## Sunday, 15 July 2012

### Analysis of the Cowley Time Handicap Results

In my earlier article, Time Handicap Tournaments, I discussed the time handicap systems used by various English chess clubs.  The results for this year’s Cowley Chess Club Time Handicap Tournament, have now been published, complete with the players’ ECF grades, see:

These results are summarised in the three tables below:

Grade   Ray     Geoff   Dave    Bill    Jothn   Score
Ray     184     X       1       0       1       1       0.75
Geoff   158     0       X       1       1       1       0.75
Dave    148     1       0       X       1       1       0.75
Bill    138     0       0       0       X       0       0
Jothn   100     0       0       0       1       X       0.25

Grade   MariaW  Anna    MariaM  Dave    Score
MariaW  175     X       0       0.5     1       0.5
Anna    166     1       X       0.5     1       0.833
MariaM  143     0.5     0.5     X       0.5     0.5
Dave    143     0       0       0.5     X       0.167

Grade   Gerard  Heather Paul    John    Jenny   Score
Gerard  213     X       0.5     1       1       0       0.625
Heather 161     0.5     X       1       0       1       0.625
Paul    157     0       0       X       0       1       0.25
John    136     0       1       1       X       0.5     0.625
Jenny   115     1       0       0       0.5     X       0.375

For each player, I worked out the average grade of his opponents, and subtracted this value from their own grade to give their grade advantage over the opposition that they faced.  I also estimated how many points stronger than the opposition each player would have had to be in order to achieve the same score in a very long match without a time handicap, using the formula:

d = 100*s-50

In this formula, s is the score (as a fraction between 0 and 1) and d is the corresponding grade difference.  This formula uses a simplified version of the ECF grading calculation, see:

(Bill’s zero score would have caused a problem for the Elo formula.)  The results of my calculations are summarised in the table below:

Ray       184     136      48     0.75     24
Geoff     158     143      16     0.75     24
Dave      148     145      3      0.75     24
Bill      138     148     -10     0.00    -50
Jothn     100     157     -57     0.25    -24
MariaW    175     151      24     0.50      0
Anna      166     189     -23     0.83     35
MariaM    143     161     -18     0.50      0
Dave      143     126      17     0.17    -35
Gerard    213     142      71     0.63     11
Heather   161     155       6     0.63     11
Paul      157     156       1     0.25    -24
John      136     162     -26     0.63     11
Jenny     115     167     -52     0.38    -11

If the time handicap had been perfect, and enough rounds were been played, the players scores would all  be close to 0.5.  In reality, of course, they are not.  The scatter graph below plots each players’ grade advantage over their opposition (horizontal axis) against the grade advantage they would need to achieve their actual score in a long match without a time handicap (vertical axis):

This graph suggests that the weakest players were at a disadvantage of about 20 ECF points, despite the time handicap.  It also suggests that the strongest players had a corresponding advantage. This result concurs with the organiser’s statement that the tournament has invariably been won by a highly graded player over the seven years that it had been running prior to this year (see the comments to the previous article).   The handicap system used in this tournament is described in the link:

In this tournament, the lower graded player always had White.  The advantage of having the White pieces corresponds to about 35 Elo points, see:

35 Elo points corresponds to 35 * 25 / 200 = 4.375 ECF points.  This tournament therefore had an additional handicap of about 2 ECF points, resulting from the weaker player having White 100% of the time rather than the usual 50% of the time.  This advantage is negligible compared with the scatter on the graph above, so I have ignored it in my calculations.  I suggest a slightly more aggressive time handicap:

0        1       2       3       4       5       6       7       8       9
0    30:00    29:29   28:58   28:27   27:55   27:24   26:54   26:23   25:52   25:22
10    24:51    24:21   23:51   23:21   22:52   22:22   21:53   21:25   20:56   20:28
20    20:00    19:32   19:05   18:38   18:12   17:46   17:20   16:54   16:29   16:05
30    15:40    15:16   14:53   14:30   14:07   13:45   13:23   13:02   12:41   12:20
40    12:00    11:40   11:21   11:02   10:43   10:25   10:08   09:50   09:33   09:17
50    09:01    08:45   08:30   08:15   08:00   07:46   07:32   07:18   07:05   06:52
60    06:40    06:28   06:16   06:04   05:53   05:42   05:32   05:22   05:12   05:02
70    04:52    04:43   04:34   04:26   04:17   04:09   04:01   03:53   03:46   03:39
80    03:32    03:25   03:18   03:12   03:06   03:00   02:54   02:48   02:43   02:38
90    02:32    02:27   02:23   02:18   02:13   02:09   02:05   02:01   01:57   01:53
100    01:49    01:45   01:42   01:39   01:35   01:32   01:29   01:26   01:23   01:21
110    01:18    01:15   01:13   01:10   01:08   01:06   01:03   01:01   00:59   00:57

This table gives the time on the clock for the higher graded player, for grade differences from 0 to 119. The corresponding time for the lower rated player is the balance of 60 minutes.   I constructed this table using the formula:

t = 60/(2^(g/20)+1)

In this formula, g is the ECF grade difference, and t is the time allocated to the higher graded player.  With this formula, the time allocated to the higher graded player, relative to that allocated to the lower graded player, halves for every 20 point difference in their grade. The time allocated to the stronger player drops below one minute at a grade difference of 118.  Nonetheless, Crowthorne Chess Club successfully uses even shorter time limits, see:

http://www.ecforum.org.uk/viewtopic.php?f=28&t=3127

The stronger player’s analysis will be 1 ply less deep if he does his thinking on his opponent’s clock time rather than his own, which is not an enormous handicap.  One minute should be enough for him to physically make all his moves, provided that he wins quickly enough!  Nonetheless, even with my proposed time limits, I expect that the stronger players will still have an advantage, but the handicaps should be fairer overall.