This may very well be. Nevertheless it surprises me that 35 of the 50 "all time" best are no longer in top 100, whereas 85 of current top 100 are not within the 50 "all time" best (if that is what typohh's list represents).

Let's take one example: Tien

He's currently 35/100, and doesn't make it to typohh's list. However, his best kgs ranking has been much stronger than demonhunt's (43/50 on typohh's list):

http://www.gokgs.com/graphPage.jsp?user=Tien
http://www.gokgs.com/graphPage.jsp?user=demonhunt

Might it be that typohh's list is based on older data?

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Since he doesn't have tartrate, whatever it is, it's not all time strongest. Perhaps it doesn't have data for players whose accounts lapsed?

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Taking a close look at the produced rankings (in more detail than shown here), I found that many of the players with only few games got stuck at local maximums. Made a new version that hopefully overcomes that problem, well see. I have the kgs 6dan and stronger games for a 2 year period, spanning from from 6.2010 to 5.2012.

Alot of bugs fixed again. Here are a 1000 iteration version of KGS ranks based on only the last years game. The reason why some names dont show up on kgs top 100 is because they dont have a solid rank. But for example Butterfly2[9d?] has played 6 games against solid kgs high-dans and won all games. Anyways, let me know if you find anything weird in the results, so I can track down any remaining bugs.

Butterfly2 (2012.4) : 2.61 (29 games)
qiusf (2013.1) : 2.59 (2 games)
kyoungnang (2012.5) : 2.53 (47 games)
MilanMilan (2012.12) : 2.49 (78 games)
xliu101 (2012.12) : 2.42 (24 games)
himountain (2012.12) : 2.36 (45 games)
eku (2012.6) : 2.13 (10 games)
XuanXuanGo (2013.2) : 1.97 (39 games)
Korondo (2012.6) : 1.96 (20 games)
high77 (2012.9) : 1.94 (5 games)
cloudnotes (2012.9) : 1.89 (57 games)
unlocke (2012.12) : 1.87 (7 games)
Hutoshi4 (2012.12) : 1.83 (54 games)
kghin (2013.1) : 1.74 (44 days)
bigbadwolf (2012.12) : 1.71 (38 games)
hjekshdf (2012.11) : 1.7 (83 days)
gowithwi (2012.6) : 1.69 (15 games)
cashewnut (2012.11) : 1.69 (11 games)
pblshtwzrs (2012.5) : 1.66 (12 games)
tooweak (2012.5) : 1.6 (15 games)
sweetrip (2012.8) : 1.57 (13 games)
channaisan (2012.5) : 1.53 (3 games)
smartrobot (2012.4) : 1.5 (38 games)
Firework (2012.5) : 1.49 (9 games)
greenpig (2012.4) : 1.48 (8 games)
mysterious (2012.10) : 1.47 (11 games)
Evildoer (2012.6) : 1.45 (5 games)
hoobastank (2012.8) : 1.44 (23 games)
floosy (2012.7) : 1.39 (7 games)
iamlunatic (2012.8) : 1.34 (13 games)
bin7674 (2012.9) : 1.34 (7 games)
goliard (2012.7) : 1.33 (95 days)
sztanguo (2012.12) : 1.3 (4 games)
roln111 (2013.1) : 1.29 (29 days)
Illuminati (2012.10) : 1.29 (45 games)
billlin (2012.9) : 1.28 (67 games)
suicidal (2012.4) : 1.24 (6 games)
mashup (2012.10) : 1.23 (24 games)
akila (2012.10) : 1.23 (8 games)
okao (2013.2) : 1.22 (70 games)
kathy (2012.5) : 1.22 (2 games)
CoolKid (2013.1) : 1.22 (2 games)
supertjc (2013.1) : 1.19 (60 days)
about2d (2012.6) : 1.19 (28 games)
TiltGo (2013.1) : 1.18 (12 games)
jove (2013.1) : 1.1 (36 games)
princewz (2012.11) : 1.09 (56 games)
xmengzhu (2012.10) : 1.02 (109 days)
Donsaku (2012.9) : 1.01 (29 games)
toobad (2012.5) : 1.0 (17 games)

Published version 4 of the list (on first page), found a way to avoid getting trapped in local maximums at the expense of considerable cpu time. This version is only based on 475 iterators so far, so the order may still change quite a bit as I let it run over night. But for now I'm quite satisfied with how the list looks.

I only have high dan games to use for my analysis (from http://www.u-go.net/gamerecords/). And Tien's current rank is based on winning against a 2dan and a 4dan with high handicap. Those low dans dont connect in any way to other players, hence the wins are effectively meaningless. What is to say tien's win wasnt against a 20kyu and 18kyu, with 6 handicap? Not very impressive. After all, since I dont have those players other games, there is no way to measure their strength and there by Tien's strength.

Maybe it is the beer, but did Cho Chikun's peak move back from 1998 in you first try to 1981 in the 4th? I was happy to root for the original. Now I just need more beer...

Ok, thanks, I didn't look at his games (I assumed he had his share of high-dan games, too). That explains it for him (and perhaps for many other players, too).

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Cho Chikun is kinda famous for remaining at the top of his game for a really long period of time?

Version 5 posted, which is the same as version, except it has 2500 runs, instead of 750. Major difference seems to be a radical decrease in older generation players.

So are you trying to prove that the KGS algorithm is good or that it is ridiculous and unstable?

Can you at least include confidence intervals or something?

Its not really unstable, just saying that it needs sufficient iterations, but that takes time to calculate. Effects of the wins and losses didn't have enough time to propagate far enough with few iterations. Hence I posted an early version with fewer iterations, and later updated it with another with more iterations.



CI is +-0.2 from sample size, assuming its measured in days, not in games. In general you can probably add in another +-0.05 stone to the CI from rank change during time window. And finally some cascade effects for maybe another +-0.1 CI. Ill update it so that it actually calculates the correct CI (as far as possible).

Had my computer calculating all time KGS strongest players for 2 days, managing 2900 iterations on the over 100k games. Updated the results to first post. Used the data available at http://www.u-go.net/gamerecords/. These are good preliminary results I think, but there are quite a few improvements I still need to make.

One problem I could use some help with is. Should I apply the distribution of player strength (each stone stronger is 2.22.. time more unlikely, proven to be quite reliably estimate, looking at any number of sources) during each phase of the iterations, or only when the final rank is calculated? Any opinions?

Another is I need to find a formula for calculating standard deviation in rank for time difference. For example, how much does a players rank change in a year, on average. I could then use that information to calculate the time frame I should use for each player so as to minimize the resulting standard deviation. Instead of the current 85 games, regardless in what time frame those 85 games were played.

Also, I need a better algorithm for finding the most likely rank at any given time, when I have decided upon the weights for games. Currently I just so somewhat random sampling in the search space (rank) to find the most likely rank, but very unefficient method of finding it, not to mention time consuming. Problem is if I try to optimize it too much I risk getting the result stuck in local maximum.

Regardless of the randomness involved in the whole process. The results seem to be remarkably consistent between runs (given same number of iterations), with only a few players changing order.

Updated to version 6 (in first post), finally have confidence intervals for players ranks. As it stands here is how the algorithm works.

Assumptions :
- 6.5 is a fair komi.
- Probability of weaker player winning is 0.5*(0.2383^strength_difference)
- Standard deviation in a players rank is 0.08 stones after 1 year.
- Standard deviation of all ranks is 1.12 stones.
- Each stone in strength is only 40% as likely as the previous.

When determining the rank for one player, at a specific game, all his game results are used. Each game result is given a weight, based upon a bell curve over time. The "width" of the bell curve is chosen such as to minimize the standard deviation. Too wide and we include games so far away in time that the players rank may have changed. Too narrow and we wont get enough samples. Then the most likely rank explaining all the game results, with given weights is chosen as the players rank at the specified game. We then perform this process for both players at every game. Since opponents ranks have changed, we need to recalculate everything, over and over again. Slowly approaching a balance (nash equalibrium), where we have a rank for each player at each of their games, that best explains all their game results.

Im tempted to dynamically try to set many of the assumptions, but afraid of the potential feedback loops.

Another big update. The GoGoD result should be accurate now. Included the most active players, that did not make it into the top 25, to both lists.

Two more major bugs crushed. Maybe, just maybe, its finally starting to give proper results. Updated first post results for GoGoD, and also added section for who are currently the strongest.

kitahama had the highest rating graph I've ever seen on KGS, it was something like 25d+. The only way to follow it was to make a mental note as to what month it knocked the "9d" marker off of the bottom of the graph and reference everything to that.

So do you think this algorithm is good enough to beat a spread wager?