The bias of schedules and playoff systems in professional sports

Article Abstract:

The methods used for seeding teams in professional playoff situations, following the end of the regular season, are studied. The research focuses on which teams are in the playoffs and which of these teams get either the home field advantage or an initial round bye. The study indicates that the schedule in the regular season is biased against good teams because of the separation of teams into divisions, and that the playoff systems add more bias against the good teams because division winners are usually ranked higher than non-division winners. This is in addition to the inherent biases of current schedules. Conditions required to make the schedule completely unbiased are described, with schedules developed that maximize intra-division rivalries.

Competitions, Professional sports, Tournaments, Sports tournaments

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A single product cycling problem under Brownian motion demand

Article Abstract:

A mathematical procedure which uses control theory is given for developing a two-number control policy for minimizing the average cost in a single-product stochastic cyclic problem and for finding optimal policy parameters. The method switches production on and off, depending on inventory critical levels. The results are compared to those given by Graves and Keilson.

Methods, Management, Inventory control, Production control, Brownian motion, Random variables

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An improved conditional Monte Carlo technique for the stochastic shortest path problem

Article Abstract:

An improved simulation method is described for determining the distribution function of the shortest path length in a stochastic network with random arc lengths. The method causes a greater reduction in the sampling dimension by using the intrinsic properties of unique arcs and uniformly directed cutsets in the network.

Stochastic analysis, Economic research, Resource allocation, Monte Carlo method, Monte Carlo methods

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