So I guess part of it is that a good coach will be watching your form and will get into the habit of using their eyesight more than you would in the ring.

I guess in the ring you will be concentrating on your own balance and the feel of their body weight, direction of punches that land or graze past etc.

Difficulty with this is that it's hard to nail down the exact reason it works isn't it Scrap? I mean how can you tell the improvment from stopping pads isn't due to a number of factors?

Or have you tested some sort of indicator to do with prioreception before and after and found it accounts for all of the change statisitcally?

Reminds me of an stats lesson at uni. They found that the incident of increase in car accidents correlated with an increase in consumption of fish and chips in the population. It doesn't mean eating fish and chips causes car crashes but there are a whole heap of things that might be related to both.