Eastern-European Journal of Enterprise Technologies ISSN 1729-3774 2/4 ( 122 ) 2023 6 MATHEMATICS AND CYBERNETICS – APPLIED ASPECTS Copyright © 2023, Authors. This is an open access article under the Creative Commons CC BY license FRAMEWORK BASED ON CONFORMAL PREDICTORS AND POWER MARTINGALES FOR DETECTION OF FIXED FOOTBALL MATCHES Oleg Chertov Corresponding author Doctor of Technical Sciences, Professor* E-mail: chertov@i.ua Ivan Zhuk Postgraduate Student* *Applied Mathematics Department National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute» Peremohy ave., 37, Kyiv, Ukraine, 03056 One of the difficult problems that arises during football com- petitions is match-fixing. In terms of negative effect, such shame- ful 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 rele- vant to conduct research that does not require a large amount of non-publicly available data but, at the same time, makes it pos- sible to effectively identify potentially suspicious matches regard- ing 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-confor- mity 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 effective- ness of the developed method for detecting suspicious football mat- ches was carried out based on precision and recall of the clas- sification 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 Keywords: football match, fixed result, measure of nonconfor- mity, p-value for conformity, degree of difference UDC 004.852 DOI: 10.15587/1729-4061.2023.276977 How to Cite: Chertov, O., Zhuk, I. (2023). Framework based on conformal predictors and power martingales for detection of fixed football matches. Eastern-European Journal of Enterprise Technologies, 2 (4 (122)), 6–15. doi: https://doi.org/ 10.15587/1729-4061.2023.276977 Received date 12.01.2023 Accepted date 23.03.2023 Published date 28.04.2023 1. Introduction Matches with a fixed result (match-fixing), as well as doping, are called cancer of sports [1]. To combat doping, high-tech tests are used, and in 1999 a specialized interna- tional organization WADA (the World Anti-Doping Agen- cy) was founded. These tests make it possible to detect with almost absolute accuracy the presence of prohibited drugs in the athlete’s body. Unlike the doping situation, the successes in the fight against match-fixing are much more modest. Although matches with a fixed result, perhaps, exist as much as the sports themselves. At least, we have historical information that such shameful acts took place at the ancient Olympic Games in Greece [2]. Suppose that an agreement on a specific final outcome of a match or certain characteristics of it (number of goals scored, goal difference, etc.) is the purpose of obtaining an illegal be- nefit on bets in betting companies. In this case, it is potentially possible to track through financial transactions or the unna- tural distribution of betting volumes on the corresponding match results [3, 4]. The main disadvantage of this approach is that the data on the number, size, and time of the correspond- ing rates are non-public information, and the known methods of privacy-preserving data mining [5] are of little use here. Nevertheless, even the availability of data from betting companies will not help in certain situations. This is possible if there is a behind-the-scenes agreement to lose one team to another with some financial or other compensation through in- dependent channels [2]. It is also possible when there is material stimulation by a third party of one team against another. It is almost impossible to establish such facts, at least without con- ducting a special police investigation. The fact is that the very nature of sports competitions ensures that a stronger team does not always win, and many relevant examples can be given in any sport. Therefore, the related literature [2–4] only states that the outcome of certain matches is suspicious, atypical, illogical, abnormal, etc. But such information is also useful and important since it acts as an additional indicator that a certain team may be related to the violation of the sports principles of fair play. Currently, almost all known [3, 4] cases of detection of match-fixing are associated with the use of data from book- makers. However, bets are not accepted for all matches in sports tournaments, and if they are accepted, information about them is a trade secret, or bets can generally be accepted on illegal sports betting platforms. Therefore, studies aimed at finding potentially suspicious results of sports matches based on the processing of exclusively publicly available data should be considered relevant.