# Machine Learning in Football Betting: Prediction of Match Results Based on Player Characteristics
## 4 Results
### Financial Analysis  
We want to leverage our good prediction results by betting against the implicitly anticipated probabilities given by the odds of the bookmaker. Each bet (if taken) generates a win or a loss, which results in a sequence of returns over time. In this section, we do a financial analysis on these time series per strategy. Table 4 summarizes classical risk-return statistics per bet for the eight strategies considered. All key results from our statistical analyses of the previous Section 4.1 hold when switching the context to a financial one. Strategies which performed best in terms of prediction quality also lead to significant profits, while the opposite is true for the simpler strategies RAN, HOM and BET. The tree based ML approaches RAF and BOO provide returns of 0.43% resp. 0.72% per bet. Linear models (LIR and SVM) cannot systematically achieve positive returns and provide \(-\)2.43% resp. \(-\)0.24% per placed bet. The ensemble approach ALL outperforms the individual models by far: a positive average return of 1.58% per match implicates that complexity pays off. The simple benchmark strategies BET and HOM cannot systematically beat the odds--they burn \(-\)4.53% (BET) resp. \(-\)4.60% (HOM) of every monetary unit spent within the strategies. Unsurprisingly, the strategy that does not use any of the information provided by the data (RAN) results in a loss of \(-\)8.17% per bet. Placing a bet using the ALL strategy results in statistically and economically significant returns per bet--the Null hypothesis of a non-parametric Wilcoxon-Test (WT) is clearly rejected (\(p\)-value below 0.0001). The minimum return of every strategies is \(-\)1--this is in line with our expectations as it reflects the fact that the predicted outcome of a match does not match reality more than once over all placed bets. More interesting is the comparison of the first quartile: the tree based ML approaches RAF, BOO and especially ALL generate a positive return in over 75% of all placed bets. Using the maximum of each strategies returns allows a segmentation into two subgroups: RAF, BOO, SVM, LIR, ALL, and BET form the first, HOM and RAN the second subgroup. Even the outcome with the largest odds (associated with the lowest anticipated probabilities of an outcome) will eventually be realized having the random experiment conducted over 40,000 times. As HOM and RAN do not consider any magnitude of the odds at all, the probability of winning a bet with a large odd is high and results in a huge payoff. Among all reported hit ratios (% of bets that result in a positive return), RAF and ALL stand out with 81.26% and 81.77% per bet. To conclude, strategies that rely on tree-based ML methods outperform strategies based on less sophisticated linear approaches (SVM, LIR) and strategies that hardly use any information at all (BET, HOM) which is clearly reflected in the vast majority of return/risk statistics--the latter is especially true for the strategy ALL. Following [45; 46; 47], we further analyze each strategies performance over time: the cumulative returns of RAF, BOO, SVM, LIR, and ALL are reported in the upper, the remaining three strategies BET, HOM, RAN in the lower graph of Figure 4 (football season 2006/2007 to 2017/2018). The time series are sorted top down in order of their cumulative return at the latest point in time series. The plateaus within the graphs relate to breaks between seasons and a different amount of executed