Never liked Poisson for score prediction, but the Dixon-Coles model is supposed to be an improvement
Dixon-Coles still uses Poisson
Leodis, just with a correction - the problem with a "pure" Poisson distribution is that it under/overestimates the most common low scoring matches of the under 2.5 goals distribution by assuming that both home and away goals are
always "independent" ...hence that their related probabilities are then multiplicative, which does not reflect the reality of how some football matches really play out.
Dixon-Coles keep the straight Poisson distribution but add a minor correction denoted by the function of "Tau" or τ. The only differences then are with the scorelines of 0-0, 1-0, 0-1 & 1-1 with all of the other possible scorelines untouched so still "pure" Poisson estimates. The Tau function is controlled by the parameter of "Rho" which was negative in the original DC paper. In a simulated 50/50 game where both teams are modeled as the same ability by way of "xG" the deltas of the correction amounts to around 1.6% on the 0-0 and 1-1 and -1.6% on the 1-0 and 0-1 when compared to straight Poisson.
All the correction does is relocate some of the probability mass to these low scoring matches.
Stuart Coles and Mark Dixon also used a separate exponential weighting added to a "team-strength" parameter which decays results by recency.
The original paper is here among a few others that use Poisson or one of it's variants
VariousFB-Aca019
Matthew Benham (Brentford/Smartodds etc) was impressed enough with DC's research that he eventually hired Stuart Coles
The opening post in this thread suggesting that "quality of opposition" should be considered is very true but at a base level the mean of a teams Poisson Distribution directly represents an expected goal scoring intensity or "rate" and serves as a fundamental building block for measuring "competitive strength". However those "raw" averages need to be decomposed to extract a team's true competitive signal. Recency weighting of those decomposed values improves things even further.
Would venture to say though that even today with the state of art being mostly Bayesian state space ensembles (SSMs) with a whole host of features engineered from data that is not in the public domain, most modelers still would agree that the old Poisson Distribution still has some utility and relevance.
What's that variation of that old quote from George Box in 1976 ?? ......"All models are wrong....but some are useful"
Often expanded with "some models are more wrong than others whilst some can be extremely harmful"
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