Definitions
| Term | Meaning |
|---|---|
| Quoted odds | The accepted or displayed payoff under operator rules |
| Raw implied probability | Reciprocal conversion of quoted odds |
| De-margined share | A stated method for reallocating a market total to 100% |
| Model probability | Output from a documented forecasting method |
| Fair odds | 1 divided by a stated probability estimate |
"True odds" is often used informally, but the true probability is not observed before the event. Use fair odds and identify the method that produced them; OpenStax provides the underlying probability terminology.
De-margin example
A market at 2.00, 3.50 and 4.00 has raw shares of 50.00%, 28.57% and 25.00%. The total is 50.00% + 28.57% + 25.00% = 103.57%.
Under proportional normalization:
| Selection | Proportional share | Fair odds under this convention |
|---|---|---|
| Home | 50.00 / 103.57 x 100 = 48.28% | 1 / 0.4828 = 2.071 |
| Draw | 28.57 / 103.57 x 100 = 27.59% | 1 / 0.2759 = 3.625 |
| Away | 25.00 / 103.57 x 100 = 24.14% | 1 / 0.2414 = 4.143 |
These are not uniquely true odds. Another margin-allocation method can produce different shares.
Model comparison
If a separately validated model estimates Home at 52%, its model fair price is 1 / 0.52 = 1.923. A quoted price of 2.00 has estimated expected net return of 0.52 x 2.00 - 1 = 0.04 units per unit staked before costs. The estimate is only as credible as the model probability; OpenStax provides the expected-value basis.
scikit-learn's calibration guidance explains how predicted probabilities are compared with observed frequencies. Evaluation should use unseen, time-appropriate data rather than a few selected results.
Name the probability source every time
A fair price has meaning only alongside its probability source. A proportional de-margin calculation, a Poisson model and a human forecast can all produce different percentages for the same outcome. Label the output, version the method and record the data cutoff so the number can be reconstructed later; OpenStax provides the probability terminology.
For example, a de-margined market share of 48% gives fair decimal odds of 1 / 0.48 = 2.083. A separate model estimate of 52% gives 1 / 0.52 = 1.923. Neither should be called the unknowable true price. The disagreement is a question for validation, not a reason to choose the more attractive number; scikit-learn describes calibration of model probabilities.
Validation record
- Define the target outcome and settlement period using the probability and calibration concepts in scikit-learn's guidance.
- Prevent future information from entering the model inputs.
- Evaluate forecasts made before the observed outcomes.
- Check calibration across probability ranges, not only overall accuracy.
- Report the evaluation period, sample composition and uncertainty.
- Keep model changes separate from market-price changes.
scikit-learn's calibration guidance explains why a well-calibrated 60% forecast should correspond to an observed frequency near 60% across comparable cases. That is a long-run evaluation statement, not a promise about one event.
Related resources
Use implied probability for conversions and price and probability matrix for a decision record.
Continue learning
- Next guide: How Correct Score Odds Can Be Modelled
- Related guide: Price and Probability Decision Matrix
Assumptions and limitations
Examples ignore commission, limits and estimation uncertainty. Proportional normalization is shown for transparency, not endorsed as uniquely correct. A model-market disagreement is not proof that the market is wrong.
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