Probabilistic model based on the Skellam distribution: application in sports betting.

Probabilistic models are widely used in various areas of knowledge to estimate the chance of random events occurring. In Brazil, the sports market has adopted this tool to assist in decisions such as investing in certain specificities of the subject, evaluating accuracy of players and predicting actions of opponents. Furthermore, this market has grown with the emergence of several betting houses, specially due to dissemination in the open TV channels. This work focused on exploring Skellam’s probabilistic models, analyzing their principles and characteristics to model the men’s Brazilian soccer championship called Brasileirão. The database includes historical match results from 2012 to 2023 and estimates of the odds provided by the Bet365 bookmaker. Three probabilistic models were proposed to calculate the probabilities outcomes (win, loss or draw) and, consequently, the odds in each game; these results were compared with those of Bet365 and it showed efficiency. However, it is important to emphasize that the models have limitations due to external factors that have not been evaluated, such as weather conditions and game strategies.