Expected Value Explained

Every bet you place has a mathematical expectation attached to it—a number that tells you whether that wager will make or lose money over time. This isn't opinion or gut feeling. It's cold, hard math.

Understanding expected value is the single most important concept separating recreational bettors from those who approach sports betting as a skilled endeavor. While most bettors chase winners and celebrate short-term streaks, profitable bettors obsess over one thing: finding bets where the math is on their side.

If you've ever wondered why some bettors can sustain profits year after year while others inevitably go broke, expected value is the answer. Let's break it down.

Expected value (EV) is a mathematical concept that calculates the average outcome of a bet if you were to place it an infinite number of times. In simpler terms, it tells you how much you can expect to win or lose per dollar wagered over the long run.

Think of it like this: imagine flipping a fair coin where you win $2 on heads and lose $1 on tails. Each individual flip is unpredictable, but over thousands of flips, you'd average a profit of $0.50 per flip. That $0.50 is your expected value.

In sports betting, every wager carries either:

• Positive expected value (+EV): You expect to profit over time
• Negative expected value (-EV): You expect to lose over time
• Zero expected value (0 EV): You break even over time

The goal of every serious bettor is simple: consistently find and place +EV bets.

The expected value formula is straightforward:

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

Let's walk through a real example. Suppose you're betting on an NFL game where you believe the Kansas City Chiefs have a 55% chance of covering the spread. The sportsbook offers -110 odds, meaning you risk $110 to win $100.

Here's the calculation:

• Probability of winning: 55% (0.55)
• Amount won if successful: $100
• Probability of losing: 45% (0.45)
• Amount lost if unsuccessful: $110

EV = (0.55 × $100) - (0.45 × $110) EV = $55 - $49.50 EV = +$4.50

This means for every $110 you wager on this bet, you can expect to profit $4.50 on average. That's a positive expected value of about 4.1%—an excellent edge in sports betting.

You might have noticed the elephant in the room: how do you know the "true" probability of an outcome?

This is where sports betting transforms from simple math into a genuine skill. The sportsbook sets odds based on their assessment of probability. Your job is to find situations where you believe the true probability differs from what the odds imply.

To convert American odds to implied probability, use these formulas:

• For negative odds: Implied Probability = |Odds| ÷ (|Odds| + 100)
• For positive odds: Implied Probability = 100 ÷ (Odds + 100)

At -110 odds, the implied probability is 110 ÷ 210 = 52.4%. If you genuinely believe a team has a 55% chance of covering, you've found value because your estimated probability exceeds the implied probability.

Sources for developing your own probability estimates include:

• Advanced statistical models and analytics platforms
• Injury reports and lineup changes
• Weather conditions for outdoor sports
• Historical performance data and situational trends
• Market movement and sharp money indicators

Example 1: The Losing Bet That Was Correct

You bet $100 on the underdog Lakers at +150 odds, believing they have a 45% chance to win. The implied probability at +150 is only 40%.

EV = (0.45 × $150) - (0.55 × $100) = $67.50 - $55 = +$12.50

The Lakers lose. You're down $100. But mathematically, this was still a good bet. Over 100 similar wagers, you'd expect to profit $1,250. One loss doesn't change the underlying math.

Example 2: The Winning Bet That Was Wrong

You bet $110 on a heavy favorite at -300 odds because "they can't lose." The implied probability is 75%, but realistic analysis suggests they only have a 70% chance.

EV = (0.70 × $36.67) - (0.30 × $110) = $25.67 - $33 = -$7.33

They win. You pocket $36.67. But this was a losing bet in terms of expected value. Make enough bets like this, and you'll slowly bleed money despite winning frequently.

"I found a +EV bet, so I'll definitely profit."

Not on any single bet. Expected value only manifests over large sample sizes. According to the law of large numbers, your actual results will converge toward your expected results as you place more bets—but variance can be brutal in the short term.

"The sportsbook always has the edge."

Sportsbooks build in a margin (the "vig" or "juice"), but they're not perfect. Lines are set based on market efficiency, and inefficiencies exist—especially in player props, smaller markets, and situations with late-breaking news. According to industry analysis from UNLV's Center for Gaming Research, sportsbooks adjust lines based on betting action, creating opportunities for sharp bettors who move first.

"Past results affect future expected value."

Each bet exists independently. Losing five bets in a row doesn't mean you're "due" for a win, nor does it change the EV of your sixth bet. This is the gambler's fallacy, and it's destroyed countless bankrolls.

Casinos don't gamble—they simply ensure every game has negative expected value for players. The house edge on roulette is about 5.26%. They don't win every spin, but they profit every year because math is undefeated over sufficient volume.

Positive EV betting flips this script. Instead of being the player at the casino, you become the casino. You accept short-term variance in exchange for long-term mathematical certainty.

This requires three things:

1. Edge identification: The ability to assess probability more accurately than the market
2. Bankroll management: Sufficient funds to survive variance without going broke
3. Volume: Enough bets to let the math play out

Expected value is the foundation upon which all profitable betting is built. Here's what you need to remember:

• EV measures long-term expectation, not individual bet outcomes
• Calculate EV using: (Win Probability × Profit) - (Loss Probability × Stake)
• Positive EV bets are the only path to sustainable profits
• Your edge comes from estimating true probability better than the market
• Variance is real—even +EV bettors experience losing streaks
• Volume matters—the more +EV bets you place, the closer your results match expectations

Stop asking "Did I win?" Start asking "Was that bet +EV?" When you make that mental shift, you've taken the first step toward betting like a professional.