(logo) (banner)

Up to DOoM Home Page

DOoM Online ratings model statistics

The following is the output of a script I wrote some time ago to see how closely the online ratings system's empirical results match is underlying theory.

The script looked at all (currently 53 316) games in the ratings database and tracked statistics by the ratings difference between the two players (to the nearest hundred points), and by the rating of each player (again, to the nearest hundred points).

The first table shows the win ratios (multiplied by 1000) in each category, along with the mean by difference and the value predicted by the Elo model.

The second table shows how many games were played in each category. Only categories with at least 50 games played appear in either table.

It has been noted that the presence of robot players, who play differently in many respects from human players (they play more games, against a wider range of opponents, and use different strategy) skews results. I have therefore also compiled tables of statistics not including games involving robot players.

John Chew (poslfit@gmail.com)

Table 1: Modelled and observed win ratios by rating bracket and difference

[ c = hundred, Elo = predicted value, Avg = mean observed]

Diff Elo Avg  2c  3c  4c  5c  6c  7c  8c  9c 10c 11c 12c 13c 14c 15c 16c 17c 18c 19c 20c
-13c 999 958                                                                     949
-12c 999 982                                                         981     964
-11c 999 961                                             974 970     980 975
-10c 999 969                                             969 957 991 988     927
 -9c 999 954                                             925 960 967 957     972 949
 -8c 997 932                                         964 946 933 932 897 887 933
 -7c 993 924                                 890 949 904 921 949 891 948 962 913
 -6c 983 900                         870 887 884 795 924 902 935 866 878 916 883 931
 -5c 961 884                     948 898 800 847 832 874 913 915 864 869 853 901     818
 -4c 921 835                 872 847 843 809 794 769 841 876 832 853 850 792 739 814 860
 -3c 855 752             754 713 728 739 713 716 708 713 795 781 738 779 727 736 768 748
 -2c 760 679         632 709 668 594 672 698 674 655 680 733 674 670 696 686 664 629 641
 -1c 638 604     558 609 504 567 561 591 600 610 592 597 630 623 644 615 593 613 579 544
  0c 500 500 492 522 491 492 519 470 492 514 512 481 497 497 501 490 509 493 504 498 517
  1c 361 395 387 432 472 429 456 411 390 407 392 388 381 367 344 385 409 402 405 470 568
  2c 239 320 328 283 351 380 323 310 321 320 322 271 341 315 291 326 340 349 387
  3c 144 247 205 282 281 256 277 292 294 259 213 221 228 232 277 256 246 264
  4c  78 164 128 114 173 185 207 215 177 118 151 161 158 198 233 220 145
  5c  38 115  31 121 137 180 162 133  82  81 142 137 122 137     140
  6c  16  99 120  95 150 172 135  90  64 135 118  93 129  50
  7c   6  75      76  71  85  82  53 100  74  34  75
  8c   2  67      39  34  58  56 102  89  95 107
  9c   0  45          60  65  17  39          37
 10c   0  30      37  40   8  10      65
 11c   0  38  16  22          41
 12c   0  17                  35
 13c   0  41                  53

Table 2: Hundreds of games played by category

Diff Tot  2c  3c  4c  5c  6c  7c  8c  9c 10c 11c 12c 13c 14c 15c 16c 17c 18c 19c 20c
-13c   2                                                                       1
-12c   3                                                           1       1
-11c   4                                               1   1       1   1
-10c   7                                               1   1   1   2       1
 -9c   8                                               1   2   2   1       1   1
 -8c  10                                           1   2   2   1   1   1   1
 -7c  13                                   1   1   1   2   2   2   1   1   1
 -6c  21                           1   1   1   1   1   4   5   2   2   1   1   1
 -5c  30                       1   1   1   2   1   2   7   5   3   2   2   1       1
 -4c  41                   1   1   2   2   3   2   3   8   6   4   3   3   1   1   2
 -3c  61               1   1   2   2   2   4   3   4   9   7   4   8   6   3   2   1
 -2c  98           1   1   2   3   3   4   5   4   6   9   9  12  15  10   8   3   2
 -1c 133       1   1   2   3   3   5   5   6   7   7  10  12  13  20  13  13   7   3
  0c 140   1   2   2   3   4   4   6   5   5   7   7  10  11  11  25  14  13   8   3
  1c 133   1   1   3   3   3   5   6   5   7   7  10  13  13  19  15  12   8   2   1
  2c  98   1   1   2   3   3   4   5   4   6   8  10  12  14  10   8   4   2
  3c  61   1   1   2   3   2   3   3   4  10   7   5   8   6   4   2   1
  4c  41   1   1   1   2   3   2   3   7   7   3   3   3   1   1   2
  5c  30   1   1   1   2   2   2   7   6   3   2   2   1       1
  6c  21   1   1   1   1   1   4   5   2   2   2   1   1
  7c  13       1   1   1   2   3   2   1   1   1
  8c  10       1   1   2   3   1   1   1   1
  9c   8           1   2   2   1           1
 10c   7       1   1   1   2       1
 11c   4   1   1           1
 12c   3                   1
 13c   2                   1