New ECF to Elo Conversion Formula
I’ve done some statistical analysis on players with both ECF and FIDE Elo grades and decided that the ECF formula for converting to Elo could use some work.
I propose that the new formula should be:
Elo = (ECF x 6.14) + 1050
This gives an R2 fit of 0.946 against the plotted data. The graph below shows my model (black line) vs the ECF model (red line).
I’ll give more details in a future post.
Thursday, June 5th 2008 at 6:23 pm
From about 175 onwards the trendline looks very tight and not surprisingly the lower end has a larger deviation. I guess those players with an Elo rating around 80-150 have played relatively few games (probably only 10) and hence their rating is not a true, settled reflection on their strength.
One point of note, Jeroen van Dorp posted a formula from an analysis of USCF vs FIDE ratings and found that;
USCF= (ELO*0.895)+367
ELO = (USCF-367)/0.895
Which implies that someone with a grade of 0 has an equivalent USCF rating of 1306.
Thursday, June 12th 2008 at 8:43 am
This came up in the ECF forum somewhere or other a while back. I’m sure they’d be interested to read your findings too. I also recall someone explaining why the current ECF formula for lower grades is definitely a fudge, because the ‘true’ formula must involve a factor of 8. I don’t recall why!
Monday, June 16th 2008 at 10:56 am
Factor of 8 - this is because a difference of 25 ECF points is supposed to score 75% win/loss which is the same at 200 points on the international ELO scales.
Fitting ECF to international ELO graphically runs into the problem that not only do the calculation methods underlying each grade differ but also the games included. For most English players, only a subset of their games will be on the international list and historically at least (when the international grades didn’t go below 2000) only their best performances. A better “type” of formula IMHO would be International = BCF*8 + factor(BCF grade) where factor(BCF grade) is the traditional 600 at the 2400 IM level, increasing to 700 at around 175 and above that as you go down the scale. So you would be fitting a curve to the observed data rather than a straight line.
Monday, June 16th 2008 at 5:55 pm
Some more thoughts :-
I suggested above that 225 = 2400 and 175 = 2100 was approximately the real world.
Turning this into algebra give a formula 8 * ECF + 600 + (225-ECF) *2 which simplifies to
6*ECF + 1050 ie very similar to yours.
You might wish to screen the FIDE data for players with K=25 and exclude them - because they are still in the provisional period for international rating. Similarly you might wish to remove D and E players from the British list.
Monday, June 16th 2008 at 8:52 pm
Many thanks for your comments - it’s certainly given me some ideas.
I removed all the E category players from the ECF data (not the Ds though) and I also removed all the juniors (with an age) as their rating usually fluctuates too much. With the Elo data I removed anyone who hadn’t played 5 recent games but unfortunately the K factor was not available in the dataset I used.
Friday, July 11th 2008 at 2:14 pm
I think the calculation does need some work. My ECF/BCF grade is 54 and the calculation you have devised seems more accurate - or should I say better reflects my own opinion.
My online ELO, using redhotpawn, peaked at 1624 and since online play is usually, but not always, a couple of hundred points higher I think the 1300-1400s would be more accurate.