**Proposal...**

Maybe (in the light of introduction of the new corrected grades) now is the right time to ask the ECF officials if they would consider switching to Ã‰lo Grading System two (Ã‰GS2) rather than continue using the current Grading System (GS)?

The main advantages (as I see it) of Ã‰GS2 over GS are as follows:

1. The relationship between expected performance 'p' and grade difference 'd' is the logistic curve (currently adopted by FIDE Ã‰lo Rating System) which is in accord with Mr David Welch's finding that chess performance as a function of difference in chess abilities matches the logistic curve (red line in the figures 1 and 2 below) closer than the curve adopted by GS (green line in the figures 1 and 2 below).

2. Grades of less active chess players change more rapidly (say the estimated grade of a junior who has just entered the system would change more rapidly than the grades of well established players he played against, or say you had been inactive for a period of time and you have re-entered the system with an old grade, your grade would change more rapidly than the grades of well established players you played against, etc., this is in fact a simplified improvement of Glicko 1 over FIDE Ã‰lo).

Note: Ã‰GS2 grades are on ECF (rather than FIDE) scale, i.e. a strong GM is around 270, not around 2800, etc.

**Logistic curve...**

Figure 1: Relationship between expected performance 'p' and grade difference 'd' as defined in GS (green line), CGS and AGS (blue line) and Ã‰GS and Ã‰GS2 (red line). Expected performance 'p' is a function of grading difference 'd', i.e. 'p = f(d)'.

Figure 2: Mr Welch's finding. The '(d>30, q)' discrete experimental points match Ã‰GS2's 'p = f(d)' closely (please note that the discrete points shown are only for illustration purposes, they are not a result of an actual analysis of the experimental data).

Note: It is impossible to measure chess abilities independently of chess performances (there is not a device one can put on the heads of chess players and get a measure of their chess abilities), but assuming that for small differences in chess abilities ('d<=30') the relationship between chess performance and difference in chess abilities is linear, one can find (using experimental data) that relationship between chess performance and difference in chess abilities matches the logistic curve closely (you assume that grades for 'd<=30' are in fact chess abilities, then you plot discrete experimental points '(d>30, q)' to find that they match Ã‰GS2's 'p = f(d)' closely).

**The formulae...**

Let 'a' and 'b' are the grades of players 'A' and 'B', 'p' expected performance of player 'A' (expected performance of player 'B' is then '100 - p'), 'q' actual performance of player 'A' (actual performance of player 'B' is then '100 - q') and 'd = a - b' the grade difference, 'na' and 'nb' the number of games players 'A' and 'B' played in the season for which grades 'a' and 'b' were calculated. Then, new grades of players 'A' and 'B', 'a2' and 'b2', are calculated as follows:

GS (current Grading System) formulae:

Code: Select all

```
(* GS *)
ClearAll[a, b, a2, b2, d, g, s, ka, kb, p, q, na, nb];
a = 120; b = 120;
q = 0;
g = 50; s = 40;
d = a - b;
ka = 1; kb = 1;
If[d >= 0, If[d > s, p = 90, p = g*(1 + d/g)],
If[d < -s, p = 10, p = g*(1 + d/g)]];
a2 = a + ka*(q - p);
b2 = b + kb*((100 - q) - (100 - p));
Round[N[a2]]
Print[];
Round[N[b2]]
```

Code: Select all

```
(* EGS2 *)
ClearAll[a, b, a2, b2, d, g, ka, kb, p, q, na, nb];
na = 40; nb = 40;
a = 120; b = 120;
q = 0;
d = a - b;
g = (25*Log[10])/Log[3];
ka = If[na + nb > 0, nb/(na + nb), 1/2]; kb =
If[na + nb > 0, na/(na + nb), 1/2];
p = 100/(1 + 10^(-d/g));
a2 = a + ka*(q - p);
b2 = b + kb*((100 - q) - (100 - p));
Round[N[a2]]
Print[];
Round[N[b2]]
```

Note: The formulae are used to calculate a new grade of player 'A' for every opponent 'B' he or she played in the season. At the end of the season an average of the calculated grades (for every opponent 'B') is taken, and this average is a new player's 'A' grade for the season (for GS, if a player has not played enough games in the season, games from previous season or seasons will be taken into calculation, for Ã‰GS2 no games from previous season or seasons would be taken into account).