A new sports ratings system: The tiddlywinks world ratings

A system for calculating relative playing strengths of tiddlywinks players is described. The method can also be used for other sports. It is specifically designed to handle cases where the number of games played in a season varies greatly between players, and thus the confidence that one can have in an assigned rating also varies greatly between players. In addition, the method is designed to handle situations in which some games in the tournament are played as individuals ("singles'), while others are played with a partner ("pairs'). These factors make application of some statistical treatments, such as the Elo rating system used in chess, difficult to apply. The new method characterizes each player's ability by a numerical rating together with an associated uncertainty in that player's rating. After each tournament, a "tournament rating' is calculated for each player based on how many points the player achieved and the relative strength of partner(s) and opponent(s). Statistical analysis is then used to estimate the likely error in the calculated tournament rating. Both the tournament rating and its estimated error are used in the calculation of new ratings. The method has been applied to calculate tiddlywinks world ratings based on over 13 r 000 national tournament games in Britain and the USA going back to 1985.     

Monopoly Versioning of Information Goods When Consumers Have Group Tastes

Large sunk costs of development, negligible costs of reproduction, and distribution resulting in economies of scale distinguish information goods from physical goods. Versioning is a way firms may take advantage of these properties. However, in a baseline model where consumers differ in their tastes for quality, an information goods monopolist only offers one version, and this differs from what we observe in practice. We explore formulations that add features to the baseline model that result in a monopolist offering multiple versions. We examine versioning where consumers differ in individual tastes for quality, and groups of consumers that share the same group taste are delineated by segments of individual tastes. We find that if groups have mutually exclusive characteristics—a horizontal dimension—that they value relative to the shared characteristics, then versioning is optimal. Consequently, any horizontal differentiation in product line design favors versioning. In addition, when group tastes are hierarchical such that higher taste groups value characteristics that lower taste groups value but not vice versa—a vertical dimension—as long as the valuations of the higher and adjacent lower taste group are sufficiently close, then versioning is also optimal. Our conditions, which also help determine how many versions are optimal, are based on exogenously defined parameters so that it is feasible to check them in practice.