This paper deals with the measure of equality of a sport championship, where each participant plays against all the others with a home and away match. We define a class of indices derived by normalising some measures of dispersion. Four of such indices are considered and studied: EQ1 (based on the standard deviation), EQ2 (Gini's concentration ratio), EQ3 (mean absolute deviation) and EQ4 (mean letter spread). We refer to two extreme schemes: the perfect balance and the completely unbalanced position. The distribution of such indices in 30 European national soccer leagues is studied, jointly with the correlation between the indices. Then, a simulation is made, under the hypothesis that the participants have the same level of skill, and some statistical features of the sample distribution are pointed out. Finally, a Beta model is fitted to the sample distribution, and it seems to be an adequate representative.