The text below is taken from http://www.brighton-webs.co.uk/distributions/poisson_football.asp .

Poisson Distribution

The Poisson can be used to model soccer matches.  The graph below shows the the distribution of goals scored by a team playing at home over a season in a league competition.  Their average was 1.00 goals/match.

As can be seen, the Poisson model describes the team’s goal scoring achievements over the season.  However, this model should be treated with care as there are a number of caveats, including:

Competing teams should be of comparable ability

Statistics should be compiled from games where the opposing teams are of comparable ability, this may be reasonable for games played in a league competition, however, games played in knock-out competitions may give a distorted impression of the team’s ability.  A good example is the early rounds of the FA Cup where well funded  Premier League teams can be drawn against ones from lower leagues.  Scores of greater than 4 goals are unusual.

Home and away performance may different

Typically teams perform better on their home ground that at away fixtures, therefore care should be taken to separate the two.

Teams change over the season

For the model to have any validity, the composition of the team should be constant over the season with the same manager working with the same squad.  However, in reality this is seldom the case.  Players come and go because of loans and transfers.  Within the squad availability will be determined by injuries and suspensions.  It may be able to get a better model of a team’s performance by considering the player’s who are available for a given game rather than rely on historic performance.

Remove Penalties and Own Goals from the data

Whilst the ability of a team to capitalize on the opportunity created by a penalty is important, penalties arise from a weakness in the opposing team and should be treated as one of the chance elements the game.

Whilst statistics can be an attempt at informed speculation, don’t ignore the roll of chance otherwise football would not have its magic.