Expected goals and goal models: turning scores into probabilities

xG and a goal model are not the same

Expected goals (xG), often shown during a broadcast, rates the quality of each shot. A penalty is worth about 0.76 goals, for example, while a long-range effort may be worth 0.03. Add up a team’s shot values and you get the total xG: how many goals its chances were worth, which can tell you more about its performance than the final score.

A goal model such as Kuponcu’s starts with match results instead. It learns how many goals each team scores and concedes, then estimates the expected goals for a future match. Shot-based xG describes the chances created in a match; a goal model uses historical results to forecast what may happen next. It needs only match results, which are available for every league and season.

Attack, defence and home advantage

The model assigns each team two ratings: attack, which measures how its scoring compares with an average team, and defence, which measures how many goals it concedes. It also estimates a home advantage for each league. The ratings use the previous two years of results, with more recent matches carrying greater weight. A game from a year ago counts half as much as one played last week.

For example, imagine a league where home teams average 1.45 goals. A home side with an attack rating 30% above average (1.3) faces visitors who concede 10% fewer goals than average (0.9). The home side’s expected goals are 1.45 × 1.3 × 0.9 ≈ 1.70. The same calculation, in reverse, gives the visitors’ expected goals.

From expected goals to every market

Goals are relatively rare in football, and the two teams’ scoring is roughly independent. That makes the Poisson distribution a useful way to estimate how many goals each side will score. With expected goals of 1.6 for the home team and 1.1 for the visitors, the most likely scores are:

• 1–1: 11.8% 1–0: 10.8% 2–1: 9.5% 2–0: 8.6%
• 0–1: 7.4% 0–0: 6.7% 1–2: 6.5% 2–2: 5.2%
• Add the probabilities of every score where the home team leads: that gives a 49% home win chance. Level scores add up to a 25% draw chance. The remaining 26% is the away win chance.
• Scores with three or more goals add up to a 51% chance of over 2.5. Scores in which both teams find the net add up to a 53% chance of both teams scoring.

The Dixon-Coles correction

The basic Poisson model is slightly off when it comes to low scores. Real matches end 0–0 and 1–1 a little more often than it predicts, and 1–0 and 0–1 a little less often. In 1997, Mark Dixon and Stuart Coles addressed this with a small adjustment to those four scores and a time-weighting system that lets team ratings respond to changes in form. Their model remains a standard starting point, and it is the model Kuponcu uses.

Where models go wrong

A model based on past goals cannot account for things such as:

• A new manager, or a major signing or departure.
• Promoted teams with little or no history in the top division.
• Injuries, suspensions or squad rotation ahead of a cup match.
• End-of-season motivation: a team may have nothing left to play for, or everything to play for.
• The weather, pitch conditions and a congested fixture schedule.

Why Kuponcu combines it with the market

The betting market reflects all of these factors, so it is more accurate on average than a model based on goals alone. In our tests, the sharp price outperformed our model in every league. That is why Kuponcu takes its fair price from the market and uses the goal model as a second opinion: to rank selections, highlight disagreements and give the AI reviewers another data-based perspective.