On the development of decision rules for bar quiz handicapping

Abstract

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.

Keywords:

• elicitation
• games
• probability
• quizzes
• subjective

Acknowledgements

The authors wish to thank the bar quiz organiser, Ed Rochead (DSTL), team-mates and opponents at OR48 for inspiring this research.