Probabilistic assessment of the organization of tournaments and examinations using paired comparisons

Abstract

In this paper a criteria of comparison different tournament organization systems in sporting contests is offered, the criteria uses a probability of winning the fairly strongest player. Two probabilistic models have been analyzed. Calculating formulas for estimating of that probability and probability density of score points by one or another player were obtained. Gotten results also provide an order of objects presenting to experts in organization of examination by paired comparison. An analytical estimation of probability of tournament results (or pared comparison) was obtained, it allows in many cases to avoid of time-consuming procedure of sorting out of possible variants.