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Hello all,

GS and AGS3 grades for 2009 and 2010...

Please note that I have estimated AGS3 grades for 2009 and 2010 using GS grades for 2009 published in gradeslive.csv and GS grades for 2010 published in grades2010v1.csv. (I assumed that 2008 EGS3 grades are equal to 2008 GS grades and that number of games on which 2008 GS and AGS3 grades are based is 0.)

The G30 rule below has been taken into account in the calculation.

Rule G30: The Grade is calculated by dividing the total number of points scored by the number of games played. If there are at least 30 games in the current period, then the Grade is based on these games alone. If there are not, results are brought forward from the previous period to make the total up to exactly thirty. If there are not 30 games in the two seasons together, results are taken from the season before that. Games are never taken from further back than this; the maximum is two prior grading periods.

The results can be found in ags3grade10.zip file which can be downloaded from... http://www.jurjevic.org.uk/chess/grade/. The Zip file contains ags3grade09.txt (textual tab delimited), ags3grade09.xls (Excel spreadsheet document), gradeslive.csv (Excel spreadsheet document, official 2009 grades), gs3grade10.txt (textual tab delimited), ags3grade10.xls (Excel spreadsheet document) and grades2010v1.csv (Excel spreadsheet document, official 2010 grades, version 1).

The calculation was performed by a Windows .net console (command line) application written in C# programming language interfacing with Oracle Database 10g Express Edition database. Histograms are obtained with Mathematica 7 (I saved relevant data in a database, I have no game results as they are not published, but as GS's and AGS3's formulae are identical and the only difference is in the value of 'k' factors, one can estimate AGS3 grades using GS grades and no actual game results, the C# program was written by me, Oracle Database 10g Express Edition database is free, but it has limitations imposed, some or all of which are lifted in commercial versions).


Figure 1: Histogram for 2009 GS grades (consisting of 10153 grades in bins [0,1), [1,2), etc., of 1 grading point width, where minimum grade is 0.00, median grade is 133.00, maximum grade is 281.00, mean grade is 133.69 and standard deviation is 37.05).


Figure 2: Histogram for 2009 AGS3 grades (consisting of 10153 grades in bins [0,1), [1,2), etc., of 1 grading point width, where minimum grade is 0.00, median grade is 133.50, maximum grade is 281.00, mean grade is 133.55 and standard deviation is 36.73).


Figure 3: Histogram for 2010 GS grades (consisting of 10074 grades in bins [0,1), [1,2), etc., of 1 grading point width, where minimum grade is 0.00, median grade is 133.00, maximum grade is 276.00, mean grade is 133.32 and standard deviation is 37.47).


Figure 4: Histogram for 2010 AGS3 grades (consisting of 10074 grades in bins [0,1), [1,2), etc., of 1 grading point width, where minimum grade is 0.00, median grade is 132.85, maximum grade is 276.00, mean grade is 133.08 and standard deviation is 36.99).

(I can't see any obvious behavioural histogram-related difference between GS and AGS3 grades. If anybody see anything could he or she please share his or her opinion with us. Thanks.)

Grading anomalies...

My point in a nutshell is that the 'k' factors (wrongly chosen) in the current grading system are causing the grade stretching and that the amount of stretch (due to the 'k' factors) is larger (in fact it is equal to '|p - q|') than grade fluctuations caused by other anomalies which may be corrected by using FIDE logistic relation for 'p = f(d)', Glickman idea on changing less trusted grades (based on frequency of play) faster than more trusted grades, or even a solution to the "junior problem".

In my opinion three candidates for replacing GS are AGS3, ÉGS5 and ÉGS6, with ÉGS6 as the best and ÉGS5 as the second best.

AGS3 is GS with the 'k' factors equal to '1/2' (the ECF's linear approximation is used for 'p = f(d)'; does not stretch the grades). (The only difference between GS and AGS3 is in 'k' factors in their formulae which are '1/2' in AGS3 and '1' in GS.)

ÉGS5 is sort of ECF equivalent of FIDE's Élo (logistic curve is used for 'p = f(d)', this is regarded as more accurate than the ECF's linear approximation; the grades are ECF grades, not FIDE ratings, i.e., a strong grandmaster is about 270 not 2800; grading is done every season rather than after every tournament; does not stretch the grades).

ÉGS6 has similar improvement (taken in a simple from) over ÉGS5 as Glicko has over FIDE's Élo which accounts for a grade trust (or establishment) based on frequency of play (i.e., less trusted or established grades change more rapidly than more trusted or established grades, consequently, in extreme case, ungraded players do not affect the grades of graded players; uses logistic curve for 'p = f(d)'; does not stretch the grades).

More details (including formulae, logical argument, etc.) can be found at:

http://www.jurjevic.org.uk/chess/grade/ ... malies.htm

Am I sure...

Of course not, it is only my belief.

I published AGS3 grades in case somebody would like to examine the difference in behaviour between GS (official) and AGS3 (in my opinion the simplest 'improvement' over official grading system) grades.

Maybe my definition of 'grade stretching' is not what the problem was (and why new GS grades were introduced), but at least it is a try.

Kind regards,

Hello all,

Peter Lalic vs Robert Jurjevic though experiment or on a possible mechanism of grade stretching...

Peter Lalic is a chess colleague and a friend of mine whose GS grade was changed from 158 in 2008 to 185 in 2010. According to AGS3 Peter's 2010 grade should have been 177 (his AGS3 grade in 2008 was taken to be the same as GS grade, i.e. 158). Robert Jurjevic (that is me) is a weaker chess player whose grade remained pretty much constant during that period at approximately 120 (both Robert's GS and AGS3 grades were 122 in 2008 and are 121 in 2010).

Let us assume that Peter and Robert decided to play a match (of sufficiently enough games) in 2011. If both players perform as expected (as their grades suggest) then according to GS Peter should score 95.1% and according to AGS3 93.0% in the match (calculated assumed logistic relationship between expected performance and grade difference, note that the grade difference is greater than 30, so one should use more accurate relationship between expected performance and grade difference). It seems that both 95.1% and 93.0% cannot be true at the same time. Which of the estimates of Peter's expected performance is more accurate?

Let us assume that Peter scored 93.0% in the match (exactly what was expected by AGS3). According to GS grades Peter under-performed in the match. This can be due to a fact that during the match Robert became relatively stronger to Peter. Another explanation could be that both Peter and Robert indeed did perform as expected (i.e. Robert's relative strength to Peter hasn't changed) but that grades were not correctly calculated. If that was the case one may have corrected Robert's grade to be 129 (it may be better to leave the grade of the stronger player unchanged) in order to match Peter's performance of 93.0%.

Let us assume now that somehow an analysis has been made which shows that all stronger players in general under-perform against weaker players. Then one may assume that this is not due to the fact that all weaker players improved in respect to stronger players (what is statistically very unlikely) but rather that something is wrong with the grade calculation. If that is the case one can make a correction to weaker player grades (increasing them) to match the observed performance of the stronger players in games against weaker players (this correction was done in 2008 and my grade went from the old 90ish to a new 120ish). My understanding is that this phenomenon was referred to as "grade stretching" (as it would seem that grade difference between stronger and weaker players is higher than what performance results suggest it should have been).

If we assumed that Peter's 2010 grade was 177 as suggested by AGS3 (rather than 185 as suggested by GS) Peter's performance of 93.0% in the match would have been exactly what one would expected and the general conclusion may have been that the stronger players when playing against weaker players do perform as expected on average (hence no grade correction would have been needed).

How AGS3 grades may be used...

My intention is to keep calculating and publishing AGS3 grades until 2013. In 2013 one may perform an analysis which establishes if all stronger players in general under-perform against weaker players or not (a similar analysis which has already been done and led to grade correction in 2008, I understand), first using GS, then AGS3 grades (2013 is chosen in order to gather 5 years of AGS3 grade data, I understand that 5 year grade data was used in the original analysis which had lead to grade corrections in 2008). If GS grades suggest that the stronger players under-perform in the games against weaker players in general and AGS3 that they do not, then it is likely that my assumption about what is causing grade stretching was correct.

If it would be shown that AGS3 does not stretch the grades and GS does then ECF may adopt AGS3 grades (which would already have been calculated by me) as official grades for 2013 and continue calculating grades in 2014, 2015, etc. either using AGS3 or ÉGS6 (which would have been better than AGS3 in cases where grade difference is greater than 30, and where players do play only a few games per season, their grade would charge more rapidly as it is less trusted as it is based on older games, also players who play more games wouldn't be so much affected by the results of games they play against players who play fewer games, their grade would change less rapidly as the grades of their opponents are less trusted, and in extreme case the games ungraded players play against graded players wouldn't affect the grades of graded players at all, actually as an extension to ÉGS6 there is a proposal in http://www.jurjevic.org.uk/chess/grade/ ... malies.htm in "Ungraded players" section for calculation of grades of ungraded players based only on the game results with no need for or reference to the estimated grades).

AGS3 and ÉGS6 (with the mentioned extension for grade calculation of ungraded players) would not require any change in gathering data or timing when the collection or calculation is done, etc., and all the procedures would remain the same. The only difference would have been in a method of calculation which would anyway be given to a computer program to do. AGS3 has a benefit of the same simplicity as GS, so a calculation by hand would still be possible if AGS3 is used.

Peter Lalic's chess videos...

Please allow me to let you know (as a digression) that Peter has done some I would dare to say great chess videos. Some of the selected videos can be found at...
http://www.ashteadchessclub.org/html/lalic.html

Peter's YouTube Channel is at...
http://www.youtube.com/user/DraganLalic

Kind regards,

Hello all,

Delta grade histograms...

Please find below delta grade histograms for GA and AGS3 grades for 2009 and 2010 (2009 GS delta grade is defined as 2009 GS grade minus 2008 GS grade, 2009 AGS3 delta grade is defined as 2009 AGS3 grade minus 2008 AGS3 grade, 2010 GS delta grade is defined as 2010 GS grade minus 2008 GS grade, 2010 AGS3 delta grade is defined as 2010 AGS3 grade minus 2008 AGS3 grade).

Delta grade is equal to a number of grading points one's 2009, 2010, etc. GS or AGS3 grade has changed in respect to his or her 2008 GS or AGS3 grade (year when new GS grades were introduced) and it is a measure or players' GS or AGS3 improvement or decline in 2009, 2010, etc. since 2008.


Figure 1: Histogram for 2009 GS delta grades (consisting of 8624 delta grades in bins [0,1), [1,2), etc., of 1 delta grading point width, where minimum delta grade is -38.00, median delta grade is 0.00, maximum delta grade is 63.00, mean delta grade is 0.33 and standard deviation of delta grades is 8.13; delta grade is defined as 2009 GS grade minus 2008 GS grade).


Figure 2: Histogram for 2009 AGS3 delta grades (consisting of 8624 delta grades in bins [0,1), [1,2), etc., of 1 delta grading point width, where minimum delta grade is -19.00, median delta grade is 0.00, maximum delta grade is 31.50, mean delta grade is 0.16 and standard deviation of delta grades is 4.07; delta grade is defined as 2009 AGS3 grade minus 2008 AGS3 grade).


Figure 3: Histogram for 2010 GS delta grades (consisting of 7582 delta grades in bins [0,1), [1,2), etc., of 1 delta grading point width, where minimum delta grade is -39.00, median delta grade is 0.00, maximum delta grade is 80.00, mean delta grade is 0.52 and standard deviation of delta grades is 10.96; delta grade is defined as 2010 GS grade minus 2008 GS grade).


Figure 4: Histogram for 2010 AGS3 delta grades (consisting of 7582 delta grades in bins [0,1), [1,2), etc., of 1 delta grading point width, where minimum delta grade is -23.39, median delta grade is -0.10, maximum delta grade is 47.75, mean delta grade is 0.39 and standard deviation of delta grades is 6.60; delta grade is defined as 2010 AGS3 grade minus 2008 AGS3 grade).

Kind regards,

Players' list in grade improvement order for 2010 season since 2008 season...

Please find the players' list in grade improvement order for 2010 season since 2008 season (PDF document) at:
http://www.jurjevic.org.uk/chess/grade/10i08.pdf

column legend:

NO - ordinal number based on player's GS grade improvement in 2010 season since 2008 season
REF - ECF grading reference ID
NAME - full player's name
SEX - player's sex
FIDECODE - player's FIDE code
NATION - player's nationality
GAMES - number of standard graded games the player played in 2010 season
CATEGORY - 2010 season grading category based on GAMES
GS - player's GS grade for 2010 season
AGS3 - player's AGS3 grade for 2010 season
GSLAST09 - player's GS grade for 2008 season
AGS3LAST09 - player's AGS3 grade for 2008 season
GS-GSLAST09 - player's GS grade improvement in 2010 season since 2008 season
AGS3-AGS3LAST09 - player's AGS3 grade improvement in 2010 season since 2008 season

GS grade - official ECF current Grading System grade
AGS3 grade - ECF Amended Grading System three grade
(player's AGS3 grade for 2008 season was taken to be the same as player's GS grade for 2008 season)

P.S. ...

what is PDF?
http://en.wikipedia.org/wiki/Portable_Document_Format

download PDF reader
http://get.adobe.com/uk/reader/enterprise/

Error in calculation of 2010 AGS3 grades...

I said...

"Please note that I have calculated AGS3 grades for 2009 and 2010 using GS grades for 2009 published in gradeslive.csv and GS grades for 2010 published in grades2010v1.csv. (I assumed that 2008 EGS3 grades are equal to 2008 GS grades and that number of games on which 2008 GS and AGS3 grades are based is 0.)"

"The calculation was performed by a Windows .net console (command line) application written in C# programming language interfacing with Oracle Database 10g Express Edition database. Histograms are obtained with Mathematica 7 (I saved relevant data in a database, I have no game results as they are not published, but as GS's and AGS3's formulae are identical and the only difference is in the value of 'k' factors, one can calculate AGS3 grades using GS grades and no actual game results, the C# program was written by me, Oracle Database 10g Express Edition database is free, but it has limitations imposed, some or all of which are lifted in commercial versions)."

I have realized that the statement ... "one can calculate AGS3 grades using GS grades and no actual game results" ...may not be true. (Calculation of AGS3 grades may not be possible without the game results.)

The formula I used is...
and the formula I should have used is...
where 'A2' is new AGS3 grade, 'A1' current AGS3 grade, 'a2' new GS grade, 'a1' current GS grade, 'p' expected performance based on GS grades and 'P' expected performance based on AGS3 grades.

I overlooked that 'p - P' is not zero.

'p - P' can be calculated from the actual game results, but if I would have actual game results I would use direct AGS3 formulae (so there would be no need to calculate 'p - P'), moreover then I would be able to calculate ÉGS6 grades as well.

It is possible that 'p - P' can be approximated by...
where 'a0' is previous GS grade, so that the formula for calculating new AGS3 grade, 'A2', may be...
where 'A2' is new AGS3 grade, 'A1' current AGS3 grade, 'a2' new GS grade, 'a1' current GS grade and 'a0' previous GS grade.

(The above approximation assumes that the average GS grade of the player's opponents did not change, which may be a fair assumption, but obviously needs not to hold in every case.)

If the above approximation is good enough I will correct AGS3 grades for 2010 (AGS3 grades for 2009 are correctly calculated as for 2009 'p - P = 0' by definition) and continue to calculate AGS3 grades for 20011, 2012, etc. using the above formula.

Correction of 2010 AGS3 grades...

The formula I used was...
and the formula I should have used is...
where 'A2' is new AGS3 grade, 'A1' current AGS3 grade, 'a2' new GS grade, 'a1' current GS grade, 'p' expected performance based on GS grades and 'P' expected performance based on AGS3 grades.

I erroneously used 'A2 = a1 +...' instead of 'A2 = A1 +...' and I overlooked that 'p - P' is not zero.

(This affects only calculation of 2010 AGS3 grades and onwards. 2009 AGS3 grades were calculated correctly, as for 2009 AGS3 grades 'a1 = A1' and '(p - P)/2 = 0'.)

(All the relevant files mentioned in the previous posts have been updated (namely ags3grade10.zip and 10i08.pdf), histogram for 2010 AGS3 grades and histogram for 2010 AGS3 delta grades have been also updated.)

AGS3 grades cannot be accurately calculated using only published GS grades, but can be estimated using formula...
where 'A2' is new AGS3 grade, 'A1' current AGS3 grade, 'a2' new GS grade, 'a1' current GS grade and 'a0' previous GS grade.

The above approximation assumes that the average GS grade of the player's opponents did not change (between current and previous season), which may be a fair assumption, but obviously needs not to hold in every case. The assumption is equivalent to approximating 'p - P' with...
where 'a0' is previous GS grade and 'a1' current GS grade.