If you answer this question by looking at results, the answer is pretty clear: the Coach of the Year award typically goes to the coach of the team that most exceeded expectations. Another way of putting it:
"Coach of the Year" analysis: Imagine you are showing these standings to yourself before the season ... which positive result would make you say "damn!" the loudest?— Bart T🏀rvik (@totally_t_bomb) March 9, 2020
I'm here to say that's the way it should be.
Just like the preseason AP poll tends to give a fairly pure view of how good knowledgeable people think a team will be—before dirty game results sully the analysis with overreactions and the like—preseason expectations for a team give us a pretty pure view of how talented people think the roster is.
There are many reason a team could outperform its presumed talent. Obviously the presumptions of talent could be quite wrong. That happens all that time. It could be just luck. That no doubt happens all the time. But generally speaking when a team outperforms its presumed talent level, I think it's fair to attribute at least some of that variance to coaching—superior training, development, and game strategy.
That's a sound theoretical justification for giving the Coach of the Year award to the coach of the team that most outperforms its preseason expectations. It's not at all dumb. Let's just accept it.
There are two main objections to this regime:
1) Why shouldn't preseason favorites be eligible for coach of the year?
and, relatedly,
2) Recruiting is coaching, too, and this doesn't account for that.
Both of these objections are wrong.
First, under this regime, coaches of preseason favorites are eligible to win Coach of the Year, and they do. Even favorites can wow us with their overachievement. For example, John Calipari was national Coach of the Year in 2015 despite having probably the most talented roster in the one-and-done era. Bo Ryan won B1G COY in 2015 leading a preseason top-5 juggernaut. There are many examples.
Second, and I cannot emphasize this enough, recruiting is not coaching. Coaching has a general meaning that applies to all sports: training players, developing players, and directing game strategy. Recruiting, program-building, fundraising, glad-handing, press conferences, etc.—these are all things college basketball coaches have to do, but none of those things are coaching. The Coach of the Year award need not (and should not) consider them.
Most sports have a Coach of the Year award. In professional sports, coaches don't get credit for having great players (even if they happen to also be the GM that drafted them) because it's understood that coaching and roster construction are different things, and the Coach of the Year award is for the coaching part. Just because the person called "Coach" happens to both coach and recruit doesn't mean recruiting is coaching. It isn't. It just isn't.
The existing regime for deciding Coach of the Year focuses, appropriately, on coaching: instruction, development, game strategy. That's reasonable and appropriate. There's no need to muddy the waters trying to evaluate the non-coaching duties.