[tournament-org] The Bar in general

[Geoff Kaniuk]

I agree with Toby's points a,b,c below.  I even agree that placement of 
the bar cannot prevent the disadvantage.

Where we disagree is with the use of the BGA table in setting the bar.

There is plenty of evidence to show that you cannot set the bar based on 
the number of rounds alone.  For a 6 round tournament, the BGA tables 
advise you to have a population range from 7 to 15 players, and in some 
tournaments that would lead to a range from 5k to 2d or worse.

It is essential to take account of the grade distribution at the top, 
and the bar depth idea is just a first step in trying to do this. I have 
created a spreadsheet showing bar-grade data for all our tournaments 
this year.

http://www.kaniuk.co.uk/articles/pairing/bga-bar-grades-2018.xls

It has a table on the sheet 'pwin' showing the probability that player 
with grade Glo (column A) beats player with grade Ghi (row 3)

In the sheet 'tours-pub' we have an anonymised table of tournaments 
presented in bar-depth order. It shows who the winner played and I have 
detailed the few cases where the winner dropped a game. This happened in 
just 5 out of 25 tournaments and in nearly all such cases the grade 
difference was just one.

There is data showing the probability that the player at the bottom of 
the bar (with grade Gbar) beats the maximum graded player. There were 7 
tournaments where the bar-depth varies from 4 to 7. In these tournaments 
the Gbar player has a winning chance against the strongest in the range 
0.1% to 8.2%

For the 10 tournaments with a bar-depth of 1 or 2 this probability lies 
in the range 18.1% to 34.1%

For the 8 tournaments with bar-depth = 3, the range is 10.7% to 26.1%

The spreadsheet also contains a useful plot of these probs vs bar-depth

Remember that these probabilities are calculated for just one game.  The 
actual probability of a Gbar winning the tournament is usually tiny.

My conclusion is that when the population at a bar-depth of 3 is small, 
(varying from 1 to 8) the bar can only be lowered if you are prepared to 
consider using handicaps above the bar.

If we do not want to do that then one possibility is to isolate the top 
group by boosting the initial MMS by a few points - in other words 
create a super group.  This protects the players below the bar from 
hugely unbalanced games.

Geoff

33 Ashbury Close, Cambridge CB1 3RW 01223 710582

On 08/11/2018 09:47, TobyManning via tournament-org wrote:
> Geoff:
> 
> Thanks for the extra information.
> 
> However, I revert to my intiial question:
> 
> Which is more inportant, to*restrict the bar depth* or to have 
> the*number of people above the bar compliant with the Table* in the 
> handbook (http://www.britgo.org/organisers/handbook/tournament4).
> 
> It is still my view that the Table limits shuld be paramount, and the 
> bar depth should be used to determine the bar within these limits.
> 
> I have re-read your article in BGJ #173, which discusses how effectively 
> the MacMahon system gives people an even spread of opponents.
> 
> We need to recognise that, *irrespective of where the bar* is set:-
> 
> a) those at the very top (the 4 dans) will have more "easy" games and we 
> expect them to have an above-average result
> 
> b) those well below the bar (the 5 kyus, say) will have a 50:50 result 
> on average
> 
> c) there is a cohort of people - in the 3 peaks case the 2d/1d - who 
> will have a below-average result as they will each have to play the 4 
> dans at some time.**
> 
> So placement of the bar cannot prevent this disadvantagement; it merely 
> alters the make up of the cohort in my group (c) above.
> 
> In the 3 peaks example, with entry at 4d/4d/2d/1d/1d/1k/1k/1k, this 
> disadvantagement  is effectively the same whether the bar is set at 4 
> dan, 3 dan, 2 dan or 1 dan. This is because the actual games played will 
> be unaffected (each 4 dan is expected to have opponents 4d 2d 1d 1d 1k 
> irrespective of the bar setting).  With the bar at 1 kyu the 
> disadvantagement is slightly more widespread and the total 
> disadvantagement starts to increase, and this then falls off a cliff 
> with the bar at 2 kyu and below.
> 
> In fact, the disadvantagement is essentially constant while the number 
> of people above the bar is less than (n+1) where n is the number of 
> rounds. As the number of people above the bar increases from (n+1) to 
> 2**n this total disadvantagement increases - the amount of the increase 
> depending upon the bar depth. So if the bar depth is shallow the number 
> above the bar should tend towards n**2, if it is deep it should tend 
> towards (n+1).
> 
> There is therefore no benefit from having the number above the bar being 
> less than (n+1); and indeed it would prevent the (rogue) 1 dan/1 kyu 
> winning the tournament, irrespective of their results against the 4 dans.
> 
> *Manual Overrides*
> 
> You are quite right to emphasise that TD's can override GoDraw's 
> defaults. However, my experience is that many TD's - particularly the 
> inexperienced ones - are reluctant to do this as they are concerned 
> about possible unintended consequences.
> 
> I think this emphasises the importance of getting the GoDraw defaults as 
> good as we can.
> 
> Toby
> 
> **I speak from (not really bitter) experience.