I think they work in reverse. I plant large potato onions and they get many smaller ones, I plant smaller ones and they get very few, but bigger ones.

Shallots I usually get 3 or 4 from 1. I do have a spot I don't harvest that much and get mounds or big clumps that keep redividing/multiplying.

One of my gardening mentors had saved her largest shallots for sets for many years. Her shalots were enormous. I do not know the variety. For the past 15 years I have grown shallots from sets from different varieties. I have not been able to increase the size of my shallots over the years and think it may be a variety and/or a soil issue. My shallots are fairly small. However, the sets keep well in my warm house for planting the following year.

Geez. Where to start. I purchased my first ever bunch of shallots from a mail order company that just called them "shallots." I have no idea what variety. They were small, red/gold (1" or less) but I stuck 20 of 'em in at 8" apart this spring using the largest cloves out of the quart that they sent me.
I got everything. Some produced three, some produced five or six per plant.
Earlier this season I posted a thread and asked your same basic question. I was told that smaller produced fewer, but larger shallots; larger produced more, but smaller shallots. I have noticed with the variety that I was sent that after harvest the larger ones seem not to keep as well. I have had several of the larger harvest go bad. None of the smaller have gone bad, yet.
I am going to plant SMALL shallots both fall (October here) and spring (March, here) to experiment and see how they fare. I relate back to the small shallots that I was sent and the great production that they provided - we will never get all of them eaten, even as much as we use shallots in cooking. I might add that all of my "smaller" shallots are now much bigger than the original batch that I was sent. This will be a learning experience! I truly hope I am not steering you down the wrong path, as this is my FIRST YEAR'S experience.
hortster