[tournament-org] WhereIsTheBar

Tue Oct 2 14:00:35 BST 2018

[[inline]]

Geoff

33 Ashbury Close, Cambridge CB1 3RW 01223 710582

On 02/10/2018 12:34, TobyManning via tournament-org wrote:
> Geoff:
> 
> 1) Your probabilities are incorrect : 86.6 +(2*1.8) + (2*0.4) does not 
> add up to 100%.
[[
I am not sure why you want to add them.

There are three different scenarios. In the first scenario the 1k wins 
in 4 tournaments out of a 100. In the second the 1d wins in 18 out of 100.
]]
> 
> 2) You state: "We have agreed so far that setting the bar at 1k or 1d 
> produces an unfair tournament". *False.* The tournament is perfectly 
> fair - one player has a greater chance of winning than others (based on 
> previous results) but this does not mean it is a foregone conclusion. 

[[
I agree the word fair is loose, but I hope it would suggest a 50% chance 
of winning a game. No one is saying that the 5d winning is guaranteed.
]]
> Heather Watson and Serena Williams both enter Wimbledon and they have 
> equal opportuities to win - you don't say "Serena is so much stronger 
> than Heather therefore she should be handicapped to give Heather a 
> chance" (or to ban Heather from entering because she is considered to 
> have no chance at all).
> 
> 3) Please remember that the purpose of a Go Tournament is for people to 
> enjoy themselves - not to produce a "perfect" result. 
[[
I cannot imagine anyone actually enjoying a tournament game that they 
know they have no chance of winning at all.
]]
And the strongest
> players - those affected by your analysis - would rather play even games 
> than handicap games.
[[
So the weaker players have no say at all?

I do think that the 'no handicaps above the bar' rule is fine when the 
top grades are reasonably well populated.

But when we have pathological entries like in the example, the rule does 
not lead to an enjoyable tournament.
]]

  Until you can provide a consensus view to the
> contrary, please stop this ridiculous idea of handicap games at the top 
> of the draw.
[[
The only way of trying to get a concensus is to alert players to the 
effect of the rules and open the subject for discussion. It seems that 
in quite a few  tournaments the entry at the top is devoid of 3,4,5 dan, 
or at least very low populations leading to strange bar settings.

There has been a growing incidence of these kind of tournaments and I do 
think that we need to adapt to changing times.

McMahon works fine when grades are well populated. For such a wide gap 
at the top it does not, and handicaps provide a solution.
]]
> 
> Toby.
> 
> 
> On 02/10/2018 12:10, Geoff Kaniuk via tournament-org wrote:
>>
>> There is overwhelming support for a bar at 1k with a spread from 2k to 
>> 1d, and a few suggestions allowing handicap above the bar.
>>
>> It seems that we expect the 5d to win no matter where we set the bar, 
>> but in order to run a McMahon tournament we are going to set the bar 
>> to 1k anyway.
>>
>> One guide to setting the bar is that all players above the bar should 
>> have a reasonable chance of winning the tournament. As stated we 
>> assume that all players are correctly rated. This means we know the 
>> win probability for each pairing.
>>
>> Let us suppose the bar is at 1k in our entry of:
>> 5d 1d 1d 1k 1k 2k 2k 3k 3k 4k 4k 5k .....
>>
>> Then given a plausible tournament, the top players have these chances 
>> of winning all three games:
>>
>> PLAYER    OPPONENTS    PER ROUND PWIN      PROB WINNER
>> 1k    1k 1d 5d     0.50*0.40*0.02 =  0.40%
>> 1d    1k 1d 5d    0.60*0.50*0.06 =  1.8%
>> 5d    1k 1d 1d     0.98*0.94*0.94 = 86.6%
>>
>> I think this makes it clear that the 1k and 1d have effectively no 
>> chance to win this tournament. Not much changes if you set the bar to 1d.
>>
>> Going back to basics, the McMahon system is designed to provide a fair 
>> pairing at every round. It does this by assigning an initial MMS 
>> determined by your grade. The fairness comes about because we assume 
>> grades are realistic and always pair players on the same MMS where 
>> possible.
>>
>> The winner is the player who ends on the maximum MMS. If there is only 
>> one strongest then he or she will have a massive advantage. Hence we 
>> have a bar - and in the old days there were plenty of 4d and 5d around 
>> in the top group so no problems.
>>
>> If an an even pairing is not possible, then it is common for players 
>> below the bar to play with handicap - often MMS difference-1 but this 
>> can of course be varied.
>>
>>
>> We have agreed so far that setting the bar at 1k or 1d produces an 
>> unfair tournament. Therefore in order to continue play in the spirit 
>> of McMahon, we should consider raising the bar to 5d. For the sake of 
>> clarity this is equivalent to setting the bar at 6d.
>>
>> In the example given, setting the bar at 1k produces an odd number in 
>> the bar, so one player chosen at random will have to play down.  The 
>> 5d therefore might play a 2k in round 1.
>>
>> Setting the bar at 6d avoids this kind of problem. We pair for the 
>> smallest MM difference so the 5d will play the 1d in round 1 with a 
>> handicap of 3 stones by usual rules.
>>
>> This levels the playing field somewhat but calculations show that this 
>> still favours the 5d and better would be: handicap is the straight MMS 
>> difference.
>>
>> My conclusion is that in these anomalous cases setting the bar 
>> anywhere without handicap goes against the basic principles of McMahon 
>> pairing.
>>
>> In looking at variants of setting the bar with handicap say in a 
>> super-group just leads to complications (e.g. when top players who 
>> miss rounds are supposed to be below the bar).
>>
>> The simplest and most elegant solution to this problem is just to set 
>> the bar to 1 higher than the highest grade. Assign handicaps by 
>> straight MMS difference where needed. Then let McMahon do its job 
>> without any further interference.
>>
>> Geoff
>>
>>
>> 33 Ashbury Close, Cambridge CB1 3RW 01223 710582
>>
>> On 02/10/2018 00:21, Richard Wheeldon via tournament-org wrote:
>>
>>
>> _______________________________________________
>> tournament-org mailing list
>> tournament-org at lists.britgo.org
>> http://lists.britgo.org/cgi-bin/mailman/listinfo/tournament-org
> 
> 
> 
> _______________________________________________
> tournament-org mailing list
> tournament-org at lists.britgo.org
> http://lists.britgo.org/cgi-bin/mailman/listinfo/tournament-org
> 