Does Bill James's Pythagorean Formula Apply to England's Premier League?

Abstract

Bill James’s Pythagorean formula relates runs scored and runs allowed to team winning in Major League Baseball.  Researchers have applied James’s Pythagorean formula to basketball, ice hockey, and tennis, among other sports.  Current literature, however, questions the applicability of the Pythagorean approach to soccer.  This paper finds that such results may be because the dependent variable is based on the Fédération Internationale de Football Association’s (FIFA) point system rather than wins and losses.  The authors successfully apply James’s Pythagorean formula to soccer and, in particular, England’s Premier League (EPL).  Between 2000/01 and 2016/17, there is a statistically significant relationship between a team’s goal ratio (defined as goals scored divided by goals allowed) and a team’s win-loss ratio.  A one percent increase in the goal ratio is associated with a 1.70 percent increase in the win-loss ratio.