And that doesn't even account for other battlefield conditions, which would only exaggerate the difference.
Or reduce the difference. It seems plausible to me that the noise, smoke, confusion and fear might increase dramatically with proximity and the aiming might get worse.
Here is something I found on another site..... I believe Blaugrana is probably more correct.
Alexander Stillwell "The Story Of A Common Soldier of Army Life In The Civil War 1861-1865" p40-42
I distinctly remember my first shot at Shiloh...I think that when the boys saw the enemy advancing they began firing of their own motion. Without waiting for orders. At least I dont remember any. I was in the front rank, but didn't fire.I preferred to wait for a good opportunity, when I could take deliberate aim at some individual foe. But when the regiment fired, the Conferderates halted and began firing also, and thefronts of both lines were at once shrouded in smoke. I had my gun at the ready, and was trying to peer under the smoke in order to get a sight of our enemies. Suddenly I heard someone in a highly excited tone calling to me from just in my rear,-"Stillwell! shoot! shoot! Why dont you shoot?" I looked around and saw that this command was being given by our second lieutenant, who was in his place, just a few steps to the rear. He was a young man, about twenty-five years old, and was fairly wild with excitement, jumping up and down "like a hen on a hot griddle." "Why lieutenant," said I, "I cant see anything to shoot at." "Shoot, Shoot, anyhow!" "All right," I responded, "if you say shoot, shoot it is;" and bringing my gun to my shoulder, I aimed low in the direction of the smoke and blazed away through the smoke. I have always doubted if this, my first shot, did any execution-but there's no telling. However, the lieutenant was clearly right. Our adversaries were in our front, in easy range, and it was our duty to aim low,fire in their general direction, and let fate do the rest. But at the time the idea to me was ridiculous that one should blindly shoot away into a cloud of smoke without having a bead on the object to be shot at...the extent of the wild shooting done in battle, especially by raw troops, is astonishing, and rather hard to understand...(At Shiloh) I heard an incessant humming sound way up above our heads,like the flight of a swarm of bees. In my ignorance, I at first hardly knew what meant, but it presently dawned on me that the noise was caused by bullets singing through the air from twenty to a hundred feet over our heads. And after the battle I noticed that the big trees in our camp, just in the rear ofour second line, were thickly pock-marked by musket balls at a distance of fully a hundred feet from the ground. And yet we were seperated from the Confederates only by a little, narrow field, and the intervening ground was perfectly level. But the fact is, those boys were fully green as we were, and doubtless as much excited...I reckon they were as nervous and badly scared as we were.
Just a thought....