Implied probability explained

The formula: decimal odds to implied probability

For decimal odds, the conversion is a single step:

Implied probability = 1 ÷ decimal odds

• Odds 1.50 → 1 / 1.50 = 0.667 = 66.7%
• Odds 2.50 → 1 / 2.50 = 0.400 = 40.0%
• Odds 5.00 → 1 / 5.00 = 0.200 = 20.0%
• Odds 10.00 → 1 / 10.00 = 0.100 = 10.0%

To go the other way — turning a probability you believe into a fair price — invert it: fair odds = 1 ÷ probability. If you rate a horse a 25% chance, fair odds are 1 / 0.25 = 4.00. Anything longer than 4.00 is potentially value; anything shorter is not.

Fractional odds, still common in Irish horse racing, convert like this: implied probability = denominator ÷ (numerator + denominator). So 5/2 = 2 / (5 + 2) = 2/7 = 28.6%. Evens (1/1) is exactly 50%.

Why the numbers never add up to 100%

Take a two-way market where both outcomes are priced 1.91. Each implies 1 / 1.91 = 52.4%. Add them: 52.4% + 52.4% = 104.8%. That extra 4.8% is the overround — the bookmaker's built-in margin.

In a fair market with no margin, both sides of a coin-flip would be 2.00 (50% + 50% = 100%). No book prices it that way, because the margin is how they make money regardless of result.

To find the true implied probability, you divide each raw figure by the book's total. In the 1.91/1.91 example: 52.4% ÷ 104.8% = 50.0% for each side. The margin has been stripped out. This normalisation matters most in tight markets — a Champions League favourite or an ATP first-round match — where a couple of percentage points decide whether a price is beatable.

Worked example: a Premier League match

Suppose a bookmaker prices a Premier League game:

• Home 2.10 → 1 / 2.10 = 47.6%
• Draw 3.40 → 1 / 3.40 = 29.4%
• Away 3.80 → 1 / 3.80 = 26.3%

Raw total = 47.6% + 29.4% + 26.3% = 103.3%. That 3.3% is the margin on this market.

Strip it out by dividing each by 103.3%:

• Home: 47.6 / 103.3 = 46.1%
• Draw: 29.4 / 103.3 = 28.5%
• Away: 26.3 / 103.3 = 25.4%

Now the true implied probabilities sum to 100%. If your own model rates the home side at, say, 50%, the fair price is 1 / 0.50 = 2.00 — and the offered 2.10 is longer than fair, so it carries value. If your model says 44%, fair odds are 2.27, the 2.10 is too short, and you pass.

That is the entire discipline: convert the price, remove the margin, compare against your own estimate, bet only when the offered price beats your fair price.

Margin data: where the implied probabilities are fairest

The lower a bookmaker's margin, the smaller the gap between the price you see and the true probability — so you keep more of any edge. From our tracked samples of Irish-facing books:

• Betfair — 4.21% average margin (216 selections), best-price share 54.6%
• Unibet — 5.71% (191)
• Ladbrokes — 5.79% (193), best-price share 22.8%
• Betway — 6.30% (195)
• Paddy Power — 6.92% (195)
• William Hill — 6.99% (219), best-price share 16.0%
• 888sport — 7.14% (219)
• bet365 — 7.44% (30)
• BetVictor — 7.54% (190)
• BoyleSports — 7.54% (195)
• LiveScore Bet — 8.39% (193)

Best-price share measures how often an operator posts the top price in a sampled market. Betfair leads at 54.6%, reflecting its exchange model where prices are set by backers and layers rather than a trading desk. A lower margin does not guarantee the top price on any single selection, but over many bets it means the implied probabilities you convert are systematically closer to fair.

These are odds figures only. Sportsbook depth, live capability and app quality are scored separately in our operator ratings.

Using implied probability to find value

Value exists when the true probability of an outcome is higher than the implied probability of the price on offer. The check is mechanical:

1. Convert the offered odds to implied probability (1 ÷ odds). 2. Normalise the full market to strip the margin. 3. Compare the true implied figure with your own estimate. 4. Bet only when your estimate exceeds the implied figure — meaning the offered price is longer than fair.

Expected value in cash terms: (probability × profit if won) − (probability of loss × stake). On a €10 bet at 2.10 where you rate the outcome 50%: (0.50 × €11.00) − (0.50 × €10.00) = €5.50 − €5.00 = +€0.50 expected. Positive EV, so it clears the bar. At the same 50% estimate but odds of 1.90, the sum is (0.50 × €9.00) − (0.50 × €10.00) = −€0.50 — negative, so you skip it.

Because margins differ by 4+ percentage points across books, line-shopping is the practical lever. The same outcome converted at Betfair's 4.21% margin will, on average, sit at a longer price than at LiveScore Bet's 8.39% — which is why comparing odds before staking is where most of the edge is won.

Quick reference: common odds and their implied probability

• 1.20 → 83.3%
• 1.50 → 66.7%
• 1.80 → 55.6%
• 1.91 → 52.4%
• 2.00 → 50.0%
• 2.50 → 40.0%
• 3.00 → 33.3%
• 4.00 → 25.0%
• 5.00 → 20.0%
• 6.00 → 16.7%
• 11.00 → 9.1%
• 21.00 → 4.8%

Remember these are raw figures straight from 1 ÷ odds. In any real market they will overstate the true chance slightly, because the margin is still inside them. Normalise across the full set of outcomes before treating any figure as the book's genuine probability estimate.