Accumulator Bet Selection Through Stochastic Diffusion Search

The global sports betting market is worth an estimated $700 billion annually Flepp et al. (2017), and association football (also known as soccer or simply football), being the world's most popular spectator sport, constitutes around 70% of this ever-growing market Constantinou et al. (2012). The last decade has thus seen the emergence of numerous online and offline bookmakers, offering bettors the possibility to place wagers on the results of football matches in more than a hundred different leagues, worldwide. The sports betting industry offers a unique and very popular betting product known as an accumulator bet. In contrast with a single bet, which consists in betting on a single event for a payout equal to the stake (i.e. the sum wagered) multiplied by the odds set by the bookmaker for that event, an accumulator bet combines more than one (and generally less than seven) events into a single wager that pays out only when all individual events are correctly predicted. The payout for a correct accumulator bet is the stake multiplied by the product of the odds of all its constituting wagers. However, if one of these wagers is incorrect, the entire accumulator bet would lose. Thus, this product offers both significantly higher potential payouts and higher risks than single bets, and the large pool of online bookmakers, leagues and, matches that bettors can access nowadays has increased both the complexity of selecting a set of matches to place an accumulator bet on, and the number of opportunities to identify winning combinations. With the rise of sports analytics, a wide variety of statistical models for predicting the outcomes of football matches have been proposed, a good review of which can be found in Langseth (2013).