Paired comparison experiments are effective tools when the characteristics of the objects cannot be measured directly. In paired comparison experiments the characteristics of the objects are estimated from the result of the comparisons. The concept of paired comparison experiments was introduced by Thurstone (1927). The method by Scheffé (1952) is widely used for complete paired comparison experiments and the method by Bradley and Terry (1952) is popularly used in incomplete paired comparison experiments. In incomplete paired comparison experiments, the design of the experiment, that is, how to form the pairs to be compared, is crucial to successful analysis. Many methods including adaptive experimental designs are proposed. The tournament systems in sports and other competitions are typical examples of such designs, but their statistical properties are not fully investigated. In this paper, we discuss how tournament systems may be evaluated and propose a new criterion. We also give examples of evaluating tournaments based on the proposed criterion.