specifically  fresh vs fairly fresh, fairly fresh vs tiring, fairly fresh vs tired? etc.

Logically to me it would seem a lesser player would come closer to a better a player if he less fatigued.

Fatigue plays a big factor especially in a press or fastbreak.  Not as much in a zone but still matters.

I think fresh and fairly fresh are pretty equal, most players at getting tired can still be effective as well. Once they get to tired they miss more shots, foul more and I would assume let up more points but I haven't really looked into that.

I can't give you that level of detail.  All I know is that, when I have my opponent showing red & orange at the end of games while mine are blue, green & yellow, I expect to foul some players out & win.  When possible, that is the basis of my gameplan.

I never thought fatigue was much more than window dressing until I took over a fastbreak/FCP team in DIII.

In actuality, I think it definitely matters in man, zone, and more traditional offenses (especially in regards to more fatigued teams fouling out quicker).

The difference is most noticable when you fun fastbreak/FCP and have players w/ high stamina ratings. You can wear the other team out pretty quick by doing this.

fatigue is a decently important factor. the low levels of being fatigued, fairly fresh and getting tired, represent relatively small decreases in skill, 5-10% or so. the lower levels really start to get you though, you really want to stay away from very tired and tired if at all possible.