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

General discussions about grading.
John McKenna
Posts: 3363
Joined: Tue May 17, 2011 2:02 pm

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

Post by John McKenna » Mon Apr 27, 2015 9:55 am

Thanks for your reply, above, and for considering those questions, Brian.

I'd just like to add something about the 40-point rule - it is said, but not universally agreed, that the ECF grading system is inherently deflationary and does not the rule tend to add to that? Earlier in this thread I was, perhaps, being inconsistent when I advocated applying the rule solely to juniors and only partially to adults. Maybe it should be applied only partially to juniors, too. Would it be fairer, I wonder, to all if the rule was only used to limit the loss of grading points of the higher-graded players who were more than 40 points above their opponents in the event of a defeat, while giving their lower-rated opponents the full gain in points in the event of a win/draw? Grading in that partially modified way of the relatively small subset of such games - roughly estimated, above, at about 3% by Roger - would not have a very noticeable inflationary effect, hopefully. It would, however, no longer make the grading of that minority of encounters - between players more than 40 points apart - a 'zero-sum' activity, but so what? The current implentation grading system is not a sacred cow and here is a view of someone other than Arpad Elo, not they they would have disagreed much about this aspect of grading, I suspect -

The average ability of a pool of players is always changing, through study, practice, and ageing, but grading provides no mechanism by which the average grade of the pool can be made to reflect these changes - indeed, if the pool of players remains constant and every game causes equal and opposite changes [my bold - this is a zero-sum condition] to the grades of all the affected players, the average grade never changes at all. What does change is the average grade of the pool is the arrival and departure of players, and if a player has a different grade when he departs the pool than when he arrived then his sojourn in the pool will have disturbed the average grade of the other players - but this change is merely an artificial consequence of the grading calculations, and does not represent any genuine change in average ability. It is, of course, open to a grading administrator to adjust the average grade of his pool [one way is by the partial application of the 40-point rule as I suggest above] to conform to any overall change in ability [the increasing(?) ability of players to draw/win against players more than 40 points higher in my suggestion, above] which he believes to have occurred, but the absence of an external standard of comparison [i.e. grades are relative not absolute] means that any such adjustment is conjectural. A grade is merely a general measure of a player's [past] performance relative to that of certain other players [his opponents] over a particular [grading] period. It is not an absolute measure of anything at all. [My bold] Source: The Mathematics of Games by John D. Beasley, 1989

The last sentence above is sometimes echoed by Roger on this forum.

And, thanks to Jack for moving this thread to 'Grading Debate'.
Last edited by John McKenna on Mon Apr 27, 2015 11:15 am, edited 1 time in total.
To find a for(u)m that accommodates the mess, that is the task of the artist now. (Samuel Beckett)

Roger de Coverly
Posts: 17319
Joined: Tue Apr 15, 2008 2:51 pm

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

Post by Roger de Coverly » Mon Apr 27, 2015 10:09 am

John McKenna wrote: indeed, if the pool of players remained constant and every game causes equal and opposite changes[/i] [my bold - this is a zero-sum condition] to the grades of all the affected players, the average grade never changes at all.


The zero sum condition doesn't apply. In Elo based systems there's almost always a differential K factor and in Clarke based systems, it's the number of games over which the games are averaged. It's easy enough to see that if you play 100 games in a grading period, every game you lose that you should have won will cost 1 grading point, whereas if you only play 30 it's more than 3. For those who do not even reach 30, the effect of one result is even greater.

John McKenna
Posts: 3363
Joined: Tue May 17, 2011 2:02 pm

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

Post by John McKenna » Mon Apr 27, 2015 11:12 am

Thanks for pointing that out, Roger.

I agree with your insightful observation, above, about the effect of the number of games played on a player's grade (and similarly the K-factor on rating).

But the quote you included, which is me quoting John D. Beasley, is not subject to your caveat because the grading calculation of each and every individual game "causes equal and opposite changes" (Beasley, above) and therefore is 'zero sum'.

However, the statement (that my suggestion about modified use of the 40-point rule) "would... no longer make the grading of that minority of encounters... a zero-sum activity" is subject to your your caveat and I stand corrected, but - regarding any single encounter that is graded - Beasley's statement remains correct, there is no overall gain/loss of grading points - what is gained by one player is always lost by the other.
To find a for(u)m that accommodates the mess, that is the task of the artist now. (Samuel Beckett)

Roger de Coverly
Posts: 17319
Joined: Tue Apr 15, 2008 2:51 pm

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

Post by Roger de Coverly » Mon Apr 27, 2015 11:21 am

John McKenna wrote:but - regarding any single encounter that is graded - Beasley's statement remains correct, there is no overall gain/loss of grading points - what is gained by one player is always lost by the other.
What type of rating system are you referring to? Whilst true in theory on an Elo type system provided all the K factors are the same, it is rarely true in practice because they aren't. On a Clarke style system it's never true when the number of games played exceeds 30 in a grading period.

John McKenna
Posts: 3363
Joined: Tue May 17, 2011 2:02 pm

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

Post by John McKenna » Mon Apr 27, 2015 11:29 am

I am not referring to a system but a game - Beasley and I are referring to individual games that are graded by the ECF or rated by FIDE. Are you implying that in the calculation of the grading/rating of an individual game, in either the ECF or FIDE system, that there is a resulting net gain/loss of points between the players?
To find a for(u)m that accommodates the mess, that is the task of the artist now. (Samuel Beckett)

Roger de Coverly
Posts: 17319
Joined: Tue Apr 15, 2008 2:51 pm

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

Post by Roger de Coverly » Mon Apr 27, 2015 12:00 pm

John McKenna wrote: Are you implying that in the calculation of the grading/rating of an individual game, in either the ECF or FIDE system, that there is a resulting net gain/loss of points between the players?
Yes. Isn't it obvious why that should be? In an Elo based system, it will be where there are different K factors and in a Clarke based system a difference in the number of games in the grading period.

A quick example. A and B have the same grade and play, but A will play 50 games over the grading period and B 10 over three grading periods. If there's a decisive result, A's grade will increase or decrease by 1 as a consequence, whilst B's grade will increase or decrease by 5.

The practical impact is limited because whatever B's grade becomes, it only affects 10 other people over three years, whereas A's grade affects 150 over the same time period.

John McKenna
Posts: 3363
Joined: Tue May 17, 2011 2:02 pm

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

Post by John McKenna » Mon Apr 27, 2015 12:19 pm

Yes, Roger, I understand that.

However, I (and Beasley) am referring to an individual game itself without reference to other games played before/after.
On that basis there is no net gain/loss between the players - ignoring the 40-point rule, though it also leaves no net gain/loss for an individual game - if two players draw they simply exchange grades and there is no net gain/loss and if there's a decisive result the winner gets the opponent's grade +50 points and the lose his opponent's grade -50 points, again there's no net gain/loss.

Of course, in the scheme of things when a system has grades, or ratings, that involve different numbers of games, (K-factors) what you say is true. That is the difference between grading a single game, in theory, and grading a number of games in practice.

Edit -

Let me try to put it another way -

Beasley and I are pointing out that, in theory, on the basis of a single game all grades (but not ratings that involve different K-factors) are calculated the same way with N (the number of games) equal to 1and that sense all grades are 'equal'. [He even says that in static pool where NO players left or arrived the average of all the grades would remain constant no matter how many games they played.]

You are pointing out that in a grading system that has different categories of grade - like the ECF's A,B,C,D,E and now F - the category is significant as it is indicative of a difference in N (the number of games) used to calculate the grades. In that sense some grades are more 'equal' than others and it is why they should really always include the category letter (A-F) because 180A is not the same as 180B, which is not the same as 180C/D/E/F.

By the way, when the X category was introduced it resulted in an enhancement to the ECF grading system and its subsequent removal resulted in a loss of information that some people obviously felt very useful. The A category now hides a greater multiplicity of games behind it than before. And, it was probable that to get into the X category a player would have had to play tournament in addition the league chess. That distinction, probably surmisable at a glance, has now been lost.

For the sake of completeness I am sorry to have to add that I believe I read on the SCCU (or Surrey CCA) site that they would not be using the new F category grades but that I cannot say exactly whether that means they regard them as being of no use to them for their own purposes or just plain irrelevant. If it does mean the latter then I wonder why the F category was introduced at the same time the X category was removed!?

Edit - to insert the word NO.
To find a for(u)m that accommodates the mess, that is the task of the artist now. (Samuel Beckett)

Post Reply