It started when a parent said to me, "My child's rating hasn't gone up in a year. Does that mean he hasn't learned anything from the expensive private lessons I've been paying for?" And I replied, "That's exactly what it means, with the small caveat that your child might have learned something about chess (like an opening) but is not a more skillful player."
Which led me to think about the problem for parents of not knowing if an expensive coach is worthwhile. Which led me to make an offer to a small group of parents that:
I would teach their child once a week for free
The child would play in a minimum of 2 tournaments a month and one hour a week at chess club or online.
The child would do all my homework and notate all games.
I would be paid every three months the gain (from the beginning of lessons) in the child's rating times a multiplier X.
My question to you is, what's a fair number for x? I would suggest it might be different for different people, or different ages, and definitely for different ratings.
Take as two examples a 9 year old rated 600 who has played chess for a year and a 13 year old rated 1650 who has played chess for 5 years; both students have previously had private and group lessons.