Framework based on conformal predictors and power martingales for detection of fixed football matches

Abstract

One of the difficult problems that arises during football competitions is match-fixing. In terms of negative effect, such shameful phenomena are commensurate with the problem of doping. This paper has analyzed known methods for the possible detection of match-fixing, including sociological analysis of participants in match-fixing, methods for predicting the outcome of the match, analysis of bets and performance of the player or team during the match. It is noted that the assessment of match-fixed results in the considered methods is carried out based on the analysis of a large amount of data. But such information is not always available. Given the insufficient formalization of the problem area, it is relevant to conduct research that does not require a large amount of non-publicly available data but, at the same time, makes it possible to effectively identify potentially suspicious matches regarding a fixed result. The description of the input data is formalized in the form of a data structure containing a chronological history of the results of football seasons, the ranking of teams and matches of the season depending on the overall result of the teams in the season. A method for detecting suspicious football matches with a fixed result has been built using conformal predictors and power martingales within which a new measure of non-conformity has been introduced to determine atypical football matches. To obtain a generalization of the statistics of atypical matches, a power submartingale was used. Evaluation of the effectiveness of the developed method for detecting suspicious football matches was carried out based on precision and recall of the classification metrics using data on the 2013–2014 season of the French II League. The quality of work of the developed method reaches 85 % in terms of precision metric, 96 % in terms of recall metric, and 0.853 in terms of metric F1.

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

“…The method for detecting MSFR proposed in [12] consists of four actions that must be performed for each new z k match:…”

“…Similar to [12], an offline algorithm is applied, that is, an algorithm in which the match result is calculated based on all matches in the class. However, the calculation of the degree of non-conformity (3) was carried out based on the degree of non-conformity of all matches in the class, and not only those matches that have already ended before the current one, that is:…”

“…Rank 1 is awarded to the best teams of the season, and rank K is awarded to a certain number of the last teams of the season, depending on the rules of the tournament. Examples of a grouping of tournament teams according to the final result are shown in works [9,12]. The grouping principle is as follows: the first cluster is formed from M+1 first teams of the season, and the last cluster is formed from L+1 last teams of the season.…”

“…In [12], it is proposed to use the apparatus of conformal predictors and power martingales to find MSFR of football tournaments. Since the precision metric of the martingale rule proposed in the study [12] for some classes of matches was less than 70 %, there is a need to improve the developed rule.…”

“…In [12], it is proposed to use the apparatus of conformal predictors and power martingales to find MSFR of football tournaments. Since the precision metric of the martingale rule proposed in the study [12] for some classes of matches was less than 70 %, there is a need to improve the developed rule. Therefore, it is expedient to conduct a study aimed at improving the precision of the detection of MSFR based on the theory of conformal predictors due to the use of the above-mentioned Stepanets indicator function.…”