From American odds to implied probability

Two formulas cover every American price. For negative odds (favorites), implied probability is -N / (-N + 100): a -200 line implies 200 / 300 = 66.67%. For positive odds (underdogs), implied probability is 100 / (N + 100): a +200 line implies 100 / 300 = 33.33%. Run any price through either formula and you get the win rate the book is effectively quoting before its margin.

Break-even probability is the floor for any bet

The implied probability is your break-even threshold. At -110, you need to win 52.38% just to make the vig back. At -250 (heavy favorite), you need 71.43%. At +400 (longshot), 20.00%. Multiply the gap between your model's probability and the break-even by the payoff per dollar staked, and you get the expected value of the bet — the only number that ultimately matters. A model that beats break-even by even a single percentage point on a high-volume market (NFL spreads, NBA totals) is a serious edge.

Worked example: a +145 underdog

A bet at +145 implies 100 / 245 = 40.82%. For the bet to be +EV, your true win probability must exceed 40.82% by enough to compensate for variance — most pros require at least 1-2 percentage points of edge after devig before placing a wager. Your model says the underdog is a 44% shot? Real edge is 44.00% - 40.82% = 3.18 percentage points; expected return per $100 stake is 0.44 × $145 − 0.56 × $100 = +$7.80, a 7.8% EV. Strong enough to bet at quarter Kelly.

American / decimal / fractional / probability reference

American	Decimal	Fractional	Implied prob
-400	1.250	1/4	80.00%
-300	1.333	1/3	75.00%
-250	1.400	2/5	71.43%
-200	1.500	1/2	66.67%
-180	1.556	5/9	64.29%
-150	1.667	2/3	60.00%
-130	1.769	10/13	56.52%
-120	1.833	5/6	54.55%
-110	1.909	10/11	52.38%
-105	1.952	20/21	51.22%
+100	2.000	1/1	50.00%
+105	2.050	21/20	48.78%
+110	2.100	11/10	47.62%
+120	2.200	6/5	45.45%
+130	2.300	13/10	43.48%
+150	2.500	3/2	40.00%
+180	2.800	9/5	35.71%
+200	3.000	2/1	33.33%
+250	3.500	5/2	28.57%
+300	4.000	3/1	25.00%
+400	5.000	4/1	20.00%

FAQ

What is implied probability and how do you calculate it from American odds? +

Implied probability is the win rate a bet must hit to break even at the offered price. For negative American odds, the formula is -N / (-N + 100) — a -150 line implies 60.00%. For positive American odds, the formula is 100 / (N + 100) — a +150 line implies 40.00%. It is the most useful single number you can extract from any sportsbook price because it converts a market quote into a probability you can compare against your own model.

What is break-even probability and why does it matter? +

Break-even probability is the win rate that makes a bet exactly zero expected value — every win pays for the losses, no profit, no loss. It is identical to implied probability when looking at a single side: a -110 line breaks even at 52.38%. Bettors track break-even rates obsessively because anything you can win at higher than that rate is profitable in the long run; anything below that rate slowly bleeds bankroll. A model that hits 53% on -110 spreads will out-earn one that hits 60% on -250 favorites.

How does implied probability relate to fair odds? +

Fair odds are the price a bookmaker would offer with zero margin baked in. On any complete market, implied probabilities sum to slightly more than 100% — the excess is the vig (hold, overround). To find fair odds, sum implied probabilities across the market and divide each side by that total. A -110 / -110 market sums to 104.76% implied; dividing each side gives a fair probability of 50.00% on each. Compare your true probability against the fair probability, not the raw implied, when computing edge.

Why is my model's probability different from the book's implied probability? +

Books and models are estimating the same probability but using different inputs and incentives. Books optimize for action balance and margin capture, not pure forecast accuracy — their published prices reflect what bettors are willing to pay on each side plus the book's overround. Your model optimizes for forecast accuracy with no skin in the game. The gap between the two — once you devig the book — is your edge. A persistent gap over many bets is the strongest signal that your model has captured something the market hasn't.

How is this different from a no-vig calculator and an odds converter? +

The Implied Odds Calculator focuses on a single side: input an American price, get the implied probability and break-even percentage in one read. The Odds Converter focuses on format translation: turn any single price into all four formats (American, decimal, fractional, implied). The No Vig Calculator takes BOTH sides of a market, strips the bookmaker margin, and returns each outcome's fair probability. Pick this page when you have one price and need to know the win rate it requires.