Direct answer
What probability do decimal odds 2.20 imply?
Decimal odds of 2.20 imply a raw weight of 1 ÷ 2.20 = 0.4545, or 45.45%. “Raw” matters: the number still belongs to a margin-included market.
One price can answer this inverse-odds question. It cannot reveal the complete market's overround or be de-vigged alone.
Complete-market check
Why do implied probabilities add to more than 100%?
Add the inverse price for every mutually exclusive outcome from one snapshot. That sum is the booksum. Books usually sum above one; booksum minus one is the overround. For 2.05 / 3.40 / 3.80, the booksum is 104.51% and the overround is 4.51 percentage points.
This site also reports (booksum − 1) ÷ booksum as normalized excess share. Neither overround nor excess share is the bookmaker's realised profit rate: stakes are not distributed evenly and prices move.
Two declared assumptions
How are proportional and Shin no-vig probabilities different?
Proportional normalization divides every raw implied weight by the booksum: pᵢ = qᵢ ÷ Σq. It removes the same relative share from each outcome and is simple to reproduce.
Shin's model fits a parameter z and can redistribute margin non-proportionally. The calculator solves z by bisection, shows both outputs and reports the largest outcome-level gap. Fitted z is a model parameter—not observed evidence of insider trading.
Both methods transform the same quotes under different assumptions. Neither authenticates the odds source, predicts the match or proves a uniquely correct probability.
See what that assumption changed across real markets in the 1,900-match proportional-versus-Shin benchmark.
One internal scale
How are fractional and American odds converted?
- Fractional a/b becomes decimal 1 + a/b. For example, 6/5 becomes 2.20.
- Positive American +A becomes decimal 1 + A/100. +120 becomes 2.20.
- Negative American −A becomes decimal 1 + 100/A. −110 becomes about 1.9091.
- The margin-removal formulas then use decimal odds, so equivalent formats produce equivalent probability outputs apart from display rounding.
Settlement scope
Which outcomes belong in a football market?
A football 1X2 market needs home win, draw and away win prices from the same bookmaker, time and settlement rule. Standard 1X2 is commonly settled on regulation time plus stoppage time, but provider rules control whether extra time or penalties are excluded. Never mix a “to qualify” price with regulation-time 1X2 prices.
A two-way market needs both complementary outcomes—for example, a correctly paired Yes and No. If an outcome is missing, the market margin is not identified and the calculator fails closed.
What this proves
A conversion is not a forecast or betting edge
The output is deterministic arithmetic on user-entered prices. It does not know the teams, kick-off, bookmaker, quote time, limits, liquidity or whether the prices were executable. Fair odds are only 1 ÷ the selected no-vig probability.
To test a forecast rather than convert one market, pair complete pre-match model probabilities and odds snapshots across settled matches in the model-vs-bookmaker benchmark. Use the 1X2 probability calculator when the starting input is a model probability split instead of bookmaker prices.
Research trail
Primary and empirical sources behind the boundary
- Shin (1992), prices of state-contingent claims with insider traders
- Štrumbelj (2014), football bookmaker odds and forecast accuracy
- Angelini & De Angelis (2022), football betting market odds-setting
These sources motivate the margin model and the need to treat market probabilities as evidence with assumptions. They do not certify a user-entered quote or turn this calculator into a profit, value or staking claim.