Those of us in the optimization business would refer to that as 'constrained optimization.' And yeah, it's fuck'n hard. More constraints, all things being equal, significantly reduce the likelihood of global optimization as you're focused on solution optimization in the constrained space. If the global optimal lies outside of the local constrained space, there's no chance to globally optimize without relaxing constraint(s). That's the real math of it. We can debate all day long what the best method for local optimization under constraints would be, but I think
@Jaxbuck is doing a pretty good job of explaining / interpreting what we would guess Day was operating under while managing through the season.
That said, I think that a more nuanced set of heuristics could be applied. Something along the lines of:
-- When there is a significant advantage for the offense and defense do whatever the hell you want to do. I'd argue that this is where you speed up play, practice things against someone who wants to take your head off your shoulders, experiment with tempo and get the starters out early after getting their reps to make room for the 2nd and 3rd lines to get significant run.
-- When there is a significant advantage for the offense but not the defense, long sustained offensive drives to burn clock OR quick strikes for TDs are a must... provided the defense is giving up field goals. Every TD you score for every FG they score creates a 4-point gap in your favor... so you want more plays than the other guy... again, provided the defense is keeping TDs from being scored.
-- Where there is a significant advantage for the defense but not the offense, I agree with the Day MO this year. Minimize where you fall shorter and just be good enough to score one more point than they do... win the games ugly and with defense. Field position is key and the special teams has to be on point.
-- Where there is no significant advantage for either side of the ball... or talent equated games as they like to call them... is really poker on grass. This is where creative play calling and self scouting are stupid important. Break tendencies, find your best match-ups for a play at the line and go play football. This is where I think Day got in trouble this year. Without good OL play to protect a QB who wasn't getting the ball out quick, offensively they were not able to get the ball to the best match-ups. And I don't know that they significantly broke tendencies. The only real tendency that I saw broken was handing the ball to CJ Donaldson when we weren't on the goal line.
Good stuff... I'm really enjoying reading the debate(s) on this.