I've actually been wondering the same thing. I wouldn't say a vital role though, but I'd like to know too as my parents are pushing me to try Astanga Yoga.
I guess it can help your core muscles. But what actually is core muscles? Doesn't it help lower back pain when running? Because I have that sometimes and was advised to strengthen my core muscles. What can you do to strengthen them? No complicated machinery please. Lol. Maybe Yoga can help doing the "banana body movement". Haha. http://www.badmintoncentral.com/forums/showthread.php?t=58229