Percy, D. & Scarf, P. J Oper Res Soc (2008) 59: 1406. doi:10.1057/palgrave.jors.2602487
Some competitions involve teams comprising different numbers of players. For informal games, such as the popular ‘pub quiz’, we argue that teams with fewer players are at a disadvantage. This paper investigates the properties of these games and develops several methods for allocating handicaps within such competitions, so that the competitions may be considered fair, based on a simple Bernoulli model for correctly answering questions and assuming exchangeability of participants. We recommend a natural conjugate prior subjective handicapping rule; with this rule handicaps may be set beforehand given the judgement of the quiz setter regarding the difficulty of the questions. We also describe a posterior rule that provides improved accuracy but is calculated after the quiz is complete. Finally, the paper considers modifications of the proposed rules to cope with multiple-choice questions and progressive quizzes.