Did clay cause this?

[TZ-OH6]

This was my first time growing potatoes and I ended up with a knot of 3-4 potatoes at the base of each plant deep in the soil, which I don't think is supposed to happen. The bed (heavy clay soil) was dug out to 2.5 ft and heavily ammended with wood chip compost. The original top soil (not too heavy but still with a good bit of clay in it) was set aside and used to hill the potatoes. In the end I had about 10 inches of topsoil hilled up on the plants and I thought that would be full of potatoes extending out from the plant, but no, just a tightly packed knot of potatoes pretty much where the seed potato was (no fun digging down 10 inches to get potatoes). It might be that rain caused clay to accumulate/pack down over top of the seed potatoes before hilling started because the tubers seemed to be packed into clay, but expansion against the soil could have caused that. Do potatoes need exceptionally light soil? did I over fertilize? not enough sun (southeast side of house, lots of morning sun and a white brick house). Varieties were Red Pontiac and Katahdin

[beeman]

Potatoes do not spread out along the roots, but form close to the seed. The amount of 'hilling' does not promote more potatoes on each plant.
A few inches are sufficient to cover and prevent greening.

[Medbury Gardens]

Potatoes will tend to send out runners if grown in a soil high in compost,i had a variety called Stan Cloak that had a habit of sending runners and growing spuds well away from where it was planted,up to two feet away.

Adding sand to your heavy clay soil may help it also

[TZ-OH6]

I avoided adding compost to the top layer because I read that high organic content promoted scab. I had hoped that the original topsoil would be loose enough, but I guess not.

[Medbury Gardens]

I think there are other factors as well,i use lots of compost on top of my potato garden and only a very limited amount scab but also not a lot of other disease problems any where else in my garden thanks to a low humidity climate