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Win rate tells you how often you cash a ticket. Expected value tells you whether you are actually making money. Here is how to calculate EV, why it matters, and how to apply it to NHL betting.
TL;DR
Expected value (EV) measures the average profit or loss per bet over time. A bet is +EV when the true probability of winning is higher than the probability implied by the odds. You do not need to win most of your bets to be profitable. You need to consistently find spots where the odds undervalue the actual likelihood of an outcome. That is the entire game.
Expected value is a concept from probability theory. It tells you the average outcome of a bet if you could repeat it an infinite number of times. Every bet has an EV, and it is either positive (you profit long-term), negative (the book profits), or zero (breakeven).
Most bets at a sportsbook are -EV because of the vig (the book's built-in margin). Finding +EV bets means finding situations where the odds are mispriced in your favor.
The EV Formula
EV = (Win Prob × Profit) − (Loss Prob × Stake)If EV is positive, the bet is profitable over time. If EV is negative, the sportsbook has the edge.
Step-by-step EV calculation
Toronto Maple Leafs
-150
Implied: 60.0%
Montreal Canadiens
+130
Implied: 43.5%
Your estimated prob
50%
Canadiens undervalued
Scenario: You believe the Canadiens have a 50% chance to win, but the +130 odds imply only 43.5%.
A $100 bet on MTL +130 pays $130 profit if it wins.
EV = (0.50 × $130) − (0.50 × $100) = $65 − $50 = +$15.00
That is +15% EV on every $100 wagered. Even though this bet only wins half the time, the payout more than compensates for the losses. Over 100 identical bets, you would expect roughly $1,500 in profit. That is why EV matters more than win rate.
Betting heavy favorites at -250 and winning 60% of the time sounds great. But the math does not work.
60 wins × $40 profit = +$2,400
40 losses × $100 lost = -$4,000
Net: -$1,600
Betting underdogs at +200 and winning 45% of the time sounds mediocre. But watch.
45 wins × $200 profit = +$9,000
55 losses × $100 lost = -$5,500
Net: +$3,500
The bettor with a 45% win rate makes money. The one with 60% loses it. The difference is expected value. Win rate without context is meaningless.
Sportsbook odds reflect implied probability, which includes the vig. The true probability of an outcome is unknowable, but models can estimate it. The gap between implied and estimated true probability is where edge lives.
When your estimated probability is higher than the implied probability, the bet is +EV. When it is lower, the bet is -EV. Simple as that.
Finding the gap
Implied probability (from odds)
43.5%
Your estimated true probability
50.0%
Edge
+6.5 points
Sportsbooks do not offer fair odds. They build in a margin called the vig (short for vigorish, also called juice). This is how they guarantee a profit regardless of the outcome.
With vig (what you see)
Leafs -150 → 60.0% implied
Canadiens +130 → 43.5% implied
Total: 103.5% (3.5% is the vig)
No-vig (fair odds)
Leafs → 58.0% true implied
Canadiens → 42.0% true implied
Total: 100.0% (vig removed)
To remove the vig, divide each side's implied probability by the total implied probability. No-vig lines give you the market's true opinion, stripped of the book's margin. Comparing your model's probability against no-vig lines gives you a cleaner read on edge.
A +EV bettor can easily lose 10 bets in a row. That does not mean the strategy is wrong. Small samples tell you almost nothing about edge.
You need hundreds of bets at minimum to know if a strategy is working. Professional bettors think in seasons, not weekends.
A losing bet on a +EV play is a good bet. A winning bet on a -EV play is a bad bet. Judge your decisions by the process, not the result.
The vig ensures the sportsbook profits over time. To overcome it, you need a consistent informational or analytical edge. Models can help find that edge.
PuckCast generates win probabilities for every NHL game using an ensemble model trained on 16 seasons of data. You can use these probabilities directly in EV calculations.
No model is perfect. PuckCast probabilities are one input among many. Always consider injuries, goalie confirmations, and other factors the model may not fully capture. Track your results over time to measure real-world performance against expected outcomes.
Expected value (EV) is the average amount you would win or lose per bet if you placed the same bet thousands of times. A positive EV (+EV) means the bet is profitable long-term. A negative EV (-EV) means the sportsbook has the edge.
Yes, in the short term. Any single bet can win regardless of EV. But over hundreds or thousands of bets, negative EV guarantees losses. The math always catches up. That is why EV matters more than any individual result.
Compare a sportsbook's implied probability to your own estimated true probability. If your model says a team wins 55% of the time but the odds imply only 45%, that is a +EV spot. The bigger and more accurate the gap, the stronger the edge.
The vig is the sportsbook's built-in margin. Both sides of a moneyline imply probabilities that add up to more than 100% (typically 105-110%). That extra percentage is the book's profit. Removing it gives you 'no-vig' or 'fair' odds.