Scaling certainly matters,
After posting yesterday I went into the battle of Antietam as CSA. When I saw that I was outnumbered more than 2:1 I went back to camp and spent all my resources on recruiting more men so as to lessen this disadvantage...only to discover that the enemy had simply scaled up, and I was still outnumbered more than 2:1. Then I thought about using my political capitol to bring up even more men, but upon further consideration this seemed to be pointless since the enemy might yet scale even higher. And so I decided to go into battle without any further adjustments.
The result was a complete massacre of my army, with a casualty rate of over two thirds. In fact, the only survivors from I corps were seven guns and James Longstreet.
So you go and tell the families of those boys that scaling doesn't matter!