Scientific studies have shown that respiratory muscle training has indubitably led to better performance. Often, the heavy, can't-catch-your-breath tired feeling has to do with the very breathing muscles fatiguing. "Perceived fatigue" is the sensation of being tired but one that is fleeting; often, it leaves you angry as you look back and see you just needed a few seconds to recover.
You may ask if breathing was, well, "just breathing," wouldn't you be able to do breathing exercises indefinitely? Actually, breathing muscle exercises can make you sweat and cramp, and you might feel exhausted (which means your muscles have been overloaded, as needed for growth). The result: an almost immediate change in your endurance when you run, swim, or just recover between sets.
But what are breathing muscles?
Imagine 600 big water cooler bottles lined up. All in all, you're talking about your breathing muscles working to move 3,000 gallons of air (or 11,000 liters) in and out of your body every day.
You have about 10 pounds of breathing muscles just languishing, that is to say, not being trained functionally. You are not training these muscles when you do cardio. Your lungs are burning on that obstacle course, but are you "training" them? Nope. The notion that you are working your breathing muscles when training couldn't be further from the truth.
Why? To work out a muscle, you have to push it to exhaustion, and to do this you, have to train breathing muscles separately from your sport. If you don't work on your inspiratory and expiratory breathing muscles separately, you are running on three cylinders. By overlooking breathing, you are unknowingly sleeping on a mattress full of money.
When your breathing muscles are strong, you can breathe easier and exercise longer at harder levels of effort, and the experience feels easier. The burn or heaviness in your arms and legs will happen later in the game. You might even bounce back faster from tough, all-out efforts. Neglecting these muscles is like going to the gym, passing by all the weights, and spending the whole time doing forearm curls.