Rivista di Diritto ed Economia dello Sport - Rdes.it

86 Kelly Goossensaverage league winning percentage of 0,5. In most European countries thepoint distribution changed in the nineties to three points for wins and onefor draws. When the latter is applied, the use of points renders a seasonalaverage different from 0,5 so it is no longer equivalent to the use of wins.RangeThe range is one of the easiest measures for competitive balance. It is thedifference between the highest and lowest win percentage. The bigger therange the more the best and worst team differ and hence the bigger theimbalance. It only takes two teams into account which is the biggestdisadvantage of this measure. We looked at the information this measuregave us but we prefer to use the standard deviation of the distribution of thewinning percentages because this takes all the teams into account.Standard deviation of winning percentageThe standard deviation 37 of the winning percentages in one season measureshow far the win percentages are spread around the average. The larger thestandard deviation, the less the competitive balance is because the winpercentages are hence very different between teams. By definition it givesmore weight to the teams at both ends of the competition which is exactlywhat we need.The standard deviation as a measure of spread has the disadvantageof the necessity of a scale when comparing over countries or years: it dependson the average. Only when the average is the same, comparison over countriesor over seasons is possible. When we use the 2-1-0 points, the average isalways 0.5 and hence comparison is possible. With the 3-1-0 points, theaverages differ so the standard deviation cannot be compared anymore andthe use of the coefficient of variation 38 is necessary.Standard deviation ratioThe standard-deviation-ratio is the ratio of the actual standard deviation toan idealized standard deviation. The ideal ratio is 1. The higher the ratio, themore the actual spread diverges from the ideal one and hence the worse thecompetitive balance.____________________37SD=n∑i=1( winperc−averagewin)in38The coefficient of variation=sd/average.2; n = number of teams.