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

2. 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 l=np ≡ Average number of occurrences over “area”
Y ≡ # occurrences in “area” is sum of 0s & 1s over “pieces”
Y ~ Bin(n,p) with p = l/n
Take limit of Binomial Distribution as n  with p = l/n

3. Poisson Distribution - Derivation

4. Poisson Distribution - Expectations

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

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

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

8. Correlations Among Goals Scored