Friday, 2 March 2012

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:  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:  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:  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:  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.


  1. Sorry if it seems that i am nagging but:
    The stronger player can calculate during the time the weaker player is thinking. Its not easy to determine how much gain can be achieved by thinking on the opponents watch. Usually >>i<< am not much supervised by my opponents move, i would say usually i already knew my opponents response to my move.
    So 200 Elo-Points is to high ( though i think a little only ).

  2. For the very fast time limits, you have to think on your opponent’s time, otherwise you cannot physically move the pieces fast enough. You have to have look at all your opponents replies (if you can!) and decide your responses in advance. For the slower time limits, I suspect most strong players will think “I can beat this patzer however much time he has” and not work that hard. Nonetheless, I expect that if you have ten minutes on your clock, and your opponent has forty, thinking on your opponent’s clock is likely to be a significant factor.

    I have always thought that thinking on my opponent’s clock was helpful in an ordinary clock game, and this is often recommended. However, an IM friend told me that this “was wrong,” and that I should rest and walk around while my opponent’s clock was running. Perhaps thinking on your opponent's clock is not the advantage that it appears to be. This is especially true if you are a strong player in a Swiss. You have a big advantage if your strong opponent's are tired when you meet them, and you are not.

    In a clock simultaneous, while all the games are in progress the stronger player is disadvantaged when all his opponents move at the same time, but he gains an advantage when one or more of the games are completed.

    Perhaps we could get both players to play a computer when their human opponent’s clock is running, to isolate the effect of extra time on the clock.

    200 points my well be too much to equalise the chances of the stronger and weaker players if you can think on your opponent’s clock. A rigorous test would not be difficult. We just need to compare the average score of the stronger players with that of the weaker players.

  3. I did watch several Masters at Games... Most of them are looking "hard" at the board even if it is not their move. If they are not "calculating" at these moments.. phuuh, then they are very ill ;-).
    But no matter what the "real" number is, 120 or 200... I think an interesting question is: is it always, say 200 , for every player? A related question might be: Why is this ( logarithmic ) factor lower for chess engines?
    The answer might be: better human player calculate less possible answers to a move, they "know" the possible best moves.

  4. I have re-jigged my conclusions a little. Crowthorne does appear to have made a good attempt to equalise the chances of the stronger and weaker players, but I am not sure about the others. I have also spelt out my suggested calculation.

  5. I have some new data on that "problem" at my blog. Seemingly the relation between speed an score is not that easy.

  6. It is not at all clear what you are measuring in that article. The Chess Tempo ratings do not have any statistical validity, as I have demonstrated previously. It is also not at all clear what significance can be placed on the time that you spend on successful solutions of problems of a particular rating, relative to the average for the players who tackle that problem.

    The exponential relationship may not be accurate, but has right mathematical form, and is reasonably consistent with the time handicaps used in practice. The value of K is problematic. It is clear that Crowthorne tried to fully compensate for the rating differences, and make the result a lottery. The others may have just wanted to give the small guy a better chance.

    A one day Swiss handicap would advance our knowledge here. Perhaps the easiest experiment is a match between a human and a computer with the computer playing very quickly at a fixed strength, and the human playing with a variety of time limits.

  7. I have got a reply from Cowley Chess Club:

    "I am replying to this on behalf of Dave Robson at the Cowley Club. The straight answer to your question is that we have been running this Tournament - or something based on similar handicaps - for 7 years now and it has invariably been won by a highly graded player. The rules for this year have been altered to try and favour the lower grades in matters other than time alone, eg choice of colour, but it does not seem to be making much difference. Bearing in mind that in some cases the strongest player is playing off 5 minutes (against 55) this may seem surprising. I suspect that there are psychological factors at work eg a very low expectation of beating the stronger player. You can get information on the Tournament from the Cowley Chess Club website but if you have more specific questions do let me know. If you wish I can let you have the full results of this year's competition (with grades) when it is concluded in a couple of months time."

    Hopefully, we will have some numbers soon!