One of the things that I'm finding is the most confusing topics as well as the least understood is mouthpiece diameter size vs. cup depth.
I have a great number of students that come to me complaining of poor range, air induced sound, and weak endurance. People who practice on a regular basis and do the assignments given to them... not able to understand why they're not improving in these areas.
Most of the problem may lay in a mouthpiece that is too large diameter wise. What I've discovered is that cup depth (or volume) is what can adversely affect a players tone, range, articulation ability, as well as endurance. Younger players tend to gravitate toward similar diameter mouthpieces with shallower cups. If a player would rethink this, perhaps even look at the physics of it, they may find that a smaller diameter cup would require less strength as we end up with less muscle / lip mass in the mouthpiece itself.
This in no way "fixes" all of the inherent problems we tend to face, but it will certainly put the right size shoes on the runner!