Time Handicap Tournaments

I looked up “chess time handicap tournament” in Google, and found that time handicap tournaments are popular in England.  In these tournaments, a fixed time is allocated for each game, and this time is split in a ratio according to the difference in the players’ ECF grades.  (An ECF grade difference of 25 points is equivalent to 200 Elo points.)  If the players are of equal strength, their times on the clock are equal.  Otherwise the weaker player receives a higher proportion of the total time available.

The Crowthorne Chess Club splits a total of 15 minutes in the ratio:

ECF   Time
Diff  Ratio
0     1.00
3     1.14
8     1.50
13    2.00
17.5  2.75
23.5  4.00
33.5  5.00
44.5  7.20
55.5  9.00
71.5  14.00
91.5  19.00

(See: http://www.ecforum.org.uk/viewtopic.php?f=28&t=3127)  A deficit of 25 ECF points is compensated by roughly quadrupling the time limit.  However, the link above makes it clear that for the larger time ratios, the stronger player barely has time to move the pieces, and virtually all his thinking takes place on his opponent’s clock!

The Calderdale Chess Club splits a total of 180 minutes in the ratio:

ECF   Time
Diff  Ratio
0     1.00
10    1.25
20    1.57
30    2.00
40    2.60
50    3.50
60    5.00
70    8.00
80    17.00

(See: http://www.bardelang.f2s.com/ko2006/rules.php)  A deficit of 25 ECF points is compensated by roughly doubling the time limit.

The Cowley Chess Club splits a total of 60 minutes in the ratio:

ECF   Time
Diff  Ratio
0     1.00
6     1.14
12    1.31
18    1.50
24    1.73
30    2.00
36    2.33
42    2.75
48    3.29
54    4.00
60    5.00
66    6.50
72    9.00

(See: https://sites.google.com/site/cowleychessclub/club-handicap-tournament-2/handicap-rules-2011-12)  A deficit of 25 ECF points is again compensated by roughly doubling the time limit.

The Stockport Chess Club splits a total of 150 minutes in the ratio:

ECF   Time
Diff  Ratio
0     1.00
5     1.14
10    1.31
15    1.50
20    1.73
25    2.00
30    2.33

(See: http://www.stockportchessclub.org/knockout.html)  A deficit of 25 ECF points is compensated by exactly doubling the time limit here.

With the exception of Crowthorne, the ratio of the time limits roughly doubles for every 25 ECF points (or 200 Elo points) of rating difference.  This result is in agreement with my results for solving the problems in Jeff Coakley’s Winning Chess Exercises for Kids, see Rating vs. Time on the Clock.  Since the stronger player can think on his opponent's (potentially much larger) clock time, I would have expected a larger time handicap.

Crowthorne allocates a much shorter time to each game, and increases the ratio of the time limits at roughly double this rate.  Crowthorne says that their handicaps have been adjusted over the years to try to give everyone an equal chance.  It is not clear whether the lower level of handicap used by the others for their longer time limits fully equalises the chances of the stronger and weaker players.

The calculations quoted above either use a table of values to determine the time limits for the respective players, or a simple formula, e.g. for Calderdale:

“Players with equal grades will have 90 minutes each to complete the game.  For each point difference in grade, the lower-graded player will have one minute extra and the higher-graded player one minute less.  If the grade difference exceeds 80 points, it is assumed to be exactly 80 points for this purpose.”

This calculation has the advantage of being easy to carry out in the head.  Nonetheless, it has two fixed parameters (90 minutes and 80 points) and the increase in the time allocated to the weaker player ought to be continuous rather than come to an abrupt end. I suggest an alternative approach.  Let:

g = (ECF grade difference) / 25

or equivalently:

g = (Elo rating difference) / 200

The ratio of the two players’ time limits is taken to be:

r = 2^g = (Weaker player’s time) / (Stronger player’s time)

Let the total time available for both players be:

T = (Weaker player’s time) + (Stronger player’s time)

Stronger player’s time = T / (1 + r) = T / (1 + 2^g)

Weaker player’s time =  T * r / (1 + r) = T * 2^g / (1 + 2^g)

This calculation has only one fixed parameter, which I have taken to be 25 ECF points (or equivalently 200 Elo points).  This value may turn out to be too large to fully equalise the chances of the stronger and weaker players, but can easily be adjusted.  This calculation is too difficult for most people to do in their head, but a table of values can easily be generated using a spreadsheet.

Also see my later article: Analysis of the Cowley time Handicap Results.