It used to be soul memory played a part, but soul level was the main influence, with big white summon stone being within a certain level range, and the "shade" stone being for anyone out of that range "hence the restricted time" now with scholar I'm not sure, but I still have had a reasonable soul memory throughout. I've not farmed, nor used any influencing rings, most area's I've got through without hitting a wall. SO unless I'm below average soul count due to a lack of hitting a wall, god knows, mind you I've just hit 3.2 mil after finishing the iron crown dlc, but this is still my first playthrough, if 5 mil is still the average soul memory for late game pvp (I really hope it isn't), I'm going to have to be very careful.