#### Help Forum

1.  CalJust
It is what it is
16 Jul '04 14:22
After looking at it from all sides, it seems to me that there may be a mistake in the WE calculation on FAQ. Maybe somebody can show me where I am wrong.

Let OR = Opponent's Rating and MR = My Rating.

The WE formula in FAQ is WE = 1/10^((OR - MR/400) +1)

It also gives an example where WE = 0,76 when OR - MR = 200

When I do the calculation, I get 0,32 for this sum. This means that if my rating is 200 HIGHER than my opponent, I am expected to win only one in three games, not three in four! What is my mistake??

I also find that if OR - MR = 0, i.e. when our ratings are the SAME, then the formula calculates a WE of 1/10, or 10%, which seems incorrect, since the intuitive answer must be 50%!

If OR - MR = - 400, then the WE is 1, i.e. I should win all games if my rating is 400 points higher. Sounds OK.

And if OR - MR = 400 (if my opponents rating is 400 points higher than mine) then the WE is 0,01,or 1%, which also makes sense, since even experts can make mistakes!

When the formula is applied in the Rating equation:
NR = OR + k(Sc - WE), then it can be seen that the WE calculation is much more lenient to the loser in a contest when you play someone stronger, than if you lose against a weaker player. I suppose that is to encourage you to play stronger players!

But there is still a problem in my mind. If there is a difference of +100 as against -100 points, the WE is 6% and 18% resp. It is difficult to understand the rationale behind this.

Can an expert perhaps explain this to me??

Muchos gracias,

CJ
2. 16 Jul '04 15:19
Originally posted by CalJust
The WE formula in FAQ is WE = 1/10^((OR - MR/400) +1)
Except it isn't:

WE = 1/(10^((OR - MR)/400)+1)
3.  CalJust
It is what it is
17 Jul '04 09:26
Originally posted by piderman
Except it isn't:

WE = 1/(10^((OR - MR)/400)+1)
OK, I forgot the last bracket at the end...

Have you checked my calculation for (OR - MR) = 200? and (OR - MR) = 0??
4. 17 Jul '04 09:33
Originally posted by CalJust
OK, I forgot the last bracket at the end...

Have you checked my calculation for (OR - MR) = 200? and (OR - MR) = 0??
Yes. those are wrong. It is the matter of where you place the +1:

WE = 1/10^ (A( (B( OR - MR/400 )B) +1 )A)

correct formula:

WE = 1/ (A( 10^ (B( (C( OR - MR )C) /400 )B) +1 )A)

As you see, the correct formula has the +1 outside the 10^, whereas in your formula you had it inside. So the calculations shown in the FAQ are correct and justifiable, with things like WE = 1 only if you have infinite more rating than your opponent (mind you, if you have only 400 more, the opponent may still win, so the win expectancy is less than 1).
Also, when you have exactly the same rating, WE = 0.5 as it should be.
5.  CalJust
It is what it is
19 Jul '04 06:13
Thanks a lot, piderman. I'm now much relieved that there is logic in this system! I missed the fac t that the last +1 is NOT part of the 10^. Perhaps I would have noticed that if the brackets were different, say [ ]and { }

CJ