Partially constrained group variable selection to adjust for complementary unit performance in American college football

Abstract

Given the importance of accurate team rankings in American college football (CFB)–due to heavy title and playoff implications–strides have been made to improve metrics for team performance evaluation, going from basic averages (e.g. points scored per game) to metrics that adjust for a team's strength of schedule, but one aspect that's yet to be accounted for is the ability of team's offense and defense to complement one another, termed ‘complementary football’. American football is unique because the same team's offensive and defensive units typically consist of separate player sets that don't share the field simultaneously, which tempts one to evaluate them independently. Yet, some aspects of your team's defensive (offensive) performance may directly impact the complementary unit, e.g. turnovers forced by your defense could lead to easier scoring chances for your offense. Our main goal is to identify the most consistently influential features of complementary football in a data-driven way, subsequently adjusting each team's offensive (defensive) performance for that of their complementary unit. To achieve that, for the 2009–2019 CFB seasons, we incorporate natural splines with group penalty approaches, conducting partially constrained optimization to guarantee the full adjustment for the strength of schedule and home-field factor.