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Poisson goal model

column: Poisson, PoissonScore, PoissonO25 votes in H:D:A

The classic goals model. Each side is given an expected number of goals from how well they attack and defend relative to the rest of the league, and the probability of every scoreline follows from the Poisson distribution. Unlike the form methods it has an opinion from the first game of a season.

How it works
  1. Work out league averages: goals per game scored by home sides (μH, usually about 1.4) and by away sides (μA, about 1.1). The gap between them is home advantage.
  2. For each team, four rates from this season's games: goals scored at home, conceded at home, scored away, conceded away. Divide by the league average to get a strength: 1.2 means 20% better than average.
  3. Early in a season those rates are shrunk towards last season's rates for the same club - six games of evidence count as much as the prior. Clubs that changed division start from the league average, so they look ordinary until results say otherwise.
  4. Expected goals: λhome = μH × home attack × away defence and λaway = μA × away attack × home defence.
  5. The chance of each exact score is P(i goals) × P(j goals) under a Poisson distribution with those means, for every score up to 8-8. Add up the cells above the diagonal for a home win, on it for a draw, below for an away win; cells with three or more goals give the over-2.5 chance; the biggest single cell is the most likely score.
Worked example
LeagueμH 1.45, μA 1.10
Home sidescores 1.8 at home (attack 1.24), concedes 0.9 at home (defence 0.82)
Away sidescores 1.0 away (attack 0.91), concedes 1.6 away (defence 1.10)
Expected goalsλhome = 1.45 × 1.24 × 1.10 = 1.98, λaway = 1.10 × 0.91 × 0.82 = 0.82
Outcomehome 63%, draw 21%, away 16%; most likely score 2-0; over 2.5 goals 56%
How BetChair calls it

The largest of the three percentages is the vote. PoissonScore is the single most likely score (which, being one cell of the grid, is rarely more than 12-15% likely on its own) and PoissonO25 the chance of three or more goals. The Poisson vote is one of the eight in the H:D:A column.

Where it shines
  • Works from matchday one thanks to the last-season prior, so it is the natural early-season signal.
  • Home advantage and opposition quality are built in, not bolted on.
  • Produces real probabilities, so it can be compared with the market.
Where it falls down
  • Promoted and relegated clubs are treated as league-average for their first few games - the "Value" flag on those games is unreliable.
  • Assumes goals are independent; real football has slightly more 0-0s and 1-1s than Poisson predicts (a known bias the Dixon-Coles correction fixes; not applied here).
  • Injuries, suspensions and line-ups do not exist to it - the line-ups data is the obvious next input.

See it on the fixtures table (tick the column under Columns → Predictions) and on every tips slip. Related: Market & Value, Score Prediction.