I ran regressions on the pick order and team win totals for each league. The higher the coefficient, the more impact the draft pick order had on a team's win total. Not surprisingly, all four leagues have a positive correlation.
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Correlation Coefficients for each league
League 1: 38.5%
League 2: 51.6%
League 3: 35.1%
League 4: 56.6%