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Decimal odds on a correct score bet tell you the gross return per unit staked if the bet wins, including your original stake. Their reciprocal is the raw implied probability—not the scoreline's true chance of occurring.
For example, a 10-unit stake at 8.00 returns 80 units gross and produces 70 units of net profit before fees or taxes. The raw implied probability is 1 / 8.00 = 12.5%. That price alone does not establish that the scoreline has a 12.5% chance.
How do you convert odds into implied probability?
For decimal odds, calculate 1 / decimal odds × 100%. Convert fractional or American odds to decimal odds before taking the reciprocal.
The same price can appear in three formats:
| Format | Odds |
|---|---|
| Decimal odds | 8.00 |
| Fractional odds | 7/1 |
| American odds | +700 |
All three represent a raw implied probability of 12.5%. The conversion formulas are:
- Fractional odds
a/b:a / b + 1. - Positive American odds
A:A / 100 + 1. - Negative American odds
−A:100 / A + 1, whereAis the absolute value.
For example, −150 converts to decimal odds of approximately 1.6667 and a raw implied probability of 60%. Here, 1.6667 is a rounded display value; the 60% is calculated from the original price, not that rounded decimal.
Use the odds converter to switch formats and the implied probability calculator to calculate the reciprocal.
Raw implied probability describes the price. It neither verifies the bookmaker's assessment nor automatically removes the market's overround.
How do you calculate overround for a complete market?
Add the reciprocals of the prices for every mutually exclusive outcome that collectively covers the whole market, then subtract 100%. A few popular scorelines cannot substitute for the complete outcome list.
The following is a fabricated teaching example, not a live bookmaker line. Its twelve outcomes are defined to be mutually exclusive and exhaustive. Each grouped selection covers the relevant scorelines not listed individually.
| Outcome | Decimal odds | Raw implied probability |
|---|---|---|
| 0–0 | 9.50 | 10.53% |
| 1–0 | 7.20 | 13.89% |
| 0–1 | 11.00 | 9.09% |
| 1–1 | 6.20 | 16.13% |
| 2–0 | 11.50 | 8.70% |
| 0–2 | 16.00 | 6.25% |
| 2–1 | 8.50 | 11.76% |
| 1–2 | 12.00 | 8.33% |
| 2–2 | 16.00 | 6.25% |
| Any other home win | 8.00 | 12.50% |
| Any other draw | 23.00 | 4.35% |
| Any other away win | 10.00 | 10.00% |
| Total | — | 117.78% |
To reproduce the calculation, calculate 1 / decimal odds for each row without intermediate rounding, then add all twelve values:
Booksum = 1.1777666350389202
As a percentage = 117.7766635…%
Overround = 117.7766635…% − 100% = 17.7766635… percentage points
Rounded to two decimal places, the booksum is 117.78% and the simple overround is 17.78 percentage points. The displayed row probabilities are rounded to two decimal places and also sum to 117.78% in this example. Nevertheless, use the original odds rather than rounded percentages for calculations.
Overround is the arithmetic excess above 100%. It is not guaranteed bookmaker profit, the operator's actual business margin, or a bettor's expected loss. You can check a complete set of prices with the margin calculator.
What does removing the vig change?
Proportional de-vig, also called proportional normalization, makes the probabilities sum to 100% but does not establish their true values. It divides each raw implied probability by the booksum of the complete market.
For 1–1 at 6.20 in the teaching example:
- Raw implied probability: 16.13%.
- Proportionally normalized estimate: 13.69%.
Using unrounded values:
(1 / 6.20) / 1.1777666350389202 × 100% = 13.694590913…%
The displayed 13.69% is rounded to two decimal places. It is the result of a particular method, not a verified true probability. Proportional normalization applies the same relative scaling to every outcome; other de-vig methods can produce different estimates. Štrumbelj's 2014 study compares probability-estimation methods, rather than establishing one universally correct adjustment.
Do not confuse no-vig odds, derived from bookmaker prices after a stated adjustment, with model fair odds, derived from a model's probability. They use different inputs.
Which settlement rules should you check?
Check the settlement period and the boundaries of grouped selections with the operator offering the market. The name “correct score” alone does not tell you whether extra time counts or which scorelines belong to a group.
For example, Betfair's standard football correct-score settlement covers 90 minutes plus stoppage time, excluding extra time unless a specifically named market states otherwise. This is an operator-specific example, not a universal rule: see Betfair's 90-minute settlement explanation and football rules.
An Any Other Score selection also depends on the market. In the teaching table, the remaining scorelines are split into other home wins, other draws and other away wins. A real operator may use a different structure. Sky Bet's football rules provide another operator-specific example of grouped score selections, not a standard for every bookmaker.
Likewise, do not assume that a 17-way correct-score market has a universal outcome list. Read the selections and group definitions shown by that operator.
Before calculating or placing a bet, check that:
- Individual scorelines and groups do not overlap.
- No possible outcome is missing.
- All prices use the same settlement period.
- Each group's coverage is clear from the market rules.
How do you use the correct-score calculator?
Open the correct-score calculator, enter expected goals for the home and away teams separately, then inspect the scoreline probabilities and model fair odds. The results describe a scenario under your assumptions, not a verified match forecast.
The local calculator accepts either direct expected goals (xG) inputs or team-strength inputs and calculates a score grid using a Poisson distribution. Use the direct expected-goals inputs to reproduce the pictured example:
- Open the calculator.
- Enter 1.65 in the home expected-goals input and 1.05 in the separate away input.
- Set the maximum score grid to 6 and leave the Dixon–Coles correction off.
- Obtain the results and find 1–1: the local interface displays 11.7% and model fair odds of 8.58.
- Interpret those figures as outputs of the entered scenario, subject to the model and display limitations below.
The expected-goals values here are assumptions, not measurements from a particular match. The finite visible score grid is normalized, so its boundaries affect the output.
The display also uses a particular rounding sequence. The probability is first rounded to four decimal places as 0.1166. That produces the displayed 11.7% and a reciprocal, 1 / 0.1166, that rounds to 8.58. Taking the reciprocal of the full-precision probability instead rounds to 8.57. The difference comes from display rounding, not a change in the scenario.
ToolsGambling local-development correct-score calculator with home expected goals of 1.65, away expected goals of 1.05, and the 1–1 result
Local-development capture, not the production site. With inputs of 1.65 and 1.05, the 1–1 result shows 11.7% and model fair odds of 8.58.
The Dixon–Coles correction relates to the model described in the 1997 paper, which used historical English league and cup data. The Reade et al. 2021 study concerns the English Premier League. Neither source establishes universal calibration, accuracy for your chosen match, or an edge over current bookmaker prices. The local capture is not verification of production behavior.
How do you compare a model estimate with an available price?
Compare an independently estimated model probability with a genuinely available price for the same outcome under the same settlement rules. Conditional positive expected value (EV) exists when the probability multiplied by the decimal odds exceeds 1.
Suppose an independent model assigns an outcome a 14% probability and the available decimal odds are 7.50:
0.14 × 7.50 − 1 = +0.05 units per unit staked
That is 5% of the stake in expected value, assuming the probability estimate is calibrated and the price is genuinely available, before fees or taxes. It is not a prediction of the next result or a guarantee of profit over a series of bets.
The 14% is a separate illustrative assumption, not the result of the calculator scenario above. Do not substitute a probability recovered from the same bookmaker price for an independent model estimate: those are different bases for comparison.
The value bet finder can support further comparison, but a calculation does not remove model uncertainty.
What should you remember?
Odds tell you the payout and allow you to calculate raw implied probability; they do not directly reveal the true chance. Calculate overround only from a complete market, and treat de-vig estimates and calculator outputs as results with explicit assumptions.
Before betting, check the settlement period, grouped-selection boundaries and price availability. For more background, read the correct score betting guide and the guide to predicting correct scores.
Frequently Asked Questions
Divide 1 by the decimal odds, then multiply by 100%. This gives raw implied probability, not the outcome's true chance. Convert fractional or American odds into decimal odds first.
High decimal odds represent a low raw implied probability. The price alone does not explain why an operator chose it: that depends on its assessment and market conditions. There is no universal explanation for every match.
No. You need the complete set of mutually exclusive outcomes, including grouped selections, that covers every possible result. A sum based on selected scorelines does not show the whole market's overround.
That universal claim is not established. Compare correct-score and match result (1X2) overround only using comparable, complete sets of prices with the same settlement conditions.
Conditional value exists when the model's estimated probability multiplied by the available decimal odds exceeds 1. The conclusion depends on the quality of the probability estimate and the betting conditions; it does not guarantee profit.
It covers scorelines that are not listed individually and belong to that group under the specific market's rules. Check whether it includes all remaining scorelines or only other home wins, away wins or draws.
It is an operator's label for a grouped correct-score market. Check that operator's outcome list and rules for the exact selections and group boundaries; there is no verified universal set.
Raw implied probability is 1 / 21.00 × 100%, or approximately 4.76%. A winning bet returns 21 times the stake, including the original stake, for a net profit of 20 times the stake before costs. This does not mean the true chance is 4.76%.
Model fair odds are the reciprocal of a specified model's probability. No-vig odds are derived from a complete set of bookmaker prices using a stated de-vig method. Neither is automatically the outcome's true price.
No. It shows results under the assumptions you enter. Any potential edge depends on probability-estimation quality, the available price and market conditions. A positive calculation does not prove future profit.
For fractional odds, divide the numerator by the denominator and add 1. For positive American odds, divide the number by 100 and add 1. For negative American odds, divide 100 by the absolute value and add 1. Thus 7/1 and +700 equal decimal 8.00, while −150 equals approximately 1.6667 and implies 60%.
Evgeniy Volkov
Verified ExpertFullstack developer with a background in mathematics. I build the calculators and game-style tools on ToolsGambling with Pixi.js and modern web tech, and every result uses transparent probability formulas you can verify yourself.