Originally posted by kw72uk
Say you're a certified 1300 player, what's the highest rating you could achieve on rhp if you never played anyone rated over 1200?
You'd have to assume that you never actually improve.
I don't know the answer, just wondering.....
1300 is your actual rating (where actual is the rating that you will play at every game).
Every person you play has an actual rating equal to their RHP rating (not always the case by a long shot, however a case for them being normally distributed with the means being the same could be made).
Win Expectancy = 1 / (10^((OpponentRating-YourRating)/400)+1)
New Rating = Old Rating + K * (Score - Win Expectancy)
Therefore your rating would increase everytime you beat the lower rated players and drop by more than that everytime you lost. Over time your win-loss ratio would be such that your rating would remain at 1300.
Now if you are going to assume you never lose then you will increase to the point at which you can gain no more rating points for beating a 1200 player.
Which is when K * (Score - Win Expectancy) < 0.5
This occurs when Win Expectancy is 0.96875.
0.96875 = 1 / (10^((1200-YourRating)/400)+1)
Solving (I used Maple because I'm lazy) gives YourRating = 1797 (rounding up).
So there you are.