Poisson Distribution Goals in English Premier Football League – 2006/2007 Regular Season

Poisson Distribution Distribution often used to model the number of incidences of some characteristic in time or space: –Arrivals of customers in a queue –Numbers of flaws in a roll of fabric –Number of typos per page of text. Distribution obtained as follows: –Break down the “area” into many small “pieces” (n pieces) –Each “piece” can have only 0 or 1 occurrences (p=P(1)) –Let =np ≡ Average number of occurrences over “area” –Y ≡ # occurrences in “area” is sum of 0 s & 1 s over “pieces” –Y ~ Bin(n,p) with p = /n –Take limit of Binomial Distribution as n  with p = /n

Poisson Distribution - Derivation

Poisson Distribution - Expectations

Example – English Premier League Total Goals Per Game (Both Teams) –Mean=2.47 Variance=2.49 Goals by Team by Half –Home Team, 1 st Half: Mean=0.68 Variance=0.73 –Road Team, 1 st Half: Mean=0.44 Variance=0.39 –Home Team, 2 nd Half: Mean=0.77 Variance=0.75 –Road Team, 2 nd Half: Mean=0.58 Variance=0.83* * Does not reject based on Goodness-of-Fit test

Goals by Team by Half Observed Counts Expected Counts Under Poisson Model

Goodness of Fit Tests (Lumping 3 and More Together for Team Halves)

Correlations Among Goals Scored