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 Post subject: Re: The 40 point Rule
PostPosted: Wed Apr 20, 2011 11:38 pm 
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Joined: Wed Jul 02, 2008 4:31 pm
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Matt Fletcher wrote:
I don't have a grade at the moment as I haven't played for a few years. My grading performance is about 180 over the 15 games I've played this season. Presumably this (roughly speaking) will be my grade when the list comes out? But if I play a 120 grade in my club championship and win, my grading performance will go down?

Yes - see the last post in this thread.


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 Post subject: Re: The 40 point Rule
PostPosted: Wed Apr 20, 2011 11:57 pm 
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Joined: Wed Mar 09, 2011 10:42 pm
Posts: 118
Alex Holowczak wrote:
Is it definitely graded? Not all Club Championships are. It's difficult to say given you're ungraded, because it is subject to my first answer.


Thanks Alex - yes, I'm pretty sure my club championship is graded. I also think Ian's link tells me roughly what I wanted to know on how my grade will be calculated (thanks Ian for digging that out).

The only thing I'm slightly unclear on is my games against other ungraded players. Am I right in saying that the "first pass" would give me and other graded players a grade based on our games against graded players (as you mention in your post Alex), then there is an iterative process based on results between ungraded players until the system settles down to consistent grades for everyone?

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 Post subject: Re: The 40 point Rule
PostPosted: Thu Apr 21, 2011 12:17 am 
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Matt Fletcher wrote:
then there is an iterative process based on results between ungraded players until the system settles down to consistent grades for everyone?


That's correct. Every so often it seems to converge to implausible values. This is connected with players scoring about 90% or 10%. The 40 point rule seems to have an effect. As an illustration suppose you won nine games out of ten against players rated an average of 130, none of whom are below 110. For an existing player of 150, that's a performance of (1300 + 8*50) /10 ie 170. But if none of the players exceeded 150, the performance of player with a grade of 190 would be (1500 + 8*50) ie 190.

The iterative process does sometimes appear to get confused as to what outcome is expected, particularly when it encounters more than one ungraded player in a results history. Still it might have been fixed behind the scenes :) .

In the unlikely event that you wished to explore this further, threads with posts by E Michael White are a good source of material.


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 Post subject: Re: The 40 point Rule
PostPosted: Thu Apr 21, 2011 7:49 am 
Matt Fletcher wrote:
The only thing I'm slightly unclear on is my games against other ungraded players. Am I right in saying that the "first pass" would give me and other graded players a grade based on our games against graded players (as you mention in your post Alex), then there is an iterative process based on results between ungraded players until the system settles down to consistent grades for everyone?

Nearly, but not quite. The iterative process used in the second step includes results against both graded and ungraded players. Hence your hypothetical game against a 120 player would receive the protection of the 40 point rule at this stage. This is the explanation from the man who wrote the software.

Howard Grist wrote:
The first step of the grading process is to calculate an 'initial grade' for new players. This is done in two stages. The first is an iteration using 40 points for a win and ignoring the 40 point rule. The second stage is to use the result of the first stage as the new player's grade and grade his results using 50 points for a win and the 40 point rule. The new player is then treated as a graded player with a grade given by the 'initial grade'.

So, to answer the questions actually asked:-

1. New player loses 10 games to opponents all graded 150
Initial grade Stage 1 gives: 10 x (150 - 40) / 10 = 110
Initial grade Stage 2 gives: 10 x (150 - 50) / 10 = 100
Published grade: 10 x (140 - 50) / 10 = 90

2. New player wins 10 games against opponents all graded 150
Initial grade Stage 1 gives: 10 x (150 + 40) / 10 = 190
Initial grade Stage 2 gives: 10 x (150 + 50) / 10 = 200
Published grade: 10 x (160 + 50) / 10 = 210

1. New player loses 10 games to opponents all graded 150 and wins 1 game against an opponent graded 50
Initial grade Stage 1 gives: (10 x (150 - 40) + (50 + 40)) / 11 = 108
Initial grade Stage 2 gives: (10 x (148 - 50) + (68 + 50)) / 11 = 100
Published grade: ((10 x (140 - 50) + (60 + 50)) / 11 = 92

2. New player wins 10 games against opponents all graded 150 and loses 1 game against an opponent graded 250
Initial grade Stage 1 gives: (10 x (150 + 40) + (250 - 40)) / 11 = 192
Initial grade Stage 2 gives: (10 x (150 + 50) + (232 - 50)) / 11 = 200
Published grade: ((10 x (160 + 50) + (240 - 50)) / 11 = 208


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