Implied probability explained

The formula: decimal odds to implied probability

For decimal odds, the conversion is:

- Implied probability (%) = (1 ÷ decimal odds) × 100

Worked examples:

• 1.80 → 1 ÷ 1.80 = 0.5556 → 55.6%
• 2.50 → 1 ÷ 2.50 = 0.40 → 40.0%
• 3.40 → 1 ÷ 3.40 = 0.2941 → 29.4%
• 6.00 → 1 ÷ 6.00 = 0.1667 → 16.7%

To reverse it — turning your own probability estimate into a fair price — divide 1 by the decimal probability: a 40% chance implies fair odds of 1 ÷ 0.40 = 2.50.

This is the single most useful calculation in betting. It converts a price you can't intuitively judge into a percentage you can reason about, and it lets you line up your read of a match against what the bookmaker is charging.

Fractional and American odds

UK racing markets still quote fractional odds, and some markets show American (moneyline) prices. The implied probability logic is identical once you convert to decimal.

Fractional to implied probability:

• Implied probability = denominator ÷ (numerator + denominator)
• 5/2 → 2 ÷ (5 + 2) = 2 ÷ 7 = 28.6%
• Evens (1/1) → 1 ÷ 2 = 50%
• 4/6 → 6 ÷ 10 = 60%

American odds:

• Positive (+150): 100 ÷ (odds + 100) → 100 ÷ 250 = 40%
• Negative (−200): |odds| ÷ (|odds| + 100) → 200 ÷ 300 = 66.7%

Whichever format you meet on a Horse Racing or Football coupon, the percentage tells you the same thing: the market's estimated chance, before margin.

Why raw implied probabilities add up to more than 100%

Add the implied probabilities of every outcome in a market and you never get a clean 100%. The excess is the bookmaker margin (overround), and it's how the operator builds in profit.

Take a two-way market priced 1.90 / 1.90:

• 1 ÷ 1.90 = 52.6%
• 52.6% + 52.6% = 105.3%

That extra 5.3% is the overround. A fair, margin-free book would total exactly 100%, so both sides would be priced 2.00 (50% each). The gap between the fair price and the offered price is your cost of doing business.

Margin scales with the number of outcomes and the operator. In our sampled UK data, average margins measured per book were:

• Betfair — 4.6% (278 markets)
• BetMGM — 5.2% (122 markets)
• Coral — 5.7% (247 markets)
• Ladbrokes — 5.9% (253 markets)
• Unibet — 5.9% (250 markets)
• Sky Bet — 6.5% (242 markets)
• Betway — 6.8% (257 markets)
• Paddy Power — 7.1% (257 markets)
• William Hill — 7.2% (266 markets)
• bet365 — 7.4% (30 markets)
• BetVictor — 7.7% (243 markets)
• BoyleSports — 7.8% (246 markets)
• Virgin Bet — 8.3% (214 markets)
• LiveScore Bet — 8.5% (214 markets)

The higher the margin, the more each implied probability is inflated above the true chance — which is why the same fixture reads as a slightly worse bet at a 8.5% book than at a 4.6% book.

Removing the margin: true probability vs implied probability

Raw implied probability overstates every outcome's chance because it includes the overround. To get closer to the market's genuine estimate, normalise each implied probability by dividing it by the book total.

Worked example — a three-way Premier League match:

• Home 2.10 → 47.6%
• Draw 3.60 → 27.8%
• Away 3.80 → 26.3%
• Book total = 47.6% + 27.8% + 26.3% = 101.7% (a 1.7% margin on this line)

Normalised (margin-removed) probabilities:

• Home: 47.6% ÷ 101.7% = 46.8%
• Draw: 27.8% ÷ 101.7% = 27.3%
• Away: 26.3% ÷ 101.7% = 25.9%
• Total = 100.0%

The home side's true implied chance is 46.8%, not the raw 47.6%. On tight football lines the correction is small; on high-margin markets with many runners — a big-field handicap on the Horse Racing card, say — the gap between raw and normalised probability widens sharply, and ignoring it flatters every price.

Using implied probability to find value

Value exists when your estimated probability is higher than the implied probability of the price.

Steps:

1. Convert the offered odds to implied probability. 2. Estimate the true probability yourself (form, xG, head-to-head, conditions). 3. Bet only when your estimate exceeds the implied figure.

Example: a tennis outright is priced 3.00, implying 33.3%. If your model puts the player at 40%, the fair price is 1 ÷ 0.40 = 2.50. Being offered 3.00 on something you rate at 2.50 is positive expected value.

Expected value in cash terms on a £10 stake at 3.00:

- EV = (0.40 × £20 profit) − (0.60 × £10 stake) = £8 − £6 = +£2 per £10 staked.

The edge only survives if the price is good. This is where best-price share matters: across our sample Betfair posted the top price in 48.6% of sampled markets, Coral in 27.1% and Ladbrokes in 20.2%, while several books rarely led on price. Taking the same selection at a lower price shrinks the implied-probability gap you're exploiting — sometimes past the point of value. Comparing prices across bookmakers before you stake is the practical half of this maths.

Quick reference: common odds and their implied probability

• 1.20 → 83.3%
• 1.50 → 66.7%
• 1.80 → 55.6%
• 2.00 → 50.0%
• 2.50 → 40.0%
• 3.00 → 33.3%
• 4.00 → 25.0%
• 5.00 → 20.0%
• 6.00 → 16.7%
• 10.00 → 10.0%
• 21.00 → 4.8%

Remember these are raw figures including margin. On a full market, normalise against the book total for the market's true estimate. All UK operators referenced are licensed by the UK Gambling Commission (UKGC); the minimum age to bet is 18.