# Predicting Football Match Results Using a Poisson Regression Model
## 5 Conclusions and Future Work  
In this paper, we investigated whether it is possible to estimate the number of goals scored by a team in a football match based on a team's past performance. The methodology used assumed that goals scored by a team follow a Poisson distribution, and as a result, the goals scored in a football match follow a double Poisson model--one Poisson distribution for each team. A Poisson regression model was used in order to calculate the expected number of goals for each team using a number of predictors, such as the attacking/defensive quality of the teams and the home team advantage.  
Even though the proposed methodology was not complicated and followed a more simplistic form for the score estimation--for example, not accounting for differences in teams from match to match due to injuries, suspensions, and the fact that some teams tend to score more goals against weak opponents and, as such, a model based on goals scored overestimates those teams--the results are rather satisfactory.  
More specifically, the model was able to estimate goals scored for each team with good accuracy. The vast majority of differences between the observed number of goals and those estimated by the model are in the range of one goal, and higher deviations occur in results that are considered'surprises', where a strong favorite side was not able to score against a weaker team. On the other hand, a weakness of the model is the strong underestimation of scores that ended with no goals.  
As future work, the following could be examined:  
* Following the weakness of the model in estimating 0-0 results, an adjustment could be calculated and applied in order to augment the probability of those results estimated by the model, i.e., the use of a zero-inflated Poisson model by estimating a zero-inflation parameter in order to increase the number of zeroes estimated by the model.
* The most recent results of a team may be more representative of the estimation of the goals of that team in a future match than older ones, a fact that was not taken into account in the present study. As such, an adjustment could be performed in the model in order to reflect that fact (i.e., a weighting factor could be calculated in order for the recent games to be more impactful on the estimation results).
* Consider the fact that certain teams in the late fixtures and towards the end of the season have no interest, since they cannot achieve anything better in the remaining fixtures. For example, they are several points away from the fourth place, which leads to the UEFA Champions League, but those points cannot be obtained with the remaining matches. In those cases, the results are not completely representative of the team's performance. This fact can impact the performance of a team in both ways: either playing worse due to the lack of an incentive or playing well, since there is no pressure for the result. The latter is especially true for young players.
* Check the performance of the model in non-national leagues, where the number of historical matches is not as high as national leagues. An example of this could be to use information from the UEFA Champions League's results, where each team plays considerably lower matches compared to their national league.  
Conceptualization, K.L.; Software, K.L.; Formal analysis, D.K.; Investigation, K.L.; Writing--original draft, K.L.; Writing--review & editing, D.K., G.F. and V.S.V. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.