The Solution
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It all depends on what you planing on doing, you won't lose any muscle mass with a 20-30 min jog regardless of BCAA's and if you running a marathon you need a whole lot more than just BCAA's.
Agree with this
For a small run or jog, you could possibly go without them (but they would not hurt if you have them)
if you were training to be an endurance athlete then i would really opt for adding carbs + BCAA's to fuel a very long run