# Machine Learning in Football Betting: Prediction of Match Results Based on Player Characteristics
## 3 Simulation Study
### Simulation Design
#### 3.2.2 Trading Period  
After the formation period, the models have been applied consecutively to each match day, beginning with match day 6. This results in the predictions which we denote as \(\hat{y}_{tra}\). We received the dependent variable by applying the learned models (RAF, BOO, SVM, LIR) as well as the player features \(x_{tra}\). The trading period contains data from the sixth match day until the final match day of each season. This simulation study assumed that players characteristics include important knowledge influencing future football matches. If our assumptions holds, the trading algorithm would be able to find market anomalies and to generate positive profits. We define the following trading signals:  
* If \(\hat{y}_{tra}>2\), we forecast that the home team wins. In consequence, we invest 1 monetary unit (\(b=1\)) on the bet \"home team wins\".
* If \(\hat{y}_{tra}<-2\), we forecast that the away team wins. In consequence, we invest 1 monetary unit (\(b=1\)) on the bet \"away team wins\".
* If \(-2\leq\hat{y}_{tra}\leq 2\), we forecast no clear victory of home team or away team. In consequence, no trading is conducted.  
We calculate the profits of each bet based on the available odds. If we bet on the home team (away team) and actually observe a win of the home team (away team), then the payout of the bet equals the corresponding betting odd. In another case, the payout is 0, i.e., we lose our monetary unit. We use the difference in goals as a kind of confidence measure. We argue that predicting a draw is way harder due to incorrect decisions and penalties than a clean win. Following the large-scale research studies of [40; 41], the trading thresholds of \(\pm 2\) are implemented. Following [42; 43], our trading strategy is based on the finding that trading strategies with the use of machine learning can significantly improve the overall performance.  
In the spirit of [44], we benchmark the strategies based on one single machine learning algorithm each against four strategies. The strategy ALL trades, if the average of the predicted goal differences yields less than \(-2\) or more than \(+2\). Having an average this extreme can result from two scenarios: either many of the algorithms come to similar, extreme predictions or one algorithm is extremely confident. In both cases, we have strong indication to place a bet on the predicted outcome. If the four machine learning predictions are quite different to each other, their average would be close to zero. In a way, the uncertainty from distinct predictions makes the ALL strategy not place a bet (conservative strategy).  
Furthermore, three baseline strategies served as a benchmark, one of which is derived directly from the betting odds: (1) Strategy BET bets on the event with the lowest odd (most probable outcome). As explained in the previous section, the lowest betting odd is always achieved by \"home team wins\" or \"away team wins\". (2) Strategy HOM bets 1 monetary unit on \"home team wins\" which reflects the well-known advantage of a team playing in their home stadium, see e.g., Table 2. Other information are not considered. (3) Strategy RAN randomly bets on the event \"home team wins\" or \"away team wins\".