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Expected score is too dependant on opponent's rating
joby.d wrote
at 6:33 AM, Wednesday December 20, 2006 EST
I assume a true 1600 player who plays 30 games against true rating 2000 players would finish with a significantly improved rating. I assume a true 2000 player who plays 30 games against true rating 1600 players would finish with a quite damaged rating. In my opinion this means there is too much damage/rewards if your opponents ratings are significantly different than yours. The obvious catch to reducing damage from losing to low rated opponents is people can inflate their rating by beating on slightly weaker opponents. However, I still recommend at least trying an expected score forumla of:
EP1 = 1/[1+4^[(Rn-R1)/400]

---

Reasoning:

iirc my current expected score = 1/[1+10^[(R2-R1)/400]] + 1/[1+10^[(R3-R1)/400)] + ...

i believe the current actual scores are: 1st - 6, 2nd - 5, ...

Case A: 2000 vs 6X1600

Let's assume this rating can get 1st - 30%, 2nd - 30%, everything else - 8% each. imo that is a generous win/loss record, correct me if I'm wrong.

(Rx-R1)/400 = -1

EP1 = .91 X 6 = 5.4545

AP1 = 6(.3) + 5(.3) + .08(4 + 3 + 2 + 1 + 0) = 4.1

EP1 >>> AP1 :(

Suggested EP1 = 4.5 which is closer to the AP1 4.1 assumption.

Case B: 1600 vs 6X2000

Let's assume this rating can get 1st - 5%, 2nd - 5%, 3rd - 10%, 4th - 10%, 5th - 20%, 6th - 25%, 7th - 25%. I'm hoping this is less than the truth so again correct me if you think I'm wrong.

EP1 = 0.91 X 6 = 0.5454

AP1 = 11(.05) + 7(.1) + 2(.2) + 1(.25) = 1.9

EP1 <<< AP1 :(

Suggested EP1 = 1.5 which is closer to the AP1 1.9 assumption.


Other Cases:

2000 vs 6X1950

Let's assume a lucky P1 shall win: 1st - 20%, 2nd - 20%, 3rd to 7th - 12% each

Current EP1 = 3.43
Suggested EP1 = 3.26
assumed AP1 = 3.4

So AP1 of a player who has 50 more rating points than his opponents may be greater than 3.26 so there is a risk of people inflating their ratings by playing against slightly lower opponents.

However: 2000 vs 6X1200
Current EP1 = 5.94
If you get 1st in 95% of these games and 2nd in the other 5% you would average a gain of 0.32 points per game.
If you get 1st in 90% of these games and 2nd in the other 10% you would still lose 1.28 points per game. I think this is pretty crazy!!
Suggested EP1 = 5.65

I'm not going to look at 1200 vs 6X2000 et cetera because I think they occur too rarely to be significant.


* Note: Unless I'm mistaken, only the difference in ratings matters. Therefore the only balancing effect from adding 1500 to everyone was now there are 1500- ratings?

« First ‹ Previous Replies 11 - 16 of 16
Ryan wrote
at 4:30 PM, Saturday February 17, 2007 EST
more constructive days on the forum :)
gohstlee wrote
at 9:37 PM, Sunday February 18, 2007 EST
Bump. I'd like for this to stay on the front page, even though I don't pretend to understand it all, based on a cursory reading.
Tech wrote
at 10:13 PM, Sunday February 18, 2007 EST
From another point of view, Mr. 2000 is punished for beating up people he's (from the ratings perspective) a lot better than. While 1600's are rewarded for bravery.

One could see it like that, if allowed.
AleaIactaSunt wrote
at 5:54 AM, Monday February 19, 2007 EST
I think a lot more people could discuss this, if joby would explain some of the variables (?rigt word?) he uses:

EP1= Expected points ?

Rx = Rank of player in question ?

R1,2,... = Rank of opponent 1,2,... ? or R1 = average rank of all opponents?

Rn = ?

AP1 = Average points ?

Actually, I need more explanation and I assume so do many others. Of course we don't want to bother, but if you want us to comment, just give us a few more explanation of the figures you use.
gohstlee wrote
at 8:41 PM, Monday February 19, 2007 EST
Bump, one more time.
montecarlo wrote
at 1:11 PM, Thursday September 24, 2009 EDT
itt Ryan makes a bump.

and its an interesting read about the inner workings of elo.
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