Here are the Top 9 benefits for  Yoga for grapplers:

1. Lesser injuries.
2. Better breathing [huge!]
3. Better use of energy, so you can spar more.
4. Moving smoother and quicker.
5. Increased flexibility, of course.
6. More powerful submissions and being able to hold them much longer.
7. Improved balance,base and control from top.
8. Your core will get much stronger, and this will help all aspects of your game.
9. The number one thing for me is the mental calmness (Keeping Cool) you get from yoga, which is paramount and crucial in a big tournament.

This video is from a BJJ guy called Sebastian Broshce who owns a website I am a member of called Yoga for BJJ. I suggest you check it out if you need some follow along stretching routines. There is a paid version and a free version of his site, but even on the free version you can get a ton of great info.

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And here is a Flexibility for BJJ video by Ryan Hall: