Well, the descriptions of the battle make it plain that the battery of Brummer on the hill were key to the victory.
F looked down on his artillery officers, as did many army commanders of that time, because the officers of the true nobility, in the cavalry and infantry couldn`t be bothered to learn the maths and science required of artillery officers. The ranks of officers were thus opened up to the non-nobles who were motivated enough to do the schooling, but these new, clever officers were considered to be of a lower social class.