BIG BAD WOLF: It's worse than that my friend. As a top 5 player it is against my interests to play outside the top 20 if I want to protect my rating. A system that makes that kind of thing even thinkable is not a good one.

In a fair system I'd be happy to play anybody, literally. With the widely used ELO Bg formula, if I were playing a single match against a beginner then I'd earn 1.25 points and lose 2.75 points. My share of the 4 available points would be about 30%. But I'd tend to win about 70% of the time so it would balance out. We'd both stay at our ratings, neither gaining nor losing over the long term.
That's what the formula is supposed to do - maintain the status quo when players are playing true to their rating.

Against an average player I'd earn 1.5 or lose 2.5 but I'd win less often - about 60% - which again makes it balance out.

A fair system doesn't penalise higher rated players when the lose against lower rated ones - the wins make up for it. Under such a system the best protection for your rating is to study the game and play it well.

But, back to BrainKing:

With this new formula I'd win 1 BKR point and lose 15 against the beginner. I'd still only win 70% of matches so ..
After 16 matches I'd have gained 11 x 1 = 11 points.
Yet I'd have lost 5 x 15 = 75 points.
I'm down 64 points - penalised for only having won what is reasonable.

In the proper system it would be win 11 x 1.25 = 13.75 and lose 5 x 2.75 = 13.75. Balance.


Against the average player I'd win 2 BKR points or lose 14. I'd still win 60% so ..
After 16 matches I'd have gained 10 x 2 = 20 points
But would have lost 6 x 14 = 84 points.
Again down 64 points.

In the proper system it would be win 10 x 1.5 = 15 and lose 6 x 2.5 = 15. Balance.


Against a top 20 player I'd win 6 BKR points or lose 9. This time I'd only be expected to win 55% of the matches.
After 16 matches I'd have gained 9 x 6 = 45 points
But I'd lose 7 x 9 = 63 points.
So even against someone closely matched I'd be losing 18 points just for winning only as many as expected.

In the proper system it would be win 9 x 1.75 = 15.75 and lose 7 x 2.25 = 15.75. Balance.