If I practise basketball with a smaller hoop than the standard..

Factual Questions
1

Would my ability in a game with a regular size hoop be better than someone who used a regular ring to practice?
Suppose the ring is the same height (10ft), same distance from the backboard, but the only difference is the circular size. Lets say its 3 centremetres (an inch and a bit) small all the way around the rim than the standard sized hoop.

I practice on this hoop daily. Will my shots now be more effective, because I’m less lazy about shooting, and can achieve it on a much more difficult ring?

You could apply this to American Football kickers as well (using less wide goal posts) etc etc.

2

My high school gym had one basket with a smaller inner hoop (1967,) so it’s not a new idea. I have no info about whether it works.

There’s a device being sold now that claims to improve a player’s shot percentage by forcing a higher shot arc. The gadget is a clear plastic wall about a foot higher than the rim, and it’s about 3 times the diameter of the hoop. Shallow-arc shots simply bounce off the gadget, never reaching the hoop.

3

This site agrees with your theory.