Answers to a couple of Roger's grading questions...

[John McKenna]

Another thread (100 Year History of the British Chess Federation - 2 questions) that began -

"The first BCF Grading List was published in 1954, the brainchild of (Sir) Richard Clarke who worked on this development with Arpad Elo." (MJMcCready)

Led to my post below -

"A British Chess Federation Rating System was described in the BCF Yearbook (Clarke 1958). The system uses the formula (below) on a periodic basis, performance ratings being calculated over a two-year period, with a thirty-game minimum required. Ratings are grouped by grades, as follows -

Grade 1a 248-241 1b 240-233 Grade 2a 232-225 etc.

Rp = Rc + 10(P-50)

[Rp is rating performance, Rc rating of opponents and P the percentage score]

The (above) equation may be used to determine ratings on a periodic basis. In rating systems... such as that of the BCF ratings are calculated at finite intervals (BCF uses one year)..." Source: The Rating of Chessplayers, A. Elo 1978

So, sometime between 1958 and 1978 the BCF changed the period from 2 years to 1 year for its grade calculations. The 'formula/equation' also changed at some point, therefore you would not be comparing like-for-like with today's grades.

Which led to to the following two questions -

Roger de Coverly>In what way do you think it changed as the equation as written makes no sense?

(So score 75% against 200 opposition. 75-50 is 25 so you add 25 to 200 making 225 as expected... There were substantive changes in the mid or late 1960s where a junior increment of 5, later 10 was introduced and also the 40 point rule. You can see why they are needed as without them the grading numbers are liable to decline.)<

Roger, you answered that when you pointed out, above, the introduction of the 40-point rule, which means that Rc is modified whenever two opponents' grades differ by more than 40 points.

RdC>That only works for those playing more than 30 games, which was all they bothered to publish. I don't know that they ever published how they estimated values for the many ungraded but moderately active players(?)<

In answer to that, here's what A. Elo wrote -

"The equation [Rp = Rc + 10(P-50)] may also be used to determine provisional ratings... to rate players having less than 25 games against rated players. A more precise formula... based on very few games is -

Rf = Rc + D(P)F

[Rf is the modified performance rating and D(P) is taken from a t-distribution table.]

For each sample size N (the number of games) a different distribution applies, and they are similar to and approach the normal (distribution) as N increases... Student (W. S. Gossett) or t-distributions [are] found in most works on statistical/probability theory... and are not readily adapted for rating purposes, but a table derived from them appears below -

Code: Select all

D(P)	50	100	150	200	250	300	350
N=5	.95	.90	.85	.79	.71	.60	.50
N=7	.96	.92	.87	.81	.74	.64	.55

...

[N=9, 11, 13, 15, 17 are also given, D(P) is rating difference from percentage score.]

The table gives the [appropriate] correction factor F to apply to D(P) and should serve, when no better means are available... to calculate Rp for a low number of games, as when giving an initial rating to a new player."[/i]

As can be surmised the modified performance rating [Rf] is calculated using a probabilistic, non-linear approximation, whereas the BCF used a linear one and here is what A. Elo wrote about that - "examination of the normal probability function percentage expectancy (Gauss) curve shows that between -1.5 and +1.5 standard deviations shows that it may be approximated by a straight line."

That provides the justification for the BCF in using a linear approximation equation to calculate grades. Note it applies only within the range of 3 standard deviations (-1.5 to + 1.5 on the curve), which means when the difference in grades is greater than that it is unreliable.

It seems to me that the 40-rule is a fudge because the linear BCF/ECF grading system cannot deal with such large differences properly so it just ignores them. I was surprised to find that the FIDE rating system employs a similar device and still wonder why it is necessary in a non-linear (probabilistic) system.

(Of course, one side effect of those devices is to protect the higher-rated/graded players rating/grading from draws and losses against much lower rated/graded players and conversely helps keep the lowly in their low down place. That's the lowdown.

[John McKenna]

Please note the following very relevant post and link (from the original thread) -

Christopher Kreuzer>An advanced search for "Richard Clarke" with "Mike Gunn" as author led to this (part of a discussion from April 2008 titled 'The Arbitrary 40 point Rule'):

http://www.ecforum.org.uk/viewtopic.php ... 1454#p1454

I think that is what Mike is referring to above with "I did post (at least part of) this article on this forum in the early days of the forum".<

Edited - to correct link.

[Roger de Coverly]

In answer to that, here's what A. Elo wrote -

"The equation [Rp = Rc + 10(P-50)] may also be used to determine provisional ratings... to rate players having less than 25 games against rated players. A more precise formula... based on very few games is -

It's all very well making quotes from what Elo wrote, but bear in mind that Elo's rating scale was measured in thousands whereas the Clarke system is measured in hundreds. The correct formula for a Clarke system is
Rp = Rc + (P-50)

The 40 point rule is a fudge and a very necessary one when dealing with games between players of wildly different grades. If you have a system where you lose points even by winning a game, it's rather naturally deflationary among the top players, as the BCF eventually realised when they noticed the numbers of top players reducing every year. Top players, by virtue of being top players, domestically at least, would expect to have a P in excess of 50%.

[John McKenna]

[Quick Reply]

Roger, thanks for your reply.

Let me ask a question or two.

Have you ever drawn or lost to a player graded more than 40 points below?

Have you ever drawn or beaten a player more than 40-points higher than you?

I've never beaten a player 40 points higher but I have drawn and felt short changed.

You know as well as I do that the "abitrary" 40-point rule is really for insurance in the event of an accident happening against under-graded juniors but it comes at a cost to adult players with genuine long-term grades. Reread the link in Chris Kreuzers post, above, and see that nobody really answered the question as to why that is allowed to be the case.

[Roger de Coverly]

Have you ever drawn or lost to a player graded more than 40 points below?

Have you ever drawn or beaten a player more than 40-points higher than you?

I think my record win was a couple of years ago where I was 184 v 244.

It's not only undergraded juniors, it's anywhere that pairings throw up disparate grading gaps. More often than not, it makes no difference as the games where you give away 50 points are balanced up by those where you are 50 points the wrong way. A system where you can lose points just by playing is wrong as well.

[John McKenna]

Roger, congratulations on the limited but precious points that fine win brought.

My best is a draw 141 v. 202 , and (probably) my worst a loss 141 v. 88. (Both subject to the 40-point rule - I have a win over a 170+ player not subject to it.)

Regarding the confusion about the formulae -

Rp = Rc + 10(P-50) is the original Harkness one and the only difference between it
and
Rp = Rc + (P-50) the Clarke one used by the BCF/ECF is a scaling factor of 10, since Rc in the Harkness system is a four-digit number and a three-digit number in the Clarke system. Such a scaling factor would be useful in the current ECF system as it would create more room at the bottom of the grading list and almost eliminate the taboo of negative grades that the ECF grading system comes close at times with grades of zero. The Welsh had the sense to introduce a four-digit system even though, like the BCF/ECF system, it is not an Elo system.

Pardon me for quoting A. Elo yet again -

The Harkness system ran downwards from 2600 and used the formula -

Rp = Rc + 10(P-50) was used only for events of over nine games,

[Rp = Rc + 50(W-L) was the working formula, W is wins, draws count a half, L losses..]

At first glance it seems appealingly simple, but thoughful examination reveals that a strong player can lose points even with a perfect score and a weak player can gain by losing all his games, circumstances not at all unlikely. The equation yielded invalid results and continued application developed uncertainties in the ratings which became disturbingly larger than could be expected from common statistical variation. Although broadly used, covering many thousands of players in the USCF between 1950 and 1960, and adopted by a number of other federations elsewhere, the results never lived up to the hoped-for-objectives, and the system has since been replaced by the Elo system almost universally.
(The Rating of Chessplayers 1978)

There you have it. I promise not to quote Arpad at you (others are fair game) in this thread, again.

The small Welsh federation relieved the lack of room at the bottom by simply going to four-digits and the big American federation changed to an Elo system to avoid the inherent chronic deflation in the Harkness system. The middling BCF/ECF recently made a little more room at the bottom of its grading system by adding points to the grades of the lower echelons on a sliding scale, and long since fudged deflation with the blanket 40-point rule. [That, in my opinion, would best be applied fully only to the results of juniors. And, only applied to adults when a stronger player wins against a player more than 40 points below - after all he is expected to win, and invariably will, but if he loses or draws he should suffer the full loss of points (as he does against his peers) and his lowly adult adversary enjoy the full gain. WARNING - my idea is untested and I've no idea what it would do the integrity of the grading system statistically.]

N.B. I didn't post all this in the "Grading Debate" category as I did not intend to start another full-on debate on grading - they all seem to lead to a great amount of heat and very little light. However, if it's moved there for tidiness' sake I don't mind.

[IM Jack Rudd]

The middling BCF/ECF recently made a little more room at the bottom of its grading system by adding points to the grades of the lower echelons on a sliding scale, and long since fudged deflation with the blanket 40-point rule. [That, in my opinion, would best be applied fully only to the results of juniors. And, only applied to adults when a stronger player wins against a player more than 40 points below - after all he is expected to win, and invariably will, but if he loses or draws he should suffer the full loss of points (as he does against his peers) and his lowly adult adversary enjoy the full gain. WARNING - my idea is untested and I've no idea what it would do the integrity of the grading system statistically.]

Well, it would mean that the same score against the same set of opponents wouldn't necessarily produce the same result. You might or might not want that feature.

[Brian Valentine]

I haven't tried to reconcile this to all games played from the January database, but here is an analysis of games with extreme grading differences looked at from the higher graded player.
low high W D L
40 49 2353 307 189 88%
50 59 1671 108 43 95%
60 69 783 27 18 96%
70 79 403 14 11 96%

[Roger de Coverly]

Such a scaling factor would be useful in the current ECF system as it would create more room at the bottom of the grading list and almost eliminate the taboo of negative grades that the ECF grading system comes close at times with grades of zero.

Whether it's three digits or four digits doesn't make much difference, since both Elo and Clarke scales were chosen arbitrarily. You could give the three digit scale more legroom by adding 50 or 100 to all values.

The traditional equivalence was agreed to be Elo = 8*Clarke + 600 so that 175 = 2000. It's the +600 that gives the Elo formula more legroom. I doubt either pioneer or Harkness envisaged the extension of grading and rating schemes into the area of players who struggle to produce of game of legal moves.

[Ian Thompson]

I haven't tried to reconcile this to all games played from the January database, but here is an analysis of games with extreme grading differences looked at from the higher graded player.
low high W D L
40 49 2353 307 189 88%
50 59 1671 108 43 95%
60 69 783 27 18 96%
70 79 403 14 11 96%

What would the figures be if you excluded low graded players from the statistics, say with the lower graded player being under 100? If someone graded 10 played someone graded 60 they'll both be making lots of mistakes, so the result is a bit of a lottery. It would be less of a lottery if it was someone graded 200 playing someone graded 250.

[John McKenna]

My thanks to Brian Valentine for posting the figures, above.

Of course, I look at those numbers from the point of view of a middling player.

I was slightly surprised that there were so many encounters between high and low graded players.

That the border area - (40-49 points) difference - is the major battleground comes as no surprise.
Nor is it unexpected that the lower graded players do best (12% as opposed to 4-5% where the difference is more than 50 points) in those encounters where the difference is smallest. You might call 40-49 the cutting edge I suppose.

However, I understand that the higher one's grade/rating the more prestigious it is and therefore it needs to be 'insured'.

If, for lower graded players, the 'premium' for playing in an Open tournament or section is the 40-point rule I think it's worth it.

I don't disagree with anything Roger has said in this thread but we all know that things are done differently elsewhere.

The ECF (and a few other federations) continue not to use an Elo system and I don't see that changing soon, if ever.
Similarly we (and a few other nations) continue to drive on the left instead of on the right like most of the rest of the world.

I'd like to thank all the hard-working people involved in the ECF grading and FIDE rating systems for their unstinting efforts.

Fin.

[John McKenna]

I haven't tried to reconcile this to all games played from the January database, but here is an analysis of games with extreme grading differences looked at from the higher graded player.
low high W D L
40 49 2353 307 189 88%
50 59 1671 108 43 95%
60 69 783 27 18 96%
70 79 403 14 11 96%

What would the figures be if you excluded low graded players from the statistics, say with the lower graded player being under 100? If someone graded 10 played someone graded 60 they'll both be making lots of mistakes, so the result is a bit of a lottery. It would be less of a lottery if it was someone graded 200 playing someone graded 250.

A very relevant question, as always, from Ian.
I'd be interested in an answer if it can be provided.

(I do think I should have posted this in the Grading Debate category and hope it can be moved there at some point.)

[Roger de Coverly]

I haven't tried to reconcile this to all games played from the January database, but here is an analysis of games with extreme grading differences looked at from the higher graded player.
low high W D L
40 49 2353 307 189 88%
50 59 1671 108 43 95%
60 69 783 27 18 96%
70 79 403 14 11 96%

Around 3% then, if this is a count of "whole" games from a year of data. ( Total number of half games is around 300,000)

[IM Jack Rudd]

Thread moved into the Grading Debate section as requested.

My games that break the 40-point barrier generally fall into two categories: (a) internal club games at Barnstaple, where nobody is currently within 40 grading points of me (this may not be the case as of next season), and (b) early-round games in international tournaments, particularly ones where there is just the one section.

[Brian Valentine]

My extract was quick and dirty and I can't easily answer the two questions about the data (one implied). The analysis come from some useful things I inherited and the extract doesn't allow an analysis by higher grade. Furthermore it is based on about 90,000 half games and I'll need to dig into why that is. I have no reason to believe the extract is biased. Maybe when I get a bit of time I'll try to get better detail, but I'm not promising anything soon.