An expected wins approach using Fisher’s Exact Test to identify the bogey effect in sports: An application to tennis

In sports, so-called "bogey" players or teams tend to beat a particular opposition with regularity despite being of similar ability.Although the existence of bogey players is widely discussed and debated among sports fans and the media, methods that could be used to identify the bogey effect have received little attention in the literature.This study proposes a statistical procedure to identify bogey players using a publicly available men's Association of Tennis Professionals (ATP) and Women's Tennis Association (WTA) dataset, which is also split into Grand Slam and non-Grand Slam matches.The proposed method iterates over all unique player pairs and applies Fisher's Exact Test to a contingency table containing expected wins and actual win distributions for historical matches between the players in the player pair.To compute expected wins, betting odds-or Elo ratings-implied probabilities for each player are aggregated over all matches between the player pair for each player.If the Fisher's Exact Test result is statistically significant (that is, actual wins and expected wins do not follow the same distribution), and the expected wins and actual win counts are contradictory, we suggest that the bogey effect exists between the two players.The obtained results suggest that the bogey player effect exists in professional tennis but is rare (and even rarer in Grand Slams), and expected wins obtained using betting odds-implied win probabilities more closely matched actual wins than Elo ratings, which resulted in fewer bogey player pairs being identified with betting odds.The number of bogey player pairs identified is intuitively found to be inversely related to the predictability of matches.