"

*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:

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)

*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 -

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.