How to Calculate Expected Value (EV) in Sports Betting: Why You Should Bet on Value Instead of Intuition

Most bettors think about sports betting the wrong way.

They try to predict who will win.

“PSG are the stronger team.”

“Naomi Osaka is more experienced.”

“This team looks unstoppable.”

“That price feels attractive.”

But there is a major problem with this approach:

being right about a winner does not necessarily mean making a good bet.

A bet can win and still be mathematically terrible.

Likewise, a losing bet can still be an excellent decision.

That may sound counterintuitive.

Yet this is exactly what separates recreational bettors from profitable ones.

Professional bettors are not obsessed with winners.

They are obsessed with price inefficiencies, situations where bookmakers offer odds that are better than the real probability of an event occurring.

This concept is called Expected Value (EV).

In this article, you will learn:

• what Expected Value (EV) means in sports betting,
• how to calculate EV step by step,
• why intuition often destroys betting bankrolls,
• how to identify value bets,
• and why profitable bettors focus on price rather than emotion.

Most importantly, we will walk through two detailed real-world betting examples:

• a football example: PSG vs Arsenal in a Champions League Final
• a tennis example: Iva Jovic vs Naomi Osaka at Roland Garros

And you may be surprised by the conclusions.

What Is Expected Value (EV) in Sports Betting?

Expected Value (EV) represents the average amount of money you can expect to win or lose over the long run if you repeatedly place the same bet hundreds or thousands of times.

In simple terms:

Expected Value tells you whether a bet is mathematically profitable.

A positive EV means:

“This bet should make money over time.”

A negative EV means:

“This bet should lose money over time.”

This is a critical distinction.

Because in sports betting:

winning a bet is not the same thing as making a profitable decision.

Professional bettors understand something most recreational gamblers ignore:

Short-term outcomes are noisy.

Long-term mathematics matter.

The Expected Value Formula

Fortunately, the formula is relatively straightforward.

Expected Value is calculated as:

EV = (Probability of Winning × Amount Won) − (Probability of Losing × Amount Lost)

In practice, this means comparing:

• how much money you win when you are correct,
• weighted by the probability of success,

against:

• how much money you lose when you are wrong,
• weighted by the probability of failure.

A Common Mistake Bettors Make

Many bettors calculate EV incorrectly.

Why?

Because they mistakenly use the total payout rather than the net profit.

Let’s take a simple example.

Imagine staking €100 on odds of 2.36.

If the bet wins, your bookmaker returns:

€236

However, your actual profit is not €236.

Your real gain is:

€136

Why?

Because €100 was simply your original stake being returned.

The correct formula is always:

Net Profit = (Odds − 1) × Stake

This small detail changes everything.

Why Recreational Bettors Bet on Intuition

Human psychology loves stories.

We naturally look for narratives.

A stronger team.

A famous player.

Recent momentum.

Past trophies.

And then we think:

“This feels like a safe bet.”

But sports betting is not about predicting winners.

It is about evaluating prices.

Bookmakers are not asking:

“Who will win?”

They are asking:

“Are you willing to pay this price?”

That distinction changes everything.

Imagine a team that wins 90% of the time.

Sounds like an easy bet, right?

Not necessarily.

If the bookmaker offers odds of 1.02, the bet becomes terrible.

Why?

Because the price is too expensive.

You may win very often and still lose money over time.

This is exactly where value betting comes in.

A profitable bet is not necessarily the most likely outcome.

A profitable bet is:

an outcome whose odds are better than its true probability.

Let’s see what this looks like in practice.

Example #1: PSG vs Arsenal, When There Is NO Value

Let’s imagine a Champions League Final between Paris Saint-Germain and Arsenal.

Bookmaker Odds

The bookmaker offers the following prices:

• Paris Saint-Germain: 2.36
• Draw: 3.37
• Arsenal: 3.20

The bookmaker margin on this market is:

3.30%

Your Estimated Probabilities

As a bettor, you estimate the following probabilities:

• PSG: 40%
• Draw: 29%
• Arsenal: 31%

At first glance, a bettor may naturally think:

“PSG have more experience in big European nights.”

Or:

“Arsenal could pull off an upset.”

Or even:

“A final can be decided by a single moment.”

All reasonable thoughts.

But betting markets do not reward compelling narratives.

They reward mathematical value.

Let’s calculate the Expected Value of every possible bet.

Step 1: Calculating EV on PSG

Assume a €100 stake.

PSG odds are:

2.36

First, we calculate net profit.

Net Profit:

(2.36 − 1) × 100

= €136

Your estimated probability of winning:

40%

Probability of losing:

60%

Now apply the formula.

EV = (0.40 × 136) − (0.60 × 100)

Breaking it down:

0.40 × 136 = 54.40

0.60 × 100 = 60

Therefore:

EV = 54.40 − 60

EV = −€5.60

Verdict on PSG

This is extremely important.

Even if PSG wins the match:

the bet is still mathematically negative.

Over the long run:

you are theoretically losing €5.60 per €100 staked.

In other words:

there is no value.

Step 2: Calculating EV on the Draw

Let’s now examine the draw.

The bookmaker offers odds of:

3.37

Again, we assume a €100 stake.

First, calculate the net profit.

Net Profit:

(3.37 − 1) × 100

= €237

Your estimated probability of a draw is:

29%

That means your probability of losing the bet is:

71%

Now apply the Expected Value formula.

EV = (0.29 × 237) − (0.71 × 100)

Breaking it down:

0.29 × 237 = 68.73

0.71 × 100 = 71

Therefore:

EV = 68.73 − 71

EV = −€2.27

Verdict on the Draw

Once again:

there is no value.

Even if a draw feels realistic in a Champions League Final, that alone does not justify the bet.

This is where many bettors go wrong.

They confuse:

“This outcome could happen”

with

“This outcome is worth betting on.”

Those are not the same thing.

A bet can feel logical and still be mathematically poor.

Step 3: Calculating EV on Arsenal

Now let’s look at Arsenal.

The odds offered are:

3.20

Assume the same €100 stake.

Net profit becomes:

(3.20 − 1) × 100

= €220

Your estimated probability of Arsenal winning is:

31%

Probability of losing:

69%

Now apply the formula.

EV = (0.31 × 220) − (0.69 × 100)

Breaking it down:

0.31 × 220 = 68.20

0.69 × 100 = 69

Therefore:

EV = 68.20 − 69

EV = −€0.80

Verdict on Arsenal

This one is interesting.

The bet is very close to becoming profitable.

But it still remains:

negative EV.

And this is a critical lesson.

Many bettors would probably convince themselves to back Arsenal here.

They might think:

“The price looks attractive.”

Or:

“Arsenal could absolutely pull off an upset.”

Or even:

“A final can be decided by one moment.”

And they may even win the bet.

But winning does not automatically mean the decision was mathematically correct.

Over the long run:

the bet still loses money.

What This Football Example Actually Teaches Us

Let’s summarize.

OutcomeExpected ValuePSG−€5.60Draw−€2.27Arsenal−€0.80

The conclusion is surprisingly brutal:

There is no profitable bet in this market.

And yet, many bettors would still place one.

Why?

Because human psychology loves narratives.

We naturally tell ourselves stories:

• PSG are more experienced
• Arsenal could surprise everyone
• Finals are unpredictable
• The draw feels plausible

All of those thoughts sound reasonable.

But sports betting does not reward reasonable stories.

It rewards:

mispriced odds.

And in this example:

there is no value anywhere.

This is exactly why professional bettors are perfectly comfortable watching a massive match…

and placing no bet at all.

Because mathematics says:

“No edge.”

But now let’s move to a much more interesting example.

Because this time:

intuition pushes bettors in one direction…

while mathematics points somewhere completely different.

Example #2: Iva Jovic vs Naomi Osaka, When Intuition Pushes You Toward the Wrong Bet

Let’s move to women’s tennis at Roland Garros.

The market offers the following odds:

• Iva Jovic: 2.06
• Naomi Osaka: 1.84

As a bettor, however, you estimate the match to be completely balanced.

Your probabilities are:

• Iva Jovic: 50%
• Naomi Osaka: 50%

At first glance, most bettors would naturally gravitate toward Naomi Osaka.

Why?

Because our brains love shortcuts.

We instantly think:

“Osaka is the more recognizable name.”

“She has more experience.”

“She has won big tournaments.”

“She feels safer.”

And this is exactly where intuition becomes dangerous.

Because bookmakers are not selling reputations.

They are selling prices.

Let’s see what mathematics has to say.

Calculating EV on Iva Jovic

Let’s start with Iva Jovic.

The bookmaker offers odds of:

2.06

Assume a €100 stake.

First, calculate the net profit.

Net Profit:

(2.06 − 1) × 100

= €106

Your estimated probability of winning is:

50%

Probability of losing:

50%

Now apply the Expected Value formula.

EV = (0.50 × 106) − (0.50 × 100)

Breaking it down:

0.50 × 106 = 53

0.50 × 100 = 50

Therefore:

EV = 53 − 50

EV = +€3

Verdict on Iva Jovic

This completely changes the picture.

For the first time:

the Expected Value is positive.

In practical terms:

you are theoretically making €3 for every €100 staked over the long run.

That means:

this is a mathematically profitable bet.

And yet, many bettors would completely ignore it.

Why?

Because human psychology naturally gravitates toward familiarity.

Most bettors feel safer backing the better-known player.

But betting markets do not reward comfort.

They reward:

pricing mistakes.

And in this case:

the market slightly undervalues Iva Jovic.

Calculating EV on Naomi Osaka

Now let’s look at Naomi Osaka.

The bookmaker offers odds of:

1.84

Again, assume a €100 stake.

Net profit:

(1.84 − 1) × 100

= €84

Your estimated probability remains:

50%

Probability of losing:

50%

Apply the formula:

EV = (0.50 × 84) − (0.50 × 100)

Breaking it down:

0.50 × 84 = 42

0.50 × 100 = 50

Therefore:

EV = 42 − 50

EV = −€8

Verdict on Naomi Osaka

The conclusion is clear:

this is a negative EV bet.

In practical terms:

you are theoretically losing €8 per €100 staked over the long run.

And this is where an uncomfortable truth about sports betting appears.

Naomi Osaka may very well win the match.

But that still would not automatically make the bet a smart decision.

Why?

Because at the price offered:

you are overpaying for her probability of winning.

This is one of the hardest concepts for recreational bettors to accept:

a winning bet can still be a bad bet.

What This Tennis Example Really Teaches Us

Let’s summarize.

PlayerExpected ValueIva Jovic+€3Naomi Osaka−€8

The contrast is fascinating.

Intuition naturally pushes bettors toward Naomi Osaka.

Why?

Because:

• she is more recognizable,
• she has more experience,
• she has won major tournaments,
• psychologically, she feels safer.

Yet mathematics says something completely different:

the better bet is Iva Jovic.

Why?

Because sports betting is not about choosing the most famous player.

It is about identifying:

the best price relative to true probability.

That is the essence of value betting.

How Professional Bettors Think

At this point, an obvious question emerges:

How do profitable bettors actually think?

Unlike recreational bettors, they do not obsess over predicting winners.

Instead, they follow a systematic process.

1. Estimate True Probability

Before even looking at bookmaker odds, they estimate their own probabilities.

For example:

PSG vs Arsenal:

• PSG: 40%
• Draw: 29%
• Arsenal: 31%

Iva Jovic vs Naomi Osaka:

• Iva Jovic: 50%
• Naomi Osaka: 50%

This step matters because:

without your own probability estimate, there is no edge.

2. Compare with Implied Probability

Every betting price contains an implied probability.

For example:

• Odds of 2.00 = 50%
• Odds of 1.50 = 66.67%
• Odds of 3.00 = 33.33%

The bettor’s goal becomes simple:

identify situations where your probability estimate is higher than the market's implied probability.

That difference is called:

an edge.

3. Bet Only When EV Is Positive

This is where discipline matters most.

Sometimes the smartest decision is:

not betting at all.

Even if:

• the match is exciting,
• the event is huge,
• your intuition feels strong.

A professional bettor can happily watch a Champions League Final…

and place no wager.

Why?

Because mathematics says:

“No value.”

Discipline beats excitement.

Every time.

A Difficult Truth to Accept: A Winning Bet Can Still Be Bad

Most bettors judge themselves based on outcomes.

They think:

“I won, therefore I made a smart bet.”

Or:

“I lost, therefore I made a terrible bet.”

This logic is flawed.

Imagine betting Naomi Osaka despite negative EV.

She wins.

Was it a good bet?

No.

You simply got a favorable short-term outcome from a poor long-term decision.

Now imagine betting Iva Jovic with positive EV.

She loses.

Was it a bad bet?

Still no.

Mathematically:

it was the correct decision.

Because betting should never be judged on one outcome.

It should be judged across hundreds or thousands of bets.

This is where another critical concept enters:

variance.

Short-term results fluctuate.

Long-term math wins.

Final Conclusion: Bet on Value, Not Intuition

Let’s go back to our two examples.

PSG vs Arsenal

Intuition could tell many stories:

• PSG are favourites,
• Arsenal could upset them,
• finals are unpredictable,
• the draw feels realistic.

But mathematics gave one clear answer:

there was no positive Expected Value anywhere in the market.

Iva Jovic vs Naomi Osaka

Intuition naturally pushed bettors toward Naomi Osaka.

Yet mathematics told a different story:

• Naomi Osaka = negative EV
• Iva Jovic = positive EV

The best bet was not the safest-looking one.

The best bet was:

the mathematically profitable one.

And that may be the single most important lesson in sports betting.

Stop asking yourself:

“Who is going to win?”

Start asking:

“Are these odds better than the true probability of the event?”

Because in the end:

Amateur bettors chase winners.

Professional bettors chase value.

And over the long run:

mathematics always wins.