Author: Eelco de Groot
Date: 15:40:23 04/27/05
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On April 27, 2005 at 16:37:24, Dieter Buerssner wrote: >On April 27, 2005 at 15:16:00, Dieter Buerssner wrote: > >> [...] I don't have erf() with me [...] > >I even have it. I am surprised - the MinGW environment does support it (it is >also part of the C99 Standard). So, if you have it too, you could change one >line: > >> printf("%d %.6f %.6f\n", d, expected_score(d), 1.0/(1.0+pow(10.0, > >to > >printf("%d %.6f %.6f %.6f\n", d, expected_score(d), > 1.0/(1.0+pow(10.0, -d/400.0)), 0.5+0.5*erf(d/400.)); > >It reproduces exactly the number I had given in the comment to the source (and >still shows, that none of the formula is able to reproduce the mumbers from >FIDE). > >Regards, >Dieter Hi Dieter, I sure wish I could follow all your C code, but I never did Study C seriously. Are there any good compilers that are not expensive and work under Windows? I think I can guess where FIDE got its numbers, I suspect they are mainly interpolations of the original table in Arpad E. Elo's 'The Rating of Chessplayers, Past & Present' (Batsford Books, 1978). Prof. Elo gave the following table: D P D P D P Rtg.Dif. H L Rtg.Dif. H L Rtg.Dif. H L 0-3 .50 .50 122-129 .67 .33 279-290 .84 .16 4-10 .51 .49 130-137 .68 .32 291-302 .85 .15 11-17 .52 .48 138-145 .69 .31 303-315 .86 .14 18-25 .53 .47 146-153 .70 .30 316-328 .87 .13 26-32 .54 .46 154-162 .71 .29 329-344 .88 .12 33-39 .55 .45 163-170 .72 .28 345-357 .89 .11 40-46 .56 .44 171-179 .73 .27 358-374 .90 .10 47-53 .57 .43 180-188 .74 .26 375-391 .91 .09 54-61 .58 .42 189-197 .75 .25 392-411 .92 .08 62-68 .59 .41 198-206 .76 .24 412-432 .93 .07 69-76 .60 .40 207-215 .77 .23 433-456 .94 .06 77-83 .61 .39 216-225 .78 .22 457-484 .95 .05 84-91 .62 .38 226-235 .79 .21 485-517 .96 .04 92-98 .63 .37 236-245 .80 .20 518-559 .97 .03 99-106 .64 .36 246-256 .81 .19 560-619 .98 .02 107-113 .65 .35 257-267 .82 .18 620-735 .99 .01 114-121 .66 .34 268-278 .83 .17 over735 1.00 .00 I think at FIDE headquarters, they wanted "exact" elo-numbers so at one point they just linearly interpolated the elo-numbers given at each percentage-point arriving at their own table. So i'm not surprised any efforts to reproduce that with a formula will not give the exact numbers back... I wish I could blame this gross oversimplification on Mr. Campomanes or the even greater crook Mr. Ilyumzhinov but I'm afraid this dates back to even longer ago... Regards, Eelco
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