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

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Presentation transcript:

Goals in English Premier Football League – 2006/2007 Regular Season 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 0s & 1s 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, 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

Expected Counts Under Poisson Model 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