Modelling λ (xG → Poisson)
- Estimate expected goals for each side:
λ_home,λ_awayfrom xG/ratings/form/pace. - Total rate:
λ = λ_home + λ_away. - Approximate goals with Poisson(λ) to get P(Total=k) for k=0…
- Adjust λ for game state factors (tempo, weather, cards, schedule density).
Pricing Common Lines
- Over 2.5:
P(Total ≥ 3) = 1 − Σ P(k) for k≤2 - Under 2.5:
P(Total ≤ 2) = Σ P(k) for k≤2 - 2.0 / 2.25 / 2.75: treat as split lines (e.g., U2.25 = ½ U2.0 + ½ U2.5).
- Convert probability to Fair (decimal):
1 / p.
EV, Vig & CLV
- De-vig the book: convert odds to implied probabilities, normalise to 100%.
- EV+ only when
Book > Fairafter vig removal. - CLV: log entry vs. close. A consistent edge should beat close over time.
Worked Examples
Example — λ = 2.65, Over/Under 2.5
Compute P(0), P(1), P(2) via Poisson, then P(Over 2.5)=1−(P0+P1+P2). Compare fair vs de-vigged book price.
Responsible Play: Totals can swing hard on red cards and late game state. Keep stakes consistent, define stop rules, and follow local regulations.