Poisson Distribution Goals in English Premier Football League
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 l=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 = l/n Take limit of Binomial Distribution as n with p = l/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: Road Team, 1 st Half: Home Team, 2 nd Half: Road Team, 2 nd Half: Mean=0. 68 Variance=0. 73 Mean=0. 44 Variance=0. 39 Mean=0. 77 Variance=0. 75 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
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