Partially Constrained Group Variable Selection to Adjust for Complementary Unit Performance in American College Football

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 evaluation metrics across statistical categories, 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 hasn't been emphasized is the complementary nature of American football. Despite the same team's offensive and defensive units typically consisting of separate player sets, some aspects of your team's defensive (offensive) performance may affect the complementary side: turnovers forced by your defense could lead to easier scoring chances for your offense, while your offense's ability to control the clock may help your defense. For 2009-2019 CFB seasons, we incorporate natural splines with group penalty approaches to identify the most consistently influential features of complementary football in a data-driven way, conducting partially constrained optimization in order to additionally guarantee the full adjustment for strength of schedule and homefield factor. We touch on the issues arising due to reverse-causal nature of certain within-game dynamics, discussing several potential remedies. Lastly, game outcome prediction performances are compared across several ranking adjustment approaches for method validation purposes.