whenever there is a large random component in performance.

I think that is a good way of explaining regression to the mean, but it's possible that "large" may be misleading. Any random component of performance will produce to regression to mean, although the amount depends on the amount of randomness (or really, unmeasured-ness). I'm not sure what to do about this. Perhaps address it at the end. Or just mislead.

People make the errors you describe, so we need some way of talking about them, but here is someone who doesn't like the way people use the phrase "regression to the mean."