Coach effect does not equal game management.
You'd have to be regularly punting on third down to cost your team three wins in one season via game management.
Game management is wrapped up in there. It is a much larger term that encompasses nearly every aspect of the team, as I tried to acknowledge. I maybe wasn't as explicit in mentioning the offense there as I had intended to be. Basically those are the areas where we are under-performing and it is costing us games.
All coach effect does is compare recruiting rankings to results.
So, assuming the recruiting rankings are unbiased, coach effect attempts to measure every single aspect of coaching from identifying underrated talent to development to roster management to motivation to team-building to game management, etc.
Game management is the most visible aspect of coaching but also the most overrated. A lot of awful fourth down decision makers have won Super Bowls and crystal footballs.