Very interesting, though I'm gonna have to disagree with you about level 9 having the same as 7. From level 1 to 4, there is a 2.5 increase, so if it is a linear function, it would make sense for level 7 to have the same 2.5-3 difference, but level 9 is roughly twice that.

Still, although interesting, looks almost useless. A difference on average of 2.5 after 5 volleys against something with no armor is small enough already, but if you take armored units, the difference will be even smaller. Plus, the standard deviation appears to be quite large. The level 9 longbows were actually worse than one group of level 0...