# Predicting Football Match Results Using a Poisson Regression Model
## 4 Analysis of the Results
### Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & \multicolumn{10}{c}{**Manchester City Goals**} \\ \hline  & & **0** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9+** \\ \hline \multirow{10}{*}{
\begin{tabular}{c} **C  
Another examination of the accuracy of the model was conducted by simulating the entire league's season matches--38 in total, 19 home and 19 away--for a number of teams. The teams selected were Manchester City, Fulham, and Southampton. The rationale behind the selection of those teams was to include teams with different qualities in the league for a more complete view. As such, Manchester City was selected as the champion, which ended the league in the number 1 spot, Fulham with a mid-table finish in league spot number 10, and finally, Southampton, which finished the league at the bottom of the table. For each of those three teams, the estimated goals for the total of 38 matches were calculated, and the aggregated results are available in Table 10. As before, the model results have been rounded to the nearest integer. Following the fact that the above tests were conducted using all the available matches of the season for the calculation of the model parameters, another test was performed in order to have model results on an independent sample, i.e., data that were not used in the model parameters' estimation. In that regard, in this test, the parameters of the model (\(\mu\), home advantage, att and def parameters for each team) were re-calculated based only on the first round of the league, i.e., the first 19 fixtures, and the matches of the next 5 fixtures were used for prediction accuracy, fixtures 20 to 24, resulting in a total of 50 matches (10 matches per fixture). The decision on selecting only the next five fixtures was reached: \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Team**} & \multicolumn{2}{c}{**Home Goals**} & \multicolumn{2}{c}{**Away Goals**} & \multicolumn{2}{c}{**Total Goals**} \\ \cline{2-7}  & **Observed** & **Model** & **Observed** & **Model** & **Observed** & **Model** \\ \hline Manchester City & 60 & 75 & 34 & 47 & 94 & 122 \\ \hline Fulham & 31 & 42 & 24 & 33 & 55 & 75 \\ \hline Southampton & 19 & 28 & 17 & 21 & 36 & 49 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Entire league estimated goals simulations. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Home Goals’ Difference**} & **Frequency** & **Percentage** \\ \hline \(-2\) & 3 & 3.9\% \\ \hline \(-1\) & 10 & 13.2\% \\ \hline
0 & 21 & 27.6\% \\ \hline
1 & 26 & 34.2\% \\ \hline
2 & 14 & 18.4\% \\ \hline
3 & 2 & 2.6\% \\ \hline Total & 76 & 100.0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Home team goals: model vs. observed. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Away Goals’ Difference**} & **Frequency** & **Percentage** \\ \hline \(-3\) & 2 & 2.6\% \\ \hline \(-2\) & 2 & 2.6\% \\ \hline \(-1\) & 12 & 15.8\% \\ \hline
0 & 31 & 40.8\% \\ \hline
1 & 26 & 34.2\% \\ \hline
2 & 3 & 3.9\% \\ \hline Total & 76 & 100.0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Away team goals: model vs. observed. * In order for the calculated parameters to be as relevant as possible, since, as the league progresses, the parameters need updating over time as new results are available, to reflect the overall performance of each team for added precision. * In order to avoid late fixtures of the league, where many teams have no incentive and many surprise results are present, such as the 0-3 loss of Arsenal at home to Brighton at fixture 36, the loss of Manchester City to Brentford in the late fixtures, or the 4-4 match between Southampton and Liverpool at the last fixture of the league (fixture 38), to name a few. Regarding the first point above, as hinted, a more optimal methodology would be to re-calculate the parameters in each fixture after each match as the league progresses and try to predict the matches of the next one for maximum precision.