# Standard Deviation Essay

Decent Essays

In investigating the impact of the regime changes on league competitiveness, the overall change in league equilibrium is charted based on the standard deviation of the team winning percentages for a particular season. One can compare the winning percentages’ actual standard deviation (ASD) with the ideal standard deviation (ISD) in a given year, assuming a perfectly competitive league. This approach was first used by Roger Noll and Scully in 1988 in their studies where they argued that the dispersion of wins could be measured by comparing the actual performance of a league to the performance that would have occurred if the league had the maximum degree of competitive balance in the sense that all teams were equal in playing strengths. The …show more content…

In a perfectly competitive league, the probability of any team winning (or losing) any given game is given by the equation P(W) = P(L) = 1 – P(W) = 0.5. Thus, for an 82-game season, ISD=0.5/(√82). The ASD is calculated by utilizing the following formula ASD=√(∑_(i=1)^N▒〖(p_i- p ̅)〗^2/N) where p ̅ is the league mean point ratio (in this case is equal to 0.5) while p_i is each teams actual winning record during the given season. N instead is the number of teams during the season. The ratio of standard deviations (RSD) is calculated by finding the ratio of ASD to ISD for a given year RSD = ASD / ISD. RSD takes the value of unity if the league is perfectly balanced, with higher values representing greater levels of imbalance. Zero, corresponds to a situation in which all teams end up with the same points ratio. John Gobok (2012) in his research paper found out that between 1976-2010 RSD diverged away from 1, signifying that the league became more unequal. The imposition of the soft cap in 1984 initially improved league competitiveness, as RSD reverted back towards 1. Nevertheless, between 1985-2000, league competitiveness went back to its original state and even worsened in the mid-90s. The exceptionally high competitive imbalance in the league in the 1990s can be attributed to the Jordan-era Bulls, where the team achieved the two winningest