Mathematical Methodology

Order a club’s last 15 completed matches from newest to oldest and number them i = 0, 1, 2 … Match i gets weight 0.9ⁱ: the newest weighs 1, the next 0.9, and the oldest of the fifteen roughly 0.23. The attack and defence ratings are weighted averages over that window:

att = Σ w_i·f_i / Σ w_i · def = Σ w_i·a_i / Σ w_i · w_i = 0.9ⁱ

f and a stand for goals scored and conceded; we swap in xG for and against once xG data accounts for 60% or more of the window’s summed weight. Measuring coverage by weight rather than by match count matters: a gap in last week’s data counts for more than a gap from months ago.

Each rating is then shrunk toward μ, the competition’s average scoring rate over its two latest seasons as of this kick-off:

shrunk = (n·v + 5·μ) / (n + 5)

where n is the number of matches in the window. The 5 acts as prior strength: after fifteen matches a club keeps three quarters of its own value, after three matches just over a third. That is how a promoted club’s first couple of results are stopped from producing an extreme rating.

The shrunk ratings combine into a scoring rate for each team, scaled by the competition’s average home and away goals (m_h, m_a), with μ the midpoint of the two:

λ_home = m_h · (att_home / μ) · (def_away / μ)
λ_away = m_a · (att_away / μ) · (def_home / μ)

There is no separate home-advantage bonus: it is already contained in m_h and m_a, measured from each competition’s own results. When a league-specific fit is available, λ_home also carries a league-fitted home multiplier. Both rates are then clamped between 0.2 and 4.5 goals, so corrupted input data cannot produce an absurd forecast.

We model each side’s goals as a separate Poisson count and then correct the four scorelines with the fewest goals. Plain Poisson consistently misjudges the 0-0, 1-1 and single-goal wins, and correcting that is exactly what Dixon and Coles proposed. For scoreline i-j:

P(i, j) ∝ Pois(i; λ_home) · Pois(j; λ_away) · τ(i, j)

τ(0,0) = 1 − λ_homeλ_awayρ
τ(0,1) = 1 + λ_homeρ
τ(1,0) = 1 + λ_awayρ
τ(1,1) = 1 − ρ
τ(i,j) = 1 everywhere else

Goals run from 0 to 10 per team, giving 121 cells, normalised to sum to one. ρ is fitted per competition where a fit exists; without one, ρ defaults to −0.10 and the prediction carries the fallback model-version tag, so you can tell the two apart.

Because all markets are cut from one distribution, our goal line cannot clash with the exact-score grid, and double chance cannot clash with 1X2. Services that model each market independently cannot promise that. For each market and the fixtures behind it, see prediction types.

For home, draw and away we take one price each: the median across all bookmakers that quote the complete three-way market for the fixture. The implied probabilities of those three prices add up to more than one, and the surplus is the bookmaker margin. We remove it by normalising:

q_k = (1 / price_k) / Σ_j (1 / price_j)

The 1X2 probability we publish is a fixed-weight mix of that market figure and our model:

final = 0.25 · model + 0.75 · market

With no recorded price, final equals the model probability and the prediction is flagged as model-only. Only 1X2 is blended. Goal-line, BTTS and exact-score probabilities are saved with zero market weight — what you read is the grid’s raw output.

The edge we show is the difference between our published probability and the market’s: final − market, in percentage points, for the same outcome. With a 25/75 mix, the edge equals one quarter of the raw gap between model and market — a cautious reading by design. Beside the best available price we also show expected return per unit staked: published probability × price − 1. Each is a statement about the price, never a promise about the result. The largest gaps are collected on value bets.