What is Expected Value and Why It's All That Matters
There is exactly one number that determines whether a bet is good or bad over the long run. Not your gut feeling. Not how confident you feel. Not the team's recent form (except insofar as it's already reflected in the odds). That number is expected value — EV for short.
Everything else in betting analytics flows from this. If you understand EV, you understand why most strategies fail and what the rare ones that work actually have in common.
The Basic Formula
Expected value is simple:
EV = (probability of winning × amount won) − (probability of losing × amount lost)
If you bet $100 on a coin flip at even odds ($100 to win $100):
- Probability of winning: 50% (0.5)
- Amount won: $100
- Probability of losing: 50% (0.5)
- Amount lost: $100
EV = (0.5 × $100) − (0.5 × $100) = $0
A zero EV bet is a fair bet. Over the long run, you neither win nor lose. It's not a good bet — but it's not a bad one either.
What Bookmakers Actually Sell
A sportsbook offering a coin flip would never give you even odds. They'd give you something like:
- Bet $110 to win $100
Now the math changes:
- Probability of winning: 50% (0.5)
- Amount won: $100
- Probability of losing: 50% (0.5)
- Amount lost: $110
EV = (0.5 × $100) − (0.5 × $110) = −$5
Every $110 you bet on this coin flip, you expect to lose $5 in the long run. That's a −4.5% return on every dollar wagered. That's what the vig (or juice, or margin) is — the bookmaker's built-in edge.
Most sports bets are between −3% and −10% EV before accounting for any skill on your part. You are playing against the house edge every single time.
The Only Path to Long-Term Profitability
For a bet to be +EV, your estimated probability of winning must be higher than what the odds imply.
Odds of 2.00 (even money in decimal format) imply a 50% probability. If you genuinely believe the probability is 55%, the EV is positive:
EV = (0.55 × 1.00) − (0.45 × 1.00) = +$0.10 per dollar bet
The $0.10 is your edge. It's small. Most sustainable edges in betting are small. Anyone claiming large, consistent edges is almost certainly lying.
Why This Matters for Everything Else
Every betting strategy — the Martingale system, Kelly Criterion, model-based betting, line shopping — can be evaluated by asking one question: does it create positive expected value, or does it just redistribute the same negative EV differently?
- Martingale: Doesn't change EV. Negative EV bets compounded are more negative EV bets.
- Kelly Criterion: Optimizes how much to bet when you already have +EV. It doesn't create EV from nothing.
- Line shopping: Can turn a −3% EV bet into a −1% EV bet by finding the best odds. Reduces negative EV, rarely creates positive.
- Model-based betting: If your model identifies genuine mispricing, you can find +EV situations. This is the real game.
The Uncomfortable Implication
If you're betting recreationally — picking games based on feeling, team loyalty, or conventional wisdom — you are almost certainly operating at negative expected value. You're paying for entertainment, like a movie ticket, but one that occasionally feels like skill.
That's not necessarily wrong. Entertainment has value. But calling it "investment" or believing you're going to beat the market long-term without a genuine edge is how recreational bettors lose significant money while convincing themselves they're doing well.
The honest framework: estimate your expected value as accurately as you can, decide if the entertainment value justifies the cost, and proceed accordingly.