サッカーにおけるチーム別ホームアドバンテイジの統計学的定義－不釣り合い型一対比較データの線型モデルへの適用－

抄録

　Sports in which teams have the same number of home and away games provide balanced paired comparison data; thus, whether home-field offers an advantage can be determined by a usual statistical test comparing home and away games. However, an unequal number of home and away games results in unbalanced paired comparison data, and a simple analysis cannot be used because it does not account for the influence of team strength. This study statistically defined the home-field advantage of Japanese soccer leagues including J. league Division 1 (J1) and Division 2 (J2), and Japan Women’s Football League Division 1 (L1) and Division 2 (L2) with an unequal number of home and away games using two linear models of multiple regression analysis and logistic regression analysis with a design matrix containing 1, 0, and -1.
　Data are based on 306 games in the J1 league, 459 games in the J2 league, 84 games in L1 league and 168 games in L2 league. “Differences between winning and losing scores” and “wins and losses” were used as two dependent variables. Data are cited from the official web site of the J-league and Japan Women’s Football league. Model fitting was determined with a coefficient of determination and maximum likelihood ratio, overall home advantage was determined with analysis of variance and analysis of deviation , and individual home advantage was determined with multiple comparison methods. Results are as follows:
1) As all leagues had significant coefficients of determination and maximum likelihood ratios, applying a linear model to home advantage and team strength was considered to be valid from the standpoint of model fitting.
2) Partial regression coefficients in two linear models showing team strength had significant value and a significant ordinal correlation coefficient with final results in the league. This fact showed that partial regression coefficients were discernible and reflected team strength. In addition, partial regression coefficients on home-field advantage computed at the same time were also considered valid.
3) Results of analysis of variance and analysis of deviation and multiple comparison method showed that the two J-leagues experienced significant home-field advantage, but Japan Women’s Football league did not. This difference was considered to be caused by the difference in audience size between the J-leagues and Japan Women’s Football league.