Validation of and improvement to cyclic designs

Abstract

In sports, a wide variety of match systems have been adopted to rank the participants. Well-known systems include the tournament system and the league match system. In order to overcome faults in these systems, a system known as cyclic design has been proposed.
A cyclic design is able to rank all of the participants and requires only one more game than those required by a tournament. We let the size of the block be 2, and we use an experimental design that compares v treatments. By calculating the observational equations that are derived from the design of the experiments, estimators (for example, estimations of an individual's strength) can be obtained.
In this paper, we validated a cyclic design with an actual dataset. We analyzed all combinations of the actual data, and we showed that there were discrepancies between the estimated ranks and the real ranks. In a cyclic design, the accuracy of the estimated rankings (AER) depends on the initial design, and so it was necessary to improve this.
We conducted a Monte Carlo simulation to compare the AER of a cyclic design to those of two common competitors: a tournament and a league match. In addition, we proposed a cyclic design combined with the Swiss system to compare the AER to other competitors. We found that the estimated ranking produced by the proposed cyclic design is more accurate than that produced by a tournament. Furthermore, we conducted a Monte Carlo simulation in which we used the similar model by adding interaction effects. We found that the AER of all methods were reduced compared to the previous results. In particular, interaction effects have a strong influence on the results of the cyclic designs. To improve performance, we proposed a further extended cyclic design that is robust to the interaction effects. We performed a Monte Carlo simulation that confirmed that the extended cyclic design is superior to the original cyclic design.