I don't know if this will answer your question exactly, but here is my approach shooting lower light sports.
I use the fastest glass I have (usually f/2.8 but not always) that will get me the zoom I need. If I am shooting low light, which is typically going to introduce some level of noise, the grains of noise are much larger relative to my intended target shooting without enough zoom. As I crop in/zoom on that target I am causing the grains to be larger as well. If I use a longer lens to get in on my target, at least the grains of noise are much smaller relative to my target.
My step-by-step
1. Lens length I need to get me reasonably close to my target.
2. Figure out the minimum speed I can shoot at. Often times it's 1/500, but can vary.
3. Widest aperture I can use.
4. Play with the ISO until I get in the neighborhood of what I want.
5. Adjust my exposure compensation to dial it in.
6. If I have lighting that can vary, or I am shooting with a telephoto where I will be moving in and out on my focal length I will kick it over to auto ISO. BUT, I shoot some test shots in the different directions to make sure that auto ISO and myself are agreeing on what I want it to do. If not adjust the exposure compensation again to get the camera back to what you wanted.
I don't know what camera you're shooting, it's not in your side profile or sig, but being familiar with how you camera lcd displays noise is valuable. My D7100 shows noise far worse than it really is. My D600 shows it accurately.
I don't know if this exactly answers your question, but maybe by sharing my approach you might extract what you're looking for.