To analyze balance we created a new metric each game: the ratio of pass attempts to rush attempts. Using these metrics we created gameplans by breaking the balance ratios into logical groupings (e.g. High Pass Attempts to Low Rush Attempts = Pass Heavy Gameplan). Based on the analysis of gameplans inbalanced offenses that are run heavy are significantly more successful than balanced or pass-heavy offenses.
Running a regression analysis using the balance metric we created as the independent variable and win differential as the dependent variable the overall R^2 was only 0.267 which is a generally weak relationship. Based on these results one can conclude that there is a weak relationship between running a balanced offense and success in the NFL.
Feel free to take a look at your favorite team and see how offensive balance contributes to success by year. The thickness of the bars represent the number of times a team ran that gameplan.