This study tries to construct an accurate ranking method for five team ball games at the Olympic Games. First, the study uses a statistical rating method for team ball games. A single parameter, called a rating, shows the strength and skill of each team. We assume that the difference between the rating values explains the scoring ratio in a match based on a logistic regression model. The rating values are estimated from the scores of major international competitions that are held before the Rio Olympic Games. The predictions at the Rio Olympic Games demonstrate that the proposed method can more accurately predict the match results than the official world rankings or world ranking points. The proposed method enabled 262 correct predictions out of 370 matches, whereas using the official world rankings resulted in only 238 correct predictions. This result shows a significant difference between the two criteria.