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One measure of sports league competitive balance uses a ratio: the standard deviation of team winning percentages is divided by the so-called ideal standard deviation, which assumes a game between evenly-skilled teams is equally likely to be won by either team.  In fact, a team is more likely to win when playing at home than when playing on the road.  The extent of this advantage differs across sports leagues.  Home advantage reduces the variability of season-long team records.  Ignoring home advantage biases upward the traditionally measured ideal standard deviation and bias downward the ratio of standard deviations.  The authors derive a balanced league standard deviation formula that accounts for home advantage, use it to recompute the ratio of standard deviations for major sports leagues, and consider how the adjustment affects comparisons of competitive balance across those leagues.

Adjusting Winning-Percentage Standard Deviations and a Measure of Competitive Balance for Home Advantage