Expected Value (EV): The Only Framework Long-Term Winners Use
Winning a single bet is luck; a positive expected value is skill
The formula and the intuition
EV = win probability × (odds − 1) × stake − (1 − win probability) × stake. In plain terms: if you placed this same bet ten thousand times, how much would you make (or lose) per bet on average.
Same 55% but with odds of only 1.75: EV = 0.55×750 − 0.45×1000 = −37.5 per bet—the same read at a different price: one wins over the long run, the other loses.
The +EV decision process
① First work out the odds' implied probability (1÷odds) → ② use your own method (a model, data, or inside information) to estimate the true win probability → ③ only bet when your true probability > the implied probability. The edge should be at least 3–5 percentage points to cover your estimation error. The expected value calculator lets you check the math directly.
Common mistakes
"This bet won, so it was a good bet"—a good outcome doesn't mean a good decision; a 1.20 heavy favorite wins often yet still loses money over the long run. "High odds = high risk, stay away"—if a 4.00 underdog truly has a 30% win probability (the implied is only 25%), it's +EV. "It just feels safe"—a "safe" feeling with no quantified win probability can't be compared to the price; that's betting with your eyes closed.
Estimating the win probability is the hardest part. You can use a quantitative model as your baseline and then adjust it by hand—Sports Radar's daily model analysis uses score-distribution simulations to produce win probabilities and over/under probabilities and compares them against the market price, which is exactly this process automated.
Frequently Asked Questions
Can I still bet when the expected value is negative?
From a profit standpoint, no—placing negative-EV bets repeatedly guarantees a long-term loss; that's math, not chance. If it's entertainment spending, keep the amount under your own control.
How much edge do I need before a bet is worth it?
In practice, your own estimated win probability should be at least 3–5 percentage points higher than the implied probability to cover your estimation error and the vig.