Evaluation of the Credibility of Ranking

—— An Analysis of the 2002 FIFA World Cup Data ——

Abstract

Various types of ranking are in evidence throughout the real world. In this paper, we consider in particular, the field of sports, where ranking is most common. The 2002 FIFA World Cup Korea/Japan, which took place in June 2002, and the winner was Brazil. Since Brazil's FIFA world ranking was 2 just before the tournament, this result seemed quite plausible. On the other hand, however, France (ranking 1), Argentine (ranking 2) and Portugal (ranking 5) were not able to go to Stage 2 (best 16). These facts raise a question as to whether the FIFA ranking is credible in predicting the winners.
In order to assess the credibility of such ranking, we introduce a simple model in this paper. Our model, which is an extension of the so-called Bradley-Terry model, contains an unknown parameter which indicates the credibility of the ranking. For the 2002 FIFA World Cup data, we estimated the credibility parameter and concluded that the FIFA world ranking for the 2002 tournament data was more credible in Stage 2 than in Stage 1.