GHSA Boys Soccer

Rating Model: Dixon-Coles Bivariate Poisson

Each team is assigned an attack rate α and defense rate β. For a matchup home team h vs. away team a:

λ = α_h · β_a · γ · (duration/80)  (expected home goals)

μ = α_a · β_h · (duration/80)  (expected away goals)

A low-score correction ρ adjusts the probability of 0–0, 0–1, 1–0, and 1–1 scorelines to account for the negative correlation between goals. Scores are drawn from a joint Poisson distribution with this correction.

Margin-of-Victory Transform

The Massey warm-start uses f(d) = sign(d) · log(1 + |d|) (FiveThirtyEight convention). This preserves ordering over all margins while compressing extreme blowouts — consistent with GHSA's own 3-goal cap in region seeding tiebreakers.

Variable Game Duration

GHSA adopts the NFHS mercy rule: a 7+ goal halftime deficit shortens the second half to 20 minutes; a 10+ goal halftime deficit terminates the game. Goal rates λ and μ are per-80-minute rates; each game scales them by duration_used / 80. Duration is observed from MaxPreps halftime scores when available; otherwise imputed from final margin via a lookup table (design §7.4).

PK-Score Contamination Recovery

GHSA rules require adding a phantom goal to the PK winner's final score. MaxPreps reports the true pre-shootout regulation score. The model likelihood uses regulation scores only, removing phantom-goal contamination. When MaxPreps is unavailable, the GHSA reported score is used as fallback.

Time Decay

Games are weighted w = exp(−ξ · Δt) with ξ = 0.015/day (half-life ≈ 46 days). Earlier games count less than recent form.

Bracket Simulation

200,000 Monte Carlo simulations per bracket. Each simulated game samples a score from the joint Dixon-Coles distribution. Ties go to overtime (20-min scaled rates), then to a PK coin flip weighted by attack ratings. Higher seeds host through the semifinals; the championship is neutral-site.

Enrichment Coverage

See the GHSA Soccer Handbook and Dixon & Coles (1997) for references.