What is Expected Value (EV)?

Expected Value — often shortened to EV — is one of the most important concepts in mathematics, probability, and betting. At its core, EV tells you the average outcome you can expect if you repeat a scenario many times.

Whether you’re investing, rolling dice, or placing sports bets, expected value is the key tool for measuring whether a decision is profitable in the long run. It doesn’t predict the outcome of a single event, but instead shows what happens “on average” if the same event plays out thousands of times.

Expected Value Formula

The formula for expected value is straightforward:

EV = (Probability of Win × Amount Won) – (Probability of Loss × Amount Lost)
            

Or more generally:

EV = Σ (Probability of Outcome × Value of Outcome)
            

This formula means you take each possible outcome, multiply it by its probability, then add them all together.

Simple Examples

Coin Toss

If you flip a fair coin and win $1 for heads but lose $1 for tails:

• 50% × $1 = +$0.50
• 50% × –$1 = –$0.50

The EV = $0. This is a fair game with no long-term profit or loss.

Casino Roulette

If you bet $10 on red in European roulette (18/37 chance of winning):

• Win: (18/37 × $10 profit) = +$4.86
• Lose: (19/37 × $10 loss) = –$5.14

EV = –$0.28 per $10 bet. This is the house edge — why casinos always win long-term.

Expected Value in Sports Betting

EV is the foundation of profitable sports betting. Unlike casino games, odds in sports are not fixed — they’re set by bookmakers, and sometimes they misprice them. If you can identify bets with a positive EV (known as +EV betting), you have an advantage.

Example: If a team has a 60% chance to win but the bookmaker’s odds imply only a 50% chance, the bet has positive expected value. Over time, consistently placing bets with positive EV means your bankroll grows.

At WagerWise, we specialise in uncovering these opportunities using data-driven models, offering tools like:

• +EV betting picks: Highlighting bets with long-term profit potential.
• Arbitrage betting: Locking in profit regardless of the outcome.
• Matched betting: Risk-free profits from bookmaker promotions.

Why EV Matters

• In betting: Helps you avoid negative-EV bets where the bookmaker has the edge.
• In investing: EV is used to weigh risk and reward in financial decisions.
• In probability: EV is the mathematical backbone of expected outcomes in any random process.

A single bet or trade might win or lose, but if the EV is positive, the strategy wins in the long run.

Key Takeaways

Expected Value (EV) is the average outcome of an event if repeated infinitely. In sports betting, EV separates recreational gambling from strategic, profitable play.

At WagerWise, we believe betting should be about having an edge — and that edge comes from consistently identifying and sticking to positive EV opportunities.