← Back to Premium

Negative Binomial Match Predictor

Model match outcomes with overdispersed scoring — better for blowout-prone matchups in baseball, hockey, and soccer

Read the guide →
Match Setup
Average runs per match
Average runs per match
Big innings add variance; r=3-6 typical
Match Probabilities
Home Win
52.7%
-112
Away Win
46.8%
+114
Scoreline Probabilities
H\A
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0
0.3
0.6
0.7
0.7
0.7
0.5
0.4
0.3
0.2
0.1
0.1
0.1
0.0
0.0
0.0
0.0
0.0
1
0.6
1.2
1.5
1.6
1.4
1.2
0.9
0.7
0.5
0.3
0.2
0.1
0.1
0.1
0.0
0.0
0.0
2
0.8
1.6
2.0
2.1
1.9
1.5
1.2
0.9
0.6
0.4
0.3
0.2
0.1
0.1
0.0
0.0
0.0
3
0.8
1.7
2.2
2.2
2.0
1.6
1.2
0.9
0.6
0.4
0.3
0.2
0.1
0.1
0.0
0.0
0.0
4
0.8
1.6
2.0
2.1
1.8
1.5
1.2
0.8
0.6
0.4
0.3
0.2
0.1
0.1
0.0
0.0
0.0
5
0.6
1.3
1.7
1.7
1.6
1.3
1.0
0.7
0.5
0.3
0.2
0.1
0.1
0.1
0.0
0.0
0.0
6
0.5
1.1
1.3
1.4
1.2
1.0
0.8
0.6
0.4
0.3
0.2
0.1
0.1
0.0
0.0
0.0
0.0
7
0.4
0.8
1.0
1.0
0.9
0.8
0.6
0.4
0.3
0.2
0.1
0.1
0.1
0.0
0.0
0.0
0.0
8
0.3
0.6
0.7
0.8
0.7
0.6
0.4
0.3
0.2
0.2
0.1
0.1
0.0
0.0
0.0
0.0
0.0
9
0.2
0.4
0.5
0.5
0.5
0.4
0.3
0.2
0.2
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.0
10
0.1
0.3
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
11
0.1
0.2
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
12
0.1
0.1
0.2
0.2
0.1
0.1
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
13
0.0
0.1
0.1
0.1
0.1
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
14
0.0
0.1
0.1
0.1
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
15
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
16
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Totals
LineOver %Over OddsUnder %Under Odds
6.566.0%-19433.5%+198
7.556.1%-12843.4%+130
8.546.4%+11653.1%-113
9.537.4%+16762.1%-164
10.529.5%+23970.0%-234
11.522.7%+34076.8%-331
Spreads
SpreadHome CoversHome OddsAway CoversAway Odds
-0.557.6%-13641.9%+139
-1.567.5%-20732.1%+212
-2.576.0%-31623.6%+324
+0.547.2%+11252.4%-110
+1.537.0%+17062.5%-167
+2.528.0%+25871.6%-252
Most Likely Scorelines
332.2%
322.2%
232.1%
432.1%
222.0%
422.0%
342.0%
241.9%
441.8%
531.7%
About the Negative Binomial Model

The Negative Binomial distribution extends the Poisson model by adding a dispersion parameter (r) that controls scoring variance. While Poisson assumes variance equals the mean, real sports often have higher variance due to blowouts, rally innings, and power plays.

The r parameter: Lower r means more variance (more blowout potential). As r increases, the model converges toward Poisson. Baseball (big innings, bullpen collapses) typically has lower r than soccer.

When to use NB over Poisson: If you believe a matchup has unusual variance — e.g., a volatile bullpen in baseball, an aggressive team in hockey, or any game where blowout risk is elevated — the Negative Binomial model will produce wider scoreline distributions and different market probabilities than Poisson.

Limitations: Like Poisson, this model assumes independence between the two teams' scoring. It also uses the same dispersion for both teams — in practice you could set different r values per team, but this simplified version uses a shared r for clarity.