# Highest Rating

kw72uk
Posers and Puzzles 02 Oct '05 12:11
1. 02 Oct '05 12:11
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.....
2. 02 Oct '05 14:13
depends if you win or lose
3. XanthosNZ
Cancerous Bus Crash
02 Oct '05 15:00
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.....
Assumptions:
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.
4. 02 Oct '05 15:24
Originally posted by XanthosNZ
Assumptions:
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-YourR ...[text shortened]... ing (I used Maple because I'm lazy) gives YourRating = 1797 (rounding up).

So there you are.
exactly what I said, and wasted more time.
5. XanthosNZ
Cancerous Bus Crash
02 Oct '05 15:32
Originally posted by Coconut
exactly what I said, and wasted more time.
Point me to where you give 1797 or 1300 in your post?

I answered better by doing a little math. Only took maybe 2 or 3 minutes.
6. 02 Oct '05 16:071 edit
Originally posted by XanthosNZ
Assumptions:
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-YourR ...[text shortened]... ing (I used Maple because I'm lazy) gives YourRating = 1797 (rounding up).

So there you are.
Thanks.

I was trying to ascertain what rating you could possibly achieve by only playing people you would generally expect to win against.

That being the case, 1797 was the answer I was looking for - that being the point where winning against a 1200 rated player would gain you zero points.
7. XanthosNZ
Cancerous Bus Crash
02 Oct '05 16:471 edit
Originally posted by kw72uk
Thanks.

I was trying to ascertain what rating you could possibly achieve by only playing people you would generally expect to win against.

That being the case, 1797 was the answer I was looking for - that being the point where winning against a 1200 rated player would gain you zero points.
If I was feeling up to it I'd work out a method to tell you how many games it would take to reach that point from 1300(non-provisional) taking into account rounding effects.

EDIT:
A quick Matlab script gives me 183. That is you would have to win 183 games in a row against 1200 level opponents to rise from 1300 to 1797 (the maximum facing this level of opponent).
8. 03 Oct '05 08:25
Originally posted by XanthosNZ
If I was feeling up to it I'd work out a method to tell you how many games it would take to reach that point from 1300(non-provisional) taking into account rounding effects.

EDIT:
A quick Matlab script gives me 183. That is you would have to win 183 games in a row against 1200 level opponents to rise from 1300 to 1797 (the maximum facing this level of opponent).
That's quite a number. I suppose for every game you lost, you would lose more and more points the higher your rating got. So if you won 182 in a row then lost the 183rd game, you'd have to then win about 30 games to get your rating back to where it was......