[tournament-org] WhereIsTheBar

[TobyManning]

Geoff:

1) Your probabilities are incorrect : 86.6 +(2*1.8) + (2*0.4) does not 
add up to 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. 
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. And the strongest 
players - those affected by your analysis - would rather play even games 
than handicap games. Until you can provide a consensus view to the 
contrary, please stop this ridiculous idea of handicap games at the top 
of the draw.

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:
>
>
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