Detection of fixed football matches based on the theory of conformal predictors using the modified Stepanets indicator function

Abstract

An urgent issue of modern football competitions is the detection of fixed matches. Known methods for predicting the outcome of a match by analyzing bets on a match or analyzing the actions of football players on the field use a large amount of data that is not always available. To overcome this obstacle, there can be applied a method for detecting suspicious fixed match results based on conformal predictors and power martingales, which uses publicly available public data. But in practice, this method does not always detect such matches with high precision. An improved method for determining a suspicious match is proposed, based on the theory of conformal predictors using a modified Stepanets indicator function, which is compared with a threshold. The modified Stepanets indicator function is applied to the power martingale and shows the relative change in the martingale value of the current match compared to the previous match. The threshold value was determined experimentally according to the criterion of the maximum of the F1 metric. Data from the 2013–2014 season of the French II League were used as a training sample, and data from the 2014–2015 season of Serie B in Italy were used as a test sample. Team clustering was performed on all samples. For each of the formed classes of matches on both samples, the measure of non-conformity, the degree of non-conformity, the power martingale, and the modified Stepanets indicator function were calculated. The resulting indicators of precision metrics and F1 are higher (average values of metrics P=0.84, F1=0.87) than the same indicators of martingale and p-value rules (average values of metrics P=0.75, F1=0.78), applied to the same data. The proposed method reveals 4 out of 5 matches of the 2014–2015 Serie B season in Italy, which are considered fixed according to information from official Italian law enforcement sources