This is related to this question: Forming a "concave" with your army
I have seen many pro casts where a concaved army beats an equal but clumped army. It's seen as a universally good thing. The answer to "why" is usually something like:
The bigger arc allows more units to shoot, taking better advantage of their range.
However, that doesn't make any logical sense to me. Consider two armies of 20 marines. It doesn't matter who has the arc, 20 marines shooting another 20 marines is going to be theoretically even. As long as both our entire armies are firing, it will be even, no matter what geometric shape they are in.
The response to this is something like, "well if you have 20 marines clumped, there will be a group in the center who are not firing". But my reply is that, unless the arc is HUGE (>180 degrees), you can simply move your clumped marines a few steps over and now they're all shooting. I would even say that move distance is less than the distance your opponent had to travel to form an arc around your army, so the clumped army gets the theoretical advantage.
I am not talking about situations where AOE damage plays a role, that scenario is obvious.
So, is there something I'm missing?