So let's deal with the first part of your ignorance first.
Pity really, since if you're actually a runner, you know all about this.
Below i've posted some of the very crucial attributes that breath control delivers.
1) Fluidity - Breathing rhythms are as vital to combinations as the punches themselves.
2) Gas - Controlling your breath allows you to stack your muscles with O2 and directly leads to the efficiency of energy expenditure.
3) Power - Understanding when to contract your diaphragm leads to increased solidity/momentum behind punches.
4) Muscle memory - Ties in with point 1 above. It provides a larger network for muscle memory since more of your body is involved in the punch/combo. Meaning that when you are tired, you have a greater reserve of pseudo-reflex action to rely upon.
5) Focus - Understanding your breath provides the fighter with a real-time feel for what's happening beneath the bonnet. It offers an internal focal point that holds the mind on task while drowning out external distractions. Also, remember the old adage, "tired players make more mistakes"? The more oxygen your brain and muscles have, the better your response and decision making is.
Anybody that is any way involved with sports that require stamina won't require an explanation as to the above.
I added the explanations just to help you on your way a tad. It's clearly necessary.
NOW, before you think of some asshole'ish thing to say, allow me to give you just one simple task.
Go out and find me a link to a video or an article where ANY PRO TRAINER, says that breath control doesn't provide a huge advantage or is unnecessary.
In other words, go an find just one trai ner that agrees with you.
We'll get to hand speed. Best to keep them separate for now.