive EV Bet Guaranteed to Win?

No.

Suppose a bet genuinely has:

+5% EV

It can still lose immediately.

Expected value measures long-term mathematical expectation, not the result of one event.

ProfitDuel's EV Matcher also explicitly notes that positive EV betting does not guarantee an individual winning wager and that short-term results vary.

How Many +EV Bets Do You Need?

There is no fixed number.

Variance depends on:

• Odds.
• Edge.
• Win probability.
• Stake size.
• Market type.

A bettor can make:

10 +EV bets

and lose money.

They can also have a poor result after:

100 bets

despite a genuine edge.

Expected value becomes more useful as sample size increases, but it never predicts the exact path your bankroll will take.

Can You Calculate EV for Parlays?

Yes.

But the probability calculation becomes more complicated.

Each leg has:

• Its own probability.
• Its own margin.
• Potential correlation with other legs.

If the legs are independent, their combined probability can be calculated by multiplying the individual probabilities.

If the legs are correlated, the maths becomes more complex.

A parlay is not automatically +EV because the individual selections appear attractive.

The price of the full parlay must still be compared with the true probability of the entire combination landing.

Can You Calculate EV for Player Props?

Yes.

The same formula applies.

Suppose:

Player Over 25.5 points

Odds:

+110

Stake:

$100

Estimated true probability:

55%

Potential profit:

$110

EV:

(0.55 × $110) - (0.45 × $100)

= $60.50 - $45

= +$15.50

So:

EV = +$15.50

or:

+15.5% EV

under those assumptions.

Can You Calculate EV for Negative Odds?

Yes.

Expected value works with:

• Positive American odds.
• Negative American odds.
• Decimal odds.
• Fractional odds.

You simply need to correctly calculate:

profit if win

before using the formula.

A bet at:

-200

can be +EV.

A bet at:

+300

can be -EV.

The odds sign does not determine expected value.

EV Betting Formula vs Arbitrage

They solve different problems.

Expected Value

The EV formula asks:

Is this individual sportsbook price favorable relative to fair probability?

The individual wager can lose.

Arbitrage

Arbitrage asks:

Do prices across different sportsbooks allow me to cover every outcome at a positive combined return?

The strategies are mathematically related but structurally different.

EV Betting Formula vs Matched Betting

Matched betting usually derives its additional value from:

Sportsbook promotion + opposing wager

EV betting derives its potential edge from:

Sportsbook price vs fair probability

You don't need a promotion to calculate or identify +EV.

ProfitDuel supports EV, arbitrage and promo-conversion strategies separately within its betting toolkit.

Do You Need to Calculate EV Manually?

No.

Understanding the formula is useful because it shows exactly where the mathematical edge comes from.

But manually doing this across hundreds or thousands of sportsbook prices is impractical.

ProfitDuel's Expected Value Calculator lets you enter:

• Wager.
• Sportsbook odds.
• True win probability.

and calculates the result automatically.

For larger-scale searching, the ProfitDuel EV Matcher scans sportsbook prices across 100+ sportsbooks, compares them with wider market pricing and highlights potential +EV opportunities.

Once you understand the formula, you don't need to spend your time manually applying it to every sportsbook line. Use the calculator to check individual bets and the EV Matcher to search the wider market.

Frequently Asked Questions About the EV Betting Formula

What is the EV betting formula?

The standard formula is:

EV = (Probability of Winning × Profit if Win) - (Probability of Losing × Stake)

A result above zero indicates positive expected value under your probability assumptions.

How do you calculate positive EV?

Calculate the probability-weighted value of winning and subtract the probability-weighted value of losing. If the result is above zero, the wager is +EV.

What does +5% EV mean?

+5% EV means the theoretical expected return is 5% of the amount wagered across repeated equivalent bets.

What does negative EV mean?

Negative EV means the wager is expected to produce a negative average return over repeated bets under the probabilities used.

How do I calculate EV with American odds?

First calculate how much profit the American odds would produce for your stake. Then use that profit in the standard EV formula with your fair win probability.

Do I use implied probability or true probability for EV?

Use an estimated true or fair probability, not simply the raw implied probability from the same sportsbook price you're evaluating.

Can a -200 bet have positive EV?

Yes. Negative American odds can still offer positive expected value if the true probability is sufficiently high relative to the sportsbook's price.

Can a +200 bet be negative EV?

Yes. Positive odds only describe the payout. If the outcome's true probability is lower than the break-even probability required at +200, the wager can be -EV.

Does positive EV guarantee profit?

No. Individual +EV bets can lose, and short-term results can vary significantly.

How do you calculate EV percentage?

Use:

EV% = EV ÷ Stake × 100

For example, +$5 EV on a $100 wager equals:

+5% EV

Can an EV calculator tell me the true probability?

No. A calculator performs the arithmetic using the probability you provide. You still need a reliable fair-probability estimate.

EV Betting Formula: The Bottom Line

The calculation itself is simple:

EV = (Win Probability × Profit) - (Loss Probability × Stake)

If:

EV > 0

the wager has positive expected value.

If:

EV = 0

the wager is theoretically break-even.

If:

EV < 0

the wager has negative expected value.

But knowing the formula is only half the job.

The hardest part is establishing a reliable true probability.

A calculator can handle the multiplication.

It cannot magically tell you how likely a team, player or outcome really is.

That's why serious EV analysis relies on:

• Fair probabilities.
• No-vig odds.
• Strong reference markets.
• Current sportsbook prices.
• Accurate market matching.

rather than simply guessing a percentage and running the formula.

Calculate EV Faster With ProfitDuel

Understanding the EV betting formula helps you see exactly where a betting edge comes from.

Applying it manually across thousands of sportsbook prices is another story.

ProfitDuel gives you two ways to simplify the process.

Use the Expected Value Calculator to enter:

• Stake.
• Sportsbook odds.
• True win probability.

and instantly calculate whether the wager has:

• Positive EV.
• Zero EV.
• Negative EV.

Then use the EV Matcher to go beyond individual calculations.

The EV Matcher scans real-time sportsbook prices across 100+ sportsbooks, compares those prices against the wider market and highlights potential value opportunities with information including the available odds, fair odds and EV%.

ProfitDuel also provides tools for:

• Implied probability.
• No-vig calculations.
• Sportsbook hold.
• Kelly Criterion staking.
• Arbitrage betting.
• Matched betting.
• Promo conversion.

Start your ProfitDuel trial and spend less time calculating every sportsbook line by hand and more time identifying where the value may actually be.

21+ and in select states. Sports betting involves risk. Positive expected value does not guarantee realized profit, and EV calculations depend on the accuracy of the probability assumptions used. Always verify sportsbook odds, manage your bankroll responsibly and gamble responsibly.