Rivista di Diritto ed Economia dello Sport - Rdes.it

Competitive balance in European football 95We start with an overview of our chosen measures based on theprevious chapter. Next we discuss our results structured into three subsectionsbased on the chosen measures.3.1. Our MeasuresFor the balance within seasons we start from the win percentages. 63Theoretical research discusses the distribution of player talents and the lattercan be represented by the number of wins. All else equal, the more talents ateam possesses the more games will be won. So a measure that is based onwin percentages seems justified. We interpret seasonal balance as the spreadof these win percentages within the season so that the use of the standarddeviation is the obvious choice. For the balance between seasons we need tomeasure dominance of teams over seasons. We include both the top 3 aswell as the Lorenz curve to have a measure that focuses on the championalone.The National Measure of Seasonal ImbalanceTo compare winnings over seasons and over countries an adaptation of theexisting measures is appropriate because the number of teams differs. Anexample clarifies this. Assume that there is perfect certainty about theoutcomes of the championship, which is of course the worst case scenario: 64team 1 wins all of its games, team 2 always wins except against the firstteam, team 3 always wins except games against the first and second, … Thestandard deviation of win percentages of such a competition with 18 teamsis: 0,305148. Suppose this league decides to increase the number of teamsin the next season to 20 teams. When the worst scenario remains the standarddeviation becomes 0,303488. So by adding two teams it has decreased itsuncertainty measure, and hence gives the impression that the within seasonal____________________63We first want to draw attention for the point schemes used by the leagues because this isrelevant for European football leagues. In general, games in the American major league sportscannot end in a draw and a win is rewarded by 1 point, a loss by zero. In the nineties mostEuropean countries changed their reward for winning from two to three points while a drawreceives one point and loosing zero. In the sports literature it is custom to take up a draw as halfa winning. This follows the old European scheme but a draw could also be included as one thirdof a winning. We compared the two possible point-schemes for all countries but the trends arequite robust. With the use of the 3-1-0 distinction we no longer get an average winning percentageof 0.5 and then the coefficient of variation (divide sd by the average) needs to be calculated. Wetherefore decided to include a tie as half a winning.64See the discussion in our introduction about the basics of team sports: we need someunpredictability to keep the interest of fans and sponsors.