Rivista di Diritto ed Economia dello Sport - Rdes.it

88 Kelly Goossenswithin season competitive balance since it understates the level. Thenumerator should be smaller. They propose an adjusted Gini-coefficient butunderline that there remain problems with it. 42 Consequently we do notconsider it for our comparison of countries.Competitive balance ratioThe standard deviation only accounts for seasonal uncertainty and not forchampionship uncertainty because the dominance of teams over seasons isnot taken into account. We show this in the next chapter. Humphreys andEckard 43 concentrated on a more dynamic measure to include both kinds ofuncertainty. Eckard decomposed the variance of winning percentages into acumulative and time varying component. Humphreys used Eckard’s idea tomodel an easier measure but with the same basics. He named it the competitivebalance ratio (CBR). Since both measures are equally valued we prefer todiscuss the CBR.The standard deviation of winning over seasons per team is nowincluded and it is named ‘within-team-standard deviation’. The standarddeviation used before is called the ‘within-season-standard deviation’. 44Within-team-standard deviationWithin-season-standard deviation:S∑22( wis,−wi)( wis,−ws)SD wt,i= s=1SD ws,s = i=1(1)SnThe Competitive Balance Ratio (CBR) is the ratio of these twostandard deviations:CBR=n∑i=1SDnwt ,in∑S∑ SDws , s(2)s=1S____________________42For an overview we refer to their paper.43W. ECKARD, ANOVA-Based Competitive Balance Measure, Defense, J. of Sp. Ec., vol. 4, n. 1,2003, 74-80; B. R. HUMPHREYS, ibidem, 2002 and B. R. HUMPHREYS, The ANOVA-Based CompetitiveBalance Measure: A reply, J. of Sp. Ec., vol. 4, n. 1, 2003, 81-82.44i= team, s= season, n= total nr of teams, S= total nr of seasons, w i,s= win percentage of team iin season s, w i= average win percentage of team i over total nr of seasons, w s= average win