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Elo Increase per Doubling
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Adam Hair



Joined: 06 May 2009
Posts: 1639
Location: Fuquay-Varina, North Carolina
PostPost subject: Re: Elo Increase per Doubling    Posted: Tue May 08, 2012 11:26 pm Reply to topic Reply with quote
Don wrote:
Adam Hair wrote:
Don wrote:
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 Smile

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?



Elo = 6028.21*e^(-12.48/(Name+8.95))

This equation fits your data well and is asymtopic to Elo = 6028.21.

Of course, 6028.21 Elo is only relevant to the Elo values assigned in your data. But, your engine, limited to only 2^18 nodes per move, seems to be ~2900 Elo away from perfection. If you let it search 2^1,000,000 nodes per move, Komodo will play virtually perfect chess (according to this model, its Elo would be 6028.13). 2^10,000 nodes/move would be within 8 Elo of perfection.


I find 4500 to be a much more believable figure than 6028 - but what do I know? It could be anything!

BTW I adjusted my data so that version 00 is calibrated to 1500 ELO - I think that is within about 100 or 200 ELO of the truth. Komodo is doing about 3.18 ply on average. At level 02, Komodo would be about 433 ELO stronger or 1933 doing on average 5.37 ply.

What would be interesting is to run the same experiment with a different program using the same basic formula (with adjusted constants) and see if they agree!


I think that it is probably closer to 4500 than 6000 also. But you are right; it could be any number.

I started a fixed node test this morning with Gaviota. I could start over using 512 nodes as the base.
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Subject Author Date/Time
Elo Increase per Doubling Adam Hair Mon May 07, 2012 11:40 am
      Re: Elo Increase per Doubling Julien MARCEL Mon May 07, 2012 12:04 pm
            Re: Elo Increase per Doubling Adam Hair Mon May 07, 2012 4:48 pm
                  Re: Elo Increase per Doubling Julien MARCEL Mon May 07, 2012 4:54 pm
            Re: Elo Increase per Doubling Adam Hair Mon May 07, 2012 8:50 pm
                  Re: Elo Increase per Doubling Julien MARCEL Mon May 07, 2012 9:00 pm
                        Re: Elo Increase per Doubling Mark Pearce Thu May 10, 2012 4:43 pm
      Re: Elo Increase per Doubling H.G.Muller Mon May 07, 2012 12:13 pm
            Re: Elo Increase per Doubling Michel Van den Bergh Mon May 07, 2012 2:01 pm
            Re: Elo Increase per Doubling Adam Hair Mon May 07, 2012 5:12 pm
                  Re: Elo Increase per Doubling Don Dailey Mon May 07, 2012 6:40 pm
                        Re: Elo Increase per Doubling Robert Wagner Campos Tue May 08, 2012 12:38 am
                              Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 3:32 am
                                    Re: Elo Increase per Doubling Adam Hair Tue May 08, 2012 10:02 am
                                          Re: Elo Increase per Doubling Julien MARCEL Tue May 08, 2012 10:55 am
                                                Re: Elo Increase per Doubling Adam Hair Tue May 08, 2012 8:08 pm
                                          Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 11:29 am
                                          Re: Elo Increase per Doubling Kai Laskos Tue May 08, 2012 11:59 am
                                                Re: Elo Increase per Doubling Adam Hair Tue May 08, 2012 8:13 pm
                                                      Re: Elo Increase per Doubling Kai Laskos Tue May 08, 2012 10:21 pm
                                                            Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 10:52 pm
                                                            Re: Elo Increase per Doubling Adam Hair Tue May 08, 2012 11:14 pm
                                                                  Re: Elo Increase per Doubling Kai Laskos Wed May 09, 2012 12:20 am
                                                                        Re: Elo Increase per Doubling Adam Hair Wed May 09, 2012 2:44 am
                                                                              Re: Elo Increase per Doubling H.G.Muller Wed May 09, 2012 8:05 am
                                                                                    Re: Elo Increase per Doubling Adam Hair Wed May 09, 2012 5:12 pm
                                                                                          Re: Elo Increase per Doubling Larry Kaufman Thu May 10, 2012 3:11 am
                                                                                          Re: Elo Increase per Doubling Don Dailey Thu May 10, 2012 5:03 am
                                                                                          Re: Elo Increase per Doubling Larry Kaufman Thu May 10, 2012 5:19 am
                                                                                          Re: Elo Increase per Doubling Don Dailey Thu May 10, 2012 12:43 pm
                                                                                          Re: Elo Increase per Doubling Peter Österlund Thu May 10, 2012 4:59 pm
                                                                                          Re: Elo Increase per Doubling Julien MARCEL Thu May 10, 2012 5:09 pm
                                                                                          Re: Elo Increase per Doubling Don Dailey Thu May 10, 2012 5:41 pm
                                                                                          Re: Elo Increase per Doubling Don Dailey Thu May 10, 2012 5:46 pm
                                          Re: Elo Increase per Doubling Ed Schroder Tue May 08, 2012 12:09 pm
                                                Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 12:10 pm
                                                      Re: Elo Increase per Doubling Ed Schroder Tue May 08, 2012 12:28 pm
                                                            Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 12:36 pm
                                                                  Re: Elo Increase per Doubling Ed Schroder Tue May 08, 2012 1:15 pm
                                                                        Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 2:37 pm
                                                                              Re: Elo Increase per Doubling Julien MARCEL Tue May 08, 2012 3:15 pm
                                                                                    Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 6:15 pm
                                                                                          Re: Elo Increase per Doubling Peter Österlund Tue May 08, 2012 8:06 pm
                                                                                          Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 8:25 pm
                                                                                          Re: Elo Increase per Doubling Peter Österlund Tue May 08, 2012 9:00 pm
                                                                                          Re: Elo Increase per Doubling Julien MARCEL Tue May 08, 2012 9:02 pm
                                                                                          Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 9:06 pm
                                                                                          Re: Elo Increase per Doubling Don Dailey Wed May 09, 2012 4:26 pm
                                                                                          Re: Elo Increase per Doubling Peter Österlund Wed May 09, 2012 4:52 pm
                                                                                          Re: Elo Increase per Doubling Don Dailey Wed May 09, 2012 5:19 pm
                                                                                          Re: Elo Increase per Doubling Don Dailey Thu May 10, 2012 1:41 pm
                                                                                          Re: Elo Increase per Doubling Don Dailey Thu May 10, 2012 4:52 pm
                                                                                          Re: Elo Increase per Doubling Adam Hair Thu May 10, 2012 9:07 pm
                                                                                          Re: Elo Increase per Doubling Don Dailey Thu May 10, 2012 10:55 pm
                                                                                          Re: Elo Increase per Doubling Adam Hair Fri May 11, 2012 12:46 am
                                                                                          Re: Elo Increase per Doubling Adam Hair Fri May 11, 2012 1:06 am
                                                                                          Re: Elo Increase per Doubling Don Dailey Wed May 09, 2012 5:00 pm
                                                                                          Re: Elo Increase per Doubling Adam Hair Tue May 08, 2012 9:05 pm
                                                                                          Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 9:18 pm
                                                                                          Re: Elo Increase per Doubling Adam Hair Tue May 08, 2012 11:26 pm
                                                                                          Re: Elo Increase per Doubling Don Dailey Wed May 09, 2012 2:50 am
                                                                                          Re: Elo Increase per Doubling Adam Hair Tue May 15, 2012 3:17 am
                                                                                    Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 6:23 pm
                                          Re: Elo Increase per Doubling Ed Schroder Tue May 08, 2012 12:18 pm
                                                Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 12:25 pm
                                                      Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 12:27 pm
                                                            Re: Elo Increase per Doubling Robert Hyatt Tue May 08, 2012 3:36 pm
                                                                  Re: Elo Increase per Doubling Don Dailey Tue May 08, 2012 5:32 pm
      Re: Elo Increase per Doubling Daniel Shawul Fri May 11, 2012 5:48 pm
            Re: Elo Increase per Doubling Don Dailey Fri May 11, 2012 6:30 pm
                  Re: Elo Increase per Doubling Julien MARCEL Fri May 11, 2012 6:52 pm
                        Re: Elo Increase per Doubling Don Dailey Fri May 11, 2012 7:05 pm
                  Re: Elo Increase per Doubling Daniel Shawul Fri May 11, 2012 7:08 pm
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