Implied Probability

Every price a sportsbook posts is really a probability wearing a disguise. When you see the Chiefs at -165, that number isn’t just a payout instruction — it’s the book telling you, in coded form, how often it thinks the Chiefs need to win for that bet to break even. Implied probability is the process of decoding that number back into a percentage, so you can actually reason about it instead of just staring at plus and minus signs.

The math is simple once you know the two formulas. For a negative (favorite) price, implied probability equals the odds figure divided by the odds figure plus 100 — so -165 becomes 165 / 265 = 62.3%. For a positive (underdog) price, it’s 100 divided by the odds figure plus 100 — so +140 becomes 100 / 240 = 41.7%. Notice that those two numbers, 62.3% and 41.7%, add up to more than 100%. That gap is the vig (or juice) — the sportsbook’s built-in margin — and it’s the reason implied probability from the raw odds is never the same as true probability. To get a fair, no-vig estimate, you have to strip that margin out, which is a step most bettors skip and shouldn’t.

Why this matters: odds by themselves tell you what you’d win, not whether the bet is good. A -165 favorite and a +140 underdog can look attractive on their face, but only implied probability tells you what the market is actually charging you to take that side. Once you have that number, you can stack it against your own handicap of the game. If you think a team wins 55% of the time and the book’s price implies only 50%, you’ve found value — the price is better than the risk. If your number is below the implied number, you’re being overcharged, no matter how “safe” the bet feels.

Example

Say the Dodgers are hosting the Padres and the moneyline reads Dodgers -145, Padres +125.

Step 1 — convert each side to raw implied probability. Dodgers: 145 / (145 + 100) = 145 / 245 = 59.18% Padres: 100 / (125 + 100) = 100 / 225 = 44.44%

Step 2 — add them up. 59.18% + 44.44% = 103.62%

That extra 3.62% is the vig. A perfectly fair, two-outcome market would sum to exactly 100%, so this book is holding about 3.6 cents of margin on the pair.

Step 3 — remove the vig to get fair probabilities. Divide each side by the total: Dodgers = 59.18 / 103.62 = 57.11%, Padres = 44.44 / 103.62 = 42.89%. Now they sum to 100%, and this is the market’s true, de-vigged view of the game.

Step 4 — compare to your own number. Suppose your own model, built on Dodgers’ rotation and Padres’ recent road struggles, has the Dodgers winning 63% of the time — six points higher than the market’s fair 57.11%. That gap is your edge. On a $50 bet at -145, a win nets $34.48; over a large sample of bets with a genuine 6-point edge, that price pays off well above what it costs, which is exactly the kind of spot worth betting into.

Contrast that with the Padres side: the book implies 44.44% raw, 42.89% fair, and if your own number for the Padres is only 40%, you’re below the market’s fair line — a bet to avoid even though +125 looks like a tempting underdog payout.

Key Points

• Raw implied probability always includes the vig: the two (or three) sides of a market will sum to more than 100%; that overage is the book’s cut, not a reflection of true chances.
• De-vig before you compare prices across books: dividing each side by the total (as in Step 3) gives you a clean number you can stack against your own projections or against a different sportsbook’s line.
• Line shopping is really implied-probability shopping: a Padres +125 at one book and +135 at another translate to 44.44% and 42.55% respectively — same team, same game, but a real difference in what you’re being asked to believe.
• Big favorites carry disproportionate implied probability weight: moving a price from -110 to -150 doesn’t feel like much, but it jumps implied probability from 52.4% to 60%, a swing bettors routinely underestimate when “just laying a bit more juice.”
• Your edge is the distance between your number and the market’s fair number, not the raw one: comparing your projection to a vig-inflated implied probability makes almost every bet look worse than it is and can talk you out of good spots.
• Implied probability is a floor for decision-making, not a prediction: it tells you what the price requires, not what will happen in this one game — treat it as the bar your own analysis needs to clear before you bet.