The main idea: implied probability is what the odds say the market believes, while model probability is what a prediction system believes. To compare them properly, convert decimal odds to raw implied probability, remove the bookmaker margin to get a fair implied probability, make sure the model is calibrated, and then judge the gap against closing lines and proper scoring rules. AlphaBench evaluates football models such as DeepSeek's deepseek-flash, OpenAI's gpt-5-mini, and xAI's grok-build-0.1 on settled fixtures, including a recent Premier League match between Khovd Western and Deren. This article is educational and is not betting advice.
Implied probability from decimal odds
Decimal odds convert to raw implied probability with a simple formula:
\[ \text{Raw implied probability} = \frac{1}{\text{decimal odds}} \]
If the decimal odds are 2.50, the raw implied probability is \(1 / 2.50 = 0.40\), or 40%. If the decimal odds are 1.50, the raw implied probability is about 66.7%. If the decimal odds are 4.00, it is 25%.
Those numbers are called “raw” because they still contain the bookmaker’s margin. They are not yet the market’s clean estimate of what will happen.
Bookmaker margin distorts implied probability
In a real market, the raw implied probabilities for all outcomes usually add up to more than 100%. The excess is the bookmaker margin, also called the overround or vig. For example, suppose a three-way market has these decimal odds:
- Home: 2.00 → 50.00%
- Draw: 3.50 → 28.57%
- Away: 4.00 → 25.00%
The sum is 103.57%. To remove the margin proportionally, divide each raw implied probability by the total:
\[ \text{Fair implied probability} = \frac{\text{Raw implied probability}}{\sum \text{Raw implied probabilities}} \]
After adjustment:
- Home: 50.00% / 103.57% ≈ 48.28%
- Draw: 28.57% / 103.57% ≈ 27.59%
- Away: 25.00% / 103.57% ≈ 24.14%
Those fair implied probabilities are the better starting point when comparing market prices with model probabilities. Margin removal is still an approximation, because bookmakers do not always apply the same margin evenly across favorites and longshots. But comparing a model against raw implied probability usually overstates the market’s true belief.
Model probability should be calibrated
A model probability is a forecast between 0 and 1. Calibration means that when a model says an event has a 30% chance, that type of event happens about 30% of the time over many predictions. A model can rank teams well and still be badly calibrated if it is consistently overconfident or underconfident.
AlphaBench uses proper scoring rules such as Brier score and log loss to measure probability quality. You can read more in How AlphaBench scores models and Brier score for football predictions. In practice, models like deepseek-flash, gpt-5-mini, or grok-build-0.1 might produce probabilities for a fixture such as Khovd Western vs Deren. Those probabilities are only comparable to fair implied probabilities if they are calibrated. If they are not, a apparent edge may just be a calibration error.
Finding edge
In probability terms, edge is often written as:
\[ \text{Edge} = \text{Model probability} - \text{Fair implied probability} \]
If a model says 45% and the fair implied probability is 40%, the simple edge is 5 percentage points, or 12.5% relative. But that gap is not automatically meaningful. It can come from a better model, a stale market price, a different information set, or random noise.
To judge edge responsibly, look at sample size, calibration, closing line behaviour, and whether the model has a repeatable process. AlphaBench's leaderboard compares models across many settled fixtures, which is far more informative than one match. This is not betting advice.
Closing line comparison
Closing odds are the final prices just before an event starts. They are often the most information-rich market estimate available. Comparing model probability with the closing implied probability is usually more useful than comparing it only with opening odds.
If a model’s probabilities consistently move toward or anticipate the closing line, that is evidence of useful information. CLV, or closing line value, measures how a price compares with the closing line. But CLV is a diagnostic, not a guarantee. A model can show positive CLV in a small sample and still be miscalibrated.
Limitations
Every comparison between implied probability and model probability has limits. Bookmaker margin removal is approximate. Odds may be unavailable, delayed, or limited to certain markets. Model probabilities can drift when teams, players, tactics, or conditions change.
Brier score, log loss, calibration, CLV, ROI, and maximum drawdown all describe different things: probability accuracy, price movement, profit and loss, and risk. A good Brier score does not ensure positive ROI, and positive ROI does not prove calibration. Small samples can make random noise look like edge. AlphaBench's methodology explains the scoring assumptions behind its evaluations. Nothing here is betting advice.