calculations.matches_13_prob_goal_diff

Skellam-distribution probabilities for the goal difference home − away (μ₁ = stats_goals_expected_home, μ₂ = stats_goals_expected_away). Evaluated for k ∈ -7…7; tails are bucketed.

P(X = k) = e^(-(μ₁+μ₂)) · (μ₁/μ₂)^(k/2) · I_|k|(2·sqrt(μ₁·μ₂))

Lineage

flowchart LR
m9[/matches_9_expected_goals/] --> me[/calculations.matches_13_prob_goal_diff/]
me --> mart[/mart.matches/]
click m9 "/calculations/matches_9_expected_goals/" "Open"
click mart "/mart/matches/" "Open"

Columns

Column	Description	Formula
event_id	Bet365 event identifier.	passthrough
event_date	Event date.	passthrough
event_partition_key	ClickHouse partition key.	passthrough
score_total	Actual total goals (carried).	passthrough
score_difference	Actual goal difference (carried).	passthrough
stats_goals_expected_home	Expected home goals.	passthrough
stats_goals_expected_away	Expected away goals.	passthrough
stats_goals_expected_total	Expected total goals.	passthrough
prob_goal_diff_neg3_minus	Probability of Δ < −3.	round(sum(if(goal_diff < -3, probability, 0)), 4)
prob_goal_diff_neg3	Probability of Δ = −3.	round(max(if(goal_diff = -3, probability, 0)), 4)
prob_goal_diff_neg2	Probability of Δ = −2.	round(max(if(goal_diff = -2, probability, 0)), 4)
prob_goal_diff_neg1	Probability of Δ = −1.	round(max(if(goal_diff = -1, probability, 0)), 4)
prob_goal_diff_0	Probability of a draw.	round(max(if(goal_diff = 0, probability, 0)), 4)
prob_goal_diff_1	Probability of Δ = 1.	round(max(if(goal_diff = 1, probability, 0)), 4)
prob_goal_diff_2	Probability of Δ = 2.	round(max(if(goal_diff = 2, probability, 0)), 4)
prob_goal_diff_3	Probability of Δ = 3.	round(max(if(goal_diff = 3, probability, 0)), 4)
prob_goal_diff_3_plus	Probability of Δ > 3.	round(sum(if(goal_diff > 3, probability, 0)), 4)
prob_goal_diff_sum	Sanity check — should be ≈ 1 within [-7, 7].	round(sum(probability), 4)

probability = round(skellam_pmf(stats_goals_expected_home, stats_goals_expected_away, goal_diff), 4) from macros/skellam_pmf.sql.