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Don Dailey

Joined: 29 Apr 2008
Posts: 4320

Post subject: Re: Elo Increase per Doubling    Posted: Tue May 08, 2012 8:25 pm

petero2 wrote:
Don wrote:
 JuLieN wrote: @Don What is the value of the asymptote to your red curve? (This is of course the maximal Elo in your system).

Is that a joke? I wish I knew where it all ended

I think if we gathered this data for several more levels and got enough data for each point we could try to estimate the value using some type of curve fitting.

If someone wants to take a crack at estimating this with curve fitting, here is the final result:

 Code: Rank Name    Elo      +      -    games   score   oppo.   draws    1 10    3127.9   25.4   25.4    2739   94.2%  2328.9   10.4%    2 09    2997.0   21.6   21.6    2739   86.8%  2341.9   15.2%    3 08    2891.6   20.4   20.4    2740   79.9%  2352.8   15.5%    4 07    2752.0   19.9   19.9    2740   70.2%  2366.7   15.8%    5 06    2615.3   20.2   20.2    2740   60.8%  2380.4   14.5%    6 05    2467.2   20.9   20.9    2740   51.2%  2395.2   13.0%    7 04    2307.4   22.1   22.1    2740   41.4%  2411.2   10.5%    8 03    2118.3   23.5   23.5    2740   30.6%  2430.1    8.6%    9 02    1932.7   25.3   25.3    2740   20.9%  2448.6    7.8%   10 01    1709.7   28.6   28.6    2740   10.9%  2470.9    5.3%   11 00    1500.0   36.9   36.9    2740    3.2%  2491.9    3.1%

After some trial and error: Elo=1500+2350*ln(1+Name/10)
.

It seems to be a really good fit, but I extrapolated it to level 1000 and it shows an ELO of over 12000!

If I go to 100000 it comes out to almost 18,000 ELO!

I don't believe perfect play goes that high. If I'm not mistaken you can achieve an arbitrarily high ELO with this formula - there is no asymptote so I guess it's just a good approximation at these low levels.

Do you have any other models that might impose some sort of limit?
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Subject Author Date/Time
Adam Hair Mon May 07, 2012 11:40 am
Julien MARCEL Mon May 07, 2012 12:04 pm
Adam Hair Mon May 07, 2012 4:48 pm
Julien MARCEL Mon May 07, 2012 4:54 pm
Adam Hair Mon May 07, 2012 8:50 pm
Julien MARCEL Mon May 07, 2012 9:00 pm
Mark Pearce Thu May 10, 2012 4:43 pm
H.G.Muller Mon May 07, 2012 12:13 pm
Michel Van den Bergh Mon May 07, 2012 2:01 pm
Adam Hair Mon May 07, 2012 5:12 pm
Don Dailey Mon May 07, 2012 6:40 pm
Robert Wagner Campos Tue May 08, 2012 12:38 am
Don Dailey Tue May 08, 2012 3:32 am
Adam Hair Tue May 08, 2012 10:02 am
Julien MARCEL Tue May 08, 2012 10:55 am
Adam Hair Tue May 08, 2012 8:08 pm
Don Dailey Tue May 08, 2012 11:29 am
Kai Laskos Tue May 08, 2012 11:59 am
Adam Hair Tue May 08, 2012 8:13 pm
Kai Laskos Tue May 08, 2012 10:21 pm
Don Dailey Tue May 08, 2012 10:52 pm
Adam Hair Tue May 08, 2012 11:14 pm
Kai Laskos Wed May 09, 2012 12:20 am
Adam Hair Wed May 09, 2012 2:44 am
H.G.Muller Wed May 09, 2012 8:05 am
Adam Hair Wed May 09, 2012 5:12 pm
Larry Kaufman Thu May 10, 2012 3:11 am
Don Dailey Thu May 10, 2012 5:03 am
Larry Kaufman Thu May 10, 2012 5:19 am
Don Dailey Thu May 10, 2012 12:43 pm
Peter Österlund Thu May 10, 2012 4:59 pm
Julien MARCEL Thu May 10, 2012 5:09 pm
Don Dailey Thu May 10, 2012 5:41 pm
Don Dailey Thu May 10, 2012 5:46 pm
Ed Schroder Tue May 08, 2012 12:09 pm
Don Dailey Tue May 08, 2012 12:10 pm
Ed Schroder Tue May 08, 2012 12:28 pm
Don Dailey Tue May 08, 2012 12:36 pm
Ed Schroder Tue May 08, 2012 1:15 pm
Don Dailey Tue May 08, 2012 2:37 pm
Julien MARCEL Tue May 08, 2012 3:15 pm
Don Dailey Tue May 08, 2012 6:15 pm
Peter Österlund Tue May 08, 2012 8:06 pm
Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 8:25 pm
Peter Österlund Tue May 08, 2012 9:00 pm
Julien MARCEL Tue May 08, 2012 9:02 pm
Don Dailey Tue May 08, 2012 9:06 pm
Don Dailey Wed May 09, 2012 4:26 pm
Peter Österlund Wed May 09, 2012 4:52 pm
Don Dailey Wed May 09, 2012 5:19 pm
Don Dailey Thu May 10, 2012 1:41 pm
Don Dailey Thu May 10, 2012 4:52 pm
Adam Hair Thu May 10, 2012 9:07 pm
Don Dailey Thu May 10, 2012 10:55 pm
Adam Hair Fri May 11, 2012 12:46 am
Adam Hair Fri May 11, 2012 1:06 am
Don Dailey Wed May 09, 2012 5:00 pm
Adam Hair Tue May 08, 2012 9:05 pm
Don Dailey Tue May 08, 2012 9:18 pm
Adam Hair Tue May 08, 2012 11:26 pm
Don Dailey Wed May 09, 2012 2:50 am
Adam Hair Tue May 15, 2012 3:17 am
Don Dailey Tue May 08, 2012 6:23 pm
Ed Schroder Tue May 08, 2012 12:18 pm
Don Dailey Tue May 08, 2012 12:25 pm
Don Dailey Tue May 08, 2012 12:27 pm
Robert Hyatt Tue May 08, 2012 3:36 pm
Don Dailey Tue May 08, 2012 5:32 pm
Daniel Shawul Fri May 11, 2012 5:48 pm
Don Dailey Fri May 11, 2012 6:30 pm
Julien MARCEL Fri May 11, 2012 6:52 pm
Don Dailey Fri May 11, 2012 7:05 pm
Daniel Shawul Fri May 11, 2012 7:08 pm

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