Expansion and Study of the Validity of the Cyclic Design  

Oleh:

Kaido, Yutaro ; Nagata, Yasushi

Jenis: Article from Proceeding
Dalam koleksi: 12th ANQ Congress in Singapore, 5-8 Agustus 2014, page 1-7.
Topik: Sports statistics; Balanced incomplete block design; Cyclic design
Fulltext: IC2-2.2-P0261.pdf (689.86KB)

Isi artikel

In sports games, a wide variety of the match game systems are adopted to determine winners. For example, a tournament system is usually used when there are many competitors like in tennis games. But we can’t evaluate the ranking of lower players in this system. A league match is also usually used in many sports like in baseball games. But if there are many players, the system takes much time. In order to improve faults of these systems, Taguchi introduced the cyclic design which is considered as one of balanced incomplete block designs. The cyclic design enables all participants to be ranked by conducting one more game than the tournament. Let the size of block be 2, and arrange the experimental design compared to treatment; T1,T2,…,Tv, in v-level. By calculating observational equations which are derived from design of experiments, estimators, such as individual strength, can be obtained. In this research, we begin with a validity of the cyclic design. We analyze all the combinations of the actual data of the professional baseball in Japan. It is shown that there are some discrepancies between the estimated ranks and the real ranks. In the cyclic design, accuracies of the estimated rankings depend on the initial design. Therefore, an improvement on the cyclic design is required. We conduct a Monte Carlo simulation to compare accuracies of the estimated rankings of the cyclic design to three common competitors: a tournament, the league match and improved cyclic design combined with Swiss method. As a result, it turns out that the estimated ranking using the cyclic design is more accurate than a tournament. And the accuracies of the estimated rankings by improved cyclic design are the second highest for almost all cases. Furthermore, we conduct a Monte Carlo simulation using the data including interaction effects. As a result, the accuracies of the estimated rankings of all method are getting smaller than the previous results. In particular, it turns out that the interaction effects have strong influence on the results of the cyclic designs

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