When is the new grading list coming out?

[John Upham]

Errrr, why does everyone seem to know more than me

Have you been asking the rating team searching questions?

[Ola Winfridsson]

Roger, this is of course a valid point in the sense that it's indeed occurring, but surely far too much is made of the influence of foreign players in individual tournaments as well as the effect of leavers and joiners? After all there are some 8,500 players on the list and the number of foreign players disappearing from one year to the next (having played in Gibraltar, Hastings or Isle of Man) can't exceed 300? And even if they tend to be concentrated at the higher end of the scale, this has been going on ever since the Grand Prix series kicked off in the early 1970s (I distinctly remember a number of Yugoslav GMs and IMs taking many of the top spots in those days).

The year-on-year effect of this ought to be negligible since they should more or less cancel each other out (new foreign players coming in to replace the ones disappearing, and the standard of joiners and leavers being roughly equal year after year).

[Alex Holowczak]

Errrr, why does everyone seem to know more than me

Have you been asking the rating team searching questions?

Well, if he's the one who has to make the changes to the website, I suppose he would naturally assume that he'd be notified about a future requirement to get the grades republished.

[Roger de Coverly]

And even if they tend to be concentrated at the higher end of the scale, this has been going on ever since the Grand Prix series kicked off in the early 1970s (I distinctly remember a number of Yugoslav GMs and IMs taking many of the top spots in those days).

The policy on whether to include or exclude visiting tournament players has varied over the years. Most published lists from that era excluded them unless there was evidence that the player was UK resident.

The year-on-year effect of this ought to be negligible since they should more or less cancel each other out (new foreign players coming in to replace the ones disappering, and the standard of joiners and leavers being roughly equal year after year).

I don't disagree but it needs to be demonstrated to those who prefer to use the recursion iteration for inflation/deflation checking to looking at the published lists.

[Roger de Coverly]

Well, if he's the one who has to make the changes to the website, I suppose he would naturally assume that he'd be notified about a future requirement to get the grades republished.

There's a scheduled update at the end of August. This is usually purely administrative, adjusting for any missing or incorrectly reported results, amalgamating new players, correcting names, ages etc.

I hear that the grading team met last weekend

Do we know who they actually are and who takes the decisions?

[Ola Winfridsson]

The year-on-year effect of this ought to be negligible since they should more or less cancel each other out (new foreign players coming in to replace the ones disappering, and the standard of joiners and leavers being roughly equal year after year).

I don't disagree but it needs to be demonstrated to those who prefer to use the recursion iteration for inflation/deflation checking to looking at the published lists.

True, although I have a feeling that it'll be "impossible" to prove them wrong - the basis of the argument will just be changed slightly.

[Brian Valentine]

If have defined overseas players as those who are not Blank, England, Ireland, Wales or Scotland. There are 529 of them listed of which 334 have a grade in 2008 and 403 in 2009. There average grade for both years is in the mid 190s. There is not enough data to work out what effect they may have, as if they don't play the following year then they will not add or take points from "local" players in either year. In the first year they are given a grade, but this is not used for grading locals and in the following year they do not play. There is potential for major distortions, but this is unlikely to be the case last year.

However they will distort the numbers I gave for effective average grades of leavers and joiners. While they count in the averages they will be adding far less proportionately to any inflation and deflation within the system.

[Roger de Coverly]

In the first year they are given a grade, but this is not used for grading locals

Actually it's used as a "estimated" grade to calculate domestic players. All the EU players in the 2008 Liverpool had (presumably recursion based) grades calculated. In at least one case, playing a 2300s player was not as good for one's event performance as it might seem because their grade came out at 180 and something.

If have defined overseas players as those who are not Blank, England, Ireland, Wales or Scotland.

Some of the Irish, Welsh and Scots players only play in one "English" event a season as well- The system busting Mr Rough being one.

[Ola Winfridsson]

Brian, I have to confess that I don't quite understand the argument. I'm now going to talk in generalities:

Leaving the tinkerings of 2008 and 2009 aside (because the system is being manually manipulated to a far greater extent than normally), if a foreign player plays one or two tournaments in this country, he will have his grade calculated for next year's list and his opponents results will then be calculated on the basis of his results = his performance in the/those tournament(s) used as an estimated grade (not the estimated grade used in the tournament, which of course may have influenced the opponent's approach to the game, and there's always a risk of the estimate being horribly incorrect, but in general the estimated grade is also likely to be fair). This calculated grade will in all likelihood reflect his real playing strength.

The aim of a grading system is to give a reasonably accurate picture of playing strength for the each individual in the entire chess playing community. The fact that some people on the grading list have played foreigners (whose calculated grades reasonably accurately reflect their strength) is actually of less importance because the results against those foreigners should, on the balance of probabilities, be roughly the same as if the player had faced native players of the same strength.

The fact that the foreigners on the list for year Y (reflecting the results of year X) are unlikely to play in any tournaments during the season Y/Z is more or less irrelevant since they're likely to be replaced by other foreigners of approximately the same strength and in similar numbers (there are always minor fluctuations between years).

I don't see how this could have any significant potential for major distorsions. Yes, the odd foreigner will over- or underperform extremely, but that is the case also with domestic players.

[Brian Valentine]

Roger, You are right, I don't know where I lost the thread, but will have to rethink my position on overseas influence. And I might end up agreeing with Ola.

It's difficult to draw the line on domestic and overseas; I took the view that many of the "blanks" would not regard themselves as English and my formula was already unwieldy, so excluded the channel Islands from the list.

[Roger de Coverly]

Roger, You are right, I don't know where I lost the thread, but will have to rethink my position on overseas influence. And I might end up agreeing with Ola.

I think you just have to be aware that they are there and potentially affect the averages if their numbers fluctuate. You might need to be careful with any analysis of E grades. With a mimimum inclusion standard of 9 games, all players at Hastings and similiar international open tournament will find themselves in the list.

There is a belief in some quarters that the fact that A graded players have higher average grades than E graded players is somehow a deflationary factor. So we need more international tournaments to combat deflation.

[Sean Hewitt]

My sources inform me that there was a very recent ECF Board meeting at which this matter was discussed and it was decided to ignore the disaster that is the new rating list on the grounds that it would sort itself out within a year!

I hear that the grading team met last weekend to consider various of the issues which had been raised with them (e.g. through the 'contact' page on the grading website, and some emails). They are making further calculations which I hope we will hear about in due course (by next weekend). So something is being done to improve matters. That is about all I know.

So, which is it?!!

[John Upham]

So, which is it?!!

Hopefully what NC has reported!

What is the best we can expect?

[E Michael White]

I have decided to make this posting because there is a need to know/show :-

1. the underlying formula for new starters
2. the range of new starter grades that may result
3. to ensure that more players are aware of what is happening as I expect the grading team will make/suggest changes
4. that the estimated grades to start the current process off are not necessary
5. consider the effects of the widened range of new starter grades
6. assess what deflationary and spread pressures this process produces

I am sorry this posting is so long but I wanted to put down what I believe is happening within the new starter process as there is insufficient information about it. Also many players seem interested in the new grading system judging by the views to this thread which now top 12000. This posting is structured so that mathematical bits are put in appendices and needn’t be read unless you like that sort of thing. Be warned some of appendix 2 contains A’level (1960s) standard maths and possibly beyond. If you reach the end of appendix 2 you should probably get out more.

There is not sufficient documentation produced by the grading team for me to know with certainty what is happening so for detail I took it that:-

1. 50 + oppos grade for a win applies not 40. A surprising discovery is that whether a win counts 40 or 50 makes little difference; what is more important is who the oppos are and who are their oppos.
2. The 40 point rule is used at the end of all iterations.
3. Also I ignored the junior increment as that is added in last and does not affect the other figures or the conclusions.

Under the old system where a grader might estimate 90 as a start grade the 40 point rule ensured that the range of a first grade would be 0 to 180. Both Keene and Hartston had first grades around 180 in the 60s although I don’t remember whether a 40 point rule existed then.

The current system probably has a theoretical range of approx -10,000 to +10,000 ! for a first grade due to pyramiding possibilities. Unless players deliberately take advantage of pyramiding we can expect a few juniors to be graded between 225 – 280 each year; I am surprised there are not more this year but it depends on the playing patterns. An extended range has been a possibility since the iterative process was introduced but only in the first year of a player being graded. Anecdotal evidence shows that some juniors in the last 10 years were receiving grades much lower or much higher than was expected including negative grades. This ties in with the mathematics of the iterative process.

Appendix 2 shows that the grade of a junior A is calculated by the formula:-

A= ((sum graded oppos +sum of ungraded oppos)/ number of games) + % score over 50

Where the ungraded oppos grades are the 2009 ( this is the critical bit) grades either during the iterative process or at the end of it. This means that A's grade cannot be calculated separately and all grades for ungraded have to be calculated at the same time. The grades of graded players remain the same throughout.

Following this calculation, I am not clear but the grading team look to be doing one further calculation for each result of A to see if the 40 point rule applies. So for each game against any ungraded oppos, the grading figure for the oppo coming out of the 2009 final iteration is set to be within + or – 40 of the iterated grade for A. For a game against a graded player the oppos 2008 grade is used in the 40 point rule calculation. Finally I expect that the junior increment is added. These adjustments could take A’s final grade up or down a few points. Some players will gain, others lose as a result of the 40 point rule and the total is unlikely to be zero.

The increased spread in grades comes mostly from the ungraded oppos, as their grades can be almost anything, and the application of the 40 rule later in the process other than in the initial steps. If the 40 point rule were used in the iteration it would not converge in most cases. The % score does not matter too much ! The important point is who the oppos are.

For an unusually high grade a junior has probably played against a high proportion of ungraded or junior oppos achieving a plus percentage and also played against some graded oppos but not too many. It is better if his ungraded oppos play very few graded players but instead score well against further ungraded players. The random walk principle makes me believe that this system will in a future years produce a junior temporarily rated higher than the highest rated adult.

Previously an effect of an increased range of possible grades was to bring in some juniors at underated very low grades < 90 and increase the number of –ve grades. In addition some juniors > 90 would be overrated. This latter group would be hidden a bit as improvement due to experience in the following years would reduce the overrating. I expect the underrated juniors < 90 entered more tournaments to win prize money than they otherwise would and would cause deflation of the internal and swap variety. Over the longer term, we are talking about 10 years since the process was introduced, the effect would be to stretch the scale around the 90 mark. The gap between 70 and 110 would become wider than say between 110 and 150. This stretch would almost certainly spill over into the surrounding areas. It is possible some low rated new starters and also those who were overrated initially who did not progress as fast as they might, became disillusioned and gave up playing.

Appendix 1 shows how a fairly innocuous set of results could produce unusual grades. I know there are only a small number of results which was necessary to keep the example simple but the conclusions apply with large numbers involved. There are 2 tables which illustrate starting estimates of 200 and 350 for the start grade for ungraded. These show that the final grades are unaffected as would be expected by this process.

Appendix 1

This section shows some example of outputs possible from the iterative process which are referred to in the main section.

1.1 For this cross table of results.

Code: Select all

\	A      B    C    D    e    g
A	X    0.5    1    1		 
B	0.5    X              1	 
C	0           X         1	 
D	0                X         1
e	       0    0         X	 
g	                 0         X

A,B,C and D being ungraded, e and g being graded.

1.2 This is the F matrix used in the iterations, see appendix 2

Code: Select all

    	A   	B   	C   	D   	e   	g
A	0.00	0.33	0.33	0.33	0.00	0.00
B	0.50	0.00	0.00	0.00	0.50	0.00
C	0.50	0.00	0.00	0.00	0.50	0.00
D	0.50	0.00	0.00	0.00	0.00	0.50
E	0.00	0.00	0.00	0.00	1.00	0.00
g	0.00	0.00	0.00	0.00	0.00	1.00

1.2 From a start estimate of 200 points for each ungraded player, iterated values are:-

Code: Select all

START                                                           after
Grade	1st	  2nd	  3rd	  4th	  5th	 10th	  20th	40 rule
200	233.3	215.0	231.7	222.5	230.8	229.1	229.97	235
200	205.0	221.7	212.5	220.8	216.3	220.1	220.00	230
200	180.0	196.7	187.5	195.8	191.3	195.1	195.00	195
200	160.0	176.7	167.5	175.8	171.3	175.1	175.00	175	
160	  160	  160	  160	  160	  160	  160	  160
120	  120	  120	  120	  120	  120	  120	  120	

1.3 From a start estimate of 350 points for each starter, iterated values are:-

Code: Select all

START	 1st	 2nd	  3rd	  4th	  5th	 10th	 20th	40 rule
350	383.3	290.0	306.7	260.0	268.3	233.8	230.1	235
350	280.0	296.7	250.0	258.3	235.0	224.8	220.1	230
350	255.0	271.7	225.0	233.3	210.0	199.8	195.1	195
350	235.0	251.7	205.0	213.3	190.0	179.8	175.1	175
160	160.0	160.0	160.0	160.0	160.0	160.0	160.0	
120	120.0	120.0	120.0	120.0	120.0	120.0	120.0	

The figures are independent of the start estimates for ungraded players and after 20 iterations have almost converged. This is a known property of markov processes; a start estimate of 0 could be used for new starters.

Appendix 2

I will attempt to show-

a) that each iteration of the ECF new starter grading process can be represented by a matrix equation where the matrix is a first order, row stochastic markov matrix and so repeated iterations will normally converge. There is nothing very stochastic about it but it fits the description in maths literature.

b) that the grade of an ungraded player A produced by the iterative process once converged is :-

U= ( b+c+d ….. etc + B+C+D……. etc ) /Na +PA

Where

• b,c etc are grades of graded oppos whose grades are known at the outset.
• B and , C etc grades of ungraded oppos whose grades are not known until the repeated iteration is completed.
• Na is the number of games played by A

Assume there are NU ungraded players who may play against each other but also play against a total of NG graded players, who collectively play one or more of the ungraded players.

Define a column matrix G of rank NU + NG where the top NU elements are the grades of the ungraded players before an iterative step is made. The lower NG elements are the grades of the graded players who do not change throughout the process.

Define a square matrix F with (NU+NG) rows and columns, which is a modified fixtures matrix. The j th row represents the fixtures but not the results for the jth player provided j is an ungraded player. F(j,i) =1 if the jth ungraded player played the ith player who may or may not be graded and F(j,i) = 0 otherwise. For an ungraded player j, a jth row of (1,1,0,0,1,0….etc) indicates that he played the 1st 2nd 5th players but not the 3rd and 4th etc. There will potentially be entries in the jth row for ungraded players in the NG rightmost columns representing games against graded players.

If k is a graded player then the F(k,s) =1 if s=k and 0 otherwise. So the bottom right hand corner of the matrix F is an identity matrix I of rank NG. For graded players there are zeros elsewhere.

Finally for any ungraded player j, divide all elements of the jth row of F by Nj the number of games that j played.

An F matirx is shown in Appendix 1 sect 1.2

A single step of the iterative process is then represented by :-

G[N+1]=F x G[N] + P

Where:-

• X is the usual matrix multiplication operation
• F is the fixtures matrix
• G[N] is the value of the Matrix G after N iterations. Also define G[N]=GN.
• P is a column matrix where P(j) = 100 x ( % score of player j ) -50 for ungraded players, and P(k) = 0 for graded players

Then

G1=F x G0 + P
G2=(F^2)xG0 +(I + F) x P, where I is the identity matrix

F^2=F x F etc ie matrix F to the power 2 in matrix multiplication

G[N+1]=F x GN + P
GN= (F^N) x G0+(SUM( F^R: R=0,N-1))xP

Matrix operations don’t always follow the rules of normal algebra but its safeish to LH multiply both sides of this equation by ( I-F) where I is the identity matrix.

GN-FxGN=(F^N)xG0 –F^(N+1) x G0 + P - (F^N)xP

For large N ie enough iterations, F^N=F^(N+1) as F is a markov matrix so

GN=FxGN +P

The final term above of (F^N)xP is Z due to the way P is defined.

Which says after enough iterations the grades going in = the grades coming out and are equal to the usual grading formulae for each player :-

A= (sum graded oppos +sum of ungraded oppos)/ number of games + % score over 50

The difference between this and last year is that grades for previously graded junior oppos aren’t known until all the equations or iterations are solved.

This means that As grade coming out of the iterative process as a junior, apart from the age increase and 40 point rule adjustment, should be equal to the ( total of the grades of graded oppos at 2008 + the total of ungraded oppos, including other juniors and adult new starters at 2009) divided by the number of games A plays plus the percentage score over 50 eg for 4/5 =80 % so P=30.

I am unclear from the information given by the grading team whether the 40 point rule is applied next or not. I am also unclear whether the points for a win in the iterative process is 50 or 40.

The most likely interpretation of what is said on the website concerning 2009 grades is that the figures coming out of the iterative process are then refined using the 40 point rule. This will increase some grades and reduce others and the total effect will not normally be 0.

Well done if you read down to here but you really should get out more if you found this interesting.

[Roger de Coverly]

Under the old system where a grader might estimate 90 as a start grade the 40 point rule ensured that the range of a first grade would be 0 to 180. Both Keene and Hartston had first grades around 180 in the 60s although I don’t remember whether a 40 point rule existed then.

Could I chuck in a bit of history/personal memory? I think there was a convention that new players were given estimated grades of 100 unless there was evidence to the contrary. There was a lot of "informal" secondary schools chess in those days which meant that younger players could get quite strong before playing their first BCF graded game. As a consequence, the starting grade was "graders estimate" and it could be as high as it needed to be. They used to grade things like the Olympiad, so I rather doubt that a game Keene-Spassky estimated Spassky a grade of 90.

The actual 40 point rule came in at the end of the sixties. There was an article by Clarke in the BCM which described its introduction. There are extracts on this site somewhere. Previously 50 point games were ignored for the "right" result and only processed on the "wrong" result. This is a both a bit deflationary and "harsh" on the higher rated player. There had been an increase in large Swiss tournaments popularised by someone called Reuben. This increased the number of mismatches by virtue of the pairing systems used and the grading range of players.

Other points on "estimated" grades. The qualification standard for a published grade was a bit higher back in the 60s/70s so you would have players that were in the system but with too few games to qualify for publication. These grades were understood to be at the disposal of the graders so if a new season's results was dramatically different, the previous grade could be discarded.

Even as late as 1988 following the introduction of the A-E system of designating grades, the E stood for Estimate - thus potentially it could be discarded.

I might suggest a "harder" system for determining estimated grades, the point being to minimise the use of the back-solver. The underlying idea is to use the concept of only counting rated players. The basic idea is that a new player's grade goes "firm" as soon as they have played 9 A-D players and this grade is then treated as their start grade for the season. You might do quarterly sweeps and publish the results on the grading website. So a new player who plays enough of the right people will get a grade in three months.

The other thing I'd like to suggest is to drop the notion that you can derive anything really useful from comparing the output of the recursion routine to either the begin season grade or the end season grade. It gives you a measure of player and result volatility but I struggle to see why it gives any particularly special insight into the correctness of either the start or the end season grades. If I've read between the lines of what's been troubling the grading team, they calculated begin season junior grades, then they ran the recursion routine using the next season's results and got comparisons which were outside their tolerances. I'd suggest all they are showing is that junior performance is volatile and that basing a junior's grade on the previous season's performance plus an age related fudge factor is about the best they will able to get and they've just got to accept that the following season's performance will shown a wider divergence from the theoretical prediction than adults of the same nominal grade.