# Machine Learning in Football Betting: Prediction of Match Results Based on Player Characteristics
## 4 Results  
### Statistical Analysis  
We provide an overview of some basic statistics of the simulation study in Table 3. The columns summarize the different betting strategies and/or methods described in the previous section--row-wise we list the measures of performance. Comparing each of the Machine Learning (ML) models individually, Random forest (RAF) achieves the best results, i.e., the highest accuracy of 81.26%, the minimal root mean squared error (RMSE) as well as the lowest mean absolute deviation (MAD) (Note that we are using regression-type ML approaches. Comparing numeric predictions with an integer truth induces an error by default. Therefore, we cannot assume the value 0 to be the minimum value of the RMSE.). RAF is followed by BOO, LIR and SVM--in this scenario, tree-based ML algorithms seem to capture the information in the data better than linear models. Finally, the unsophisticated approaches BET and HOM perform strictly worse than the machine learning strategies. Forseeably, the random strategy RAN is performing worst of all the strategies by all measures. The ensembling strategy ALL results in the highest accuracy of 81.77% in combination with a slightly higher RMSE and MAD as the best single ML strategy RAF. In general, accuracy seems to be correlated with a lower number of bets, which indicates that a conservative betting behavior is favorable in this context.  
Comparing the ML algorithms monetary success individually, we find that high accuracy of an approach is associated with a high resulting average payoff. ALL achieves the highest average payoff with a value of 1.0158. Note that with an average payoff that is greater than 1 one can beat the bookmaker over the long term as for each monetary unit spend, on average the return is strictly positive. As expected, the higher the complexity of a strategy, the higher the quality of our predictions which is reflected in higher average payoffs. Additionally, RAN is the only approach that does not favor the home team in contrast to each other more sophisticated strategies. Apart from RAN, all methods confirm the advantage of the home-team as pointed out in Section 3. Also, Table 3 highlights that an increasing number of bets is associated with a lower payoff on average. Summarizing these findings, we carefully conclude that the ML methods can capture signals from the data that identify those bets which have an outcome that is well predictable.  
As a sanity check it is worth mentioning that the predicted outcomes of each of the strategies seems to be within an appropriate range--we can report a predicted goal difference between 5.9 goals for the home and 4.5 goals difference for the away team.  
\begin{table}
\begin{tabular}{l r r r r r r r r} \hline \hline  & **RAF** & **BOO** & **SVM** & **LIR** & **ALL** & **BET** & **HOM** & **RAN** \\ \hline
**Prediction Quality** & & & & & & & & \\ Accuracy & 0.8126 & 0.7912 & 0.6971 & 0.7292 & 0.8177 & 0.4991 & 0.4544 & 0.3605 \\ RMSE & 1.8717 & 1.9606 & 2.0827 & 2.0210 & 1.9079 & 9.5602 & 9.7600 & 10.1493 \\ MAD & 1.4736 & 1.5417 & 1.6939 & 1.6346 & 1.4945 & 9.4253 & 9.6190 & 10.0065 \\ \hline
**Betting details** & & & & & & & & \\ Average Payoff & 1.0043 & 1.0072 & 0.9757 & 0.9932 & 1.0158 & 0.9547 & 0.9540 & 0.9183 \\ Placed bets & 555 & 613 & 1238 & 1156 & 598 & 41077 & 41681 & 41681 \\ Home team bet & 0.8595 & 0.8173 & 0.8102 & 0.8183 & 0.8428 & 0.7907 & 1.0000 & 0.4981 \\ Away team bet & 0.1405 & 0.1827 & 0.1898 & 0.1817 & 0.1572 & 0.2093 & 0.0000 & 0.5019 \\ \hline
**Predicted Values** & & & & & & & & \\ Maximum & 4.8715 & 5.1226 & 5.8372 & 5.9047 & 5.2657 & - & - & - \\ Minimum & \(-2.8546\) & \(-2.6029\) & \(-3.9798\) & \(-4.5213\) & \(-2.9441\) & - & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical performance indicators for the betting strategies for the football seasons 2006/2007 to 2017/2018.