[tournament-org] The Bar in general
TobyManning
ptm at tobymanning.co.uk
Thu Nov 8 09:47:50 GMT 2018
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.
On 07/11/2018 13:31, Geoff Kaniuk via tournament-org wrote:
> A. THREE PEAKS
> The 3P incident was interesting. I has a conversation with Bob after
> the event and it transpired that initially Bob had a top group of 6
> players something like 5d,4d, 1k,1k, 1k,1k. After closing the
> register GoDraw set the bar at 1k, as this provides a jump from 2 to 6
> players, even though the bar-depth exceeds 3.
>
> At this point two more players pitched up: a 2d and a 1d. I am not
> sure if Bob had already done the draw, but there would have been no
> problem - just pair them and sort out the draw later after entering
> results. This would have left the bar at 1k as it does not get
> re-computed.
>
> I assume he had not done the draw, and may have tried to add these two
> players. This would be refused by GoDraw because it had already
> worked out the bar. Now you have to re-open the register, add the two
> players, and close the register.
>
> Now GoDraw sets the bar afresh. At 2d the bar depth is 3 but still not
> enough players to exceed the number of rounds. So it leaves the bar at
> 4d.
>
> I do understand the tension involved in getting the first round going,
> so Bob did the right thing and carried on with the draw. But actually
> there is a simple way to deal with this:
>
> After closing the register,
> If you do not like the bar,
> Just change it!
>
> There is a field for setting the bar manually and you can adjust it to
> what you want. The philosophy underlying GoDraw is that it is a TD's
> toolkit, not a TD's boss!
>
> You cannot change the bar after doing the draw. The only thing setting
> the bar does, is to specify the player's initial McMahon score. Again
> there is a field in the register editor which allows you to change the
> player's initial MMS and this of course adjusts the players current
> MMS as well. By making this adjustment for all the players you want
> above the bar, you achieve what you want!
>
> B. THE BGA BAR TABLE CONDITIONS
> Toby reproduces four conditions which an ideal bar setting should
> meet. These are indeed aspirations. But on their own they do not
> provide any information that is useful for setting the bar. A 5 round
> tournament would require exactly 32 players above the bar to guarantee
> a unique winner. Three Peaks had a total of 34 so almost everybody
> above the bar?. It might be well worth while having a look at BGJ 173
> - Finding the Bar which discusses
>
> C. THE BGA BAR TABLE VALUES
> I have in the past tried to find some documentation on the origins of
> the table and the best I got was that it is lost in the mists of time.
>
> When the table was invented, people did not have a good measure of the
> probability of win between players of different strengths. But now
> through the data collected by EGD we do have a good model. This
> enables us to simulate McMahon tournaments to assess the effect of
> different bar settings and that work is cited in the BGJ 173 article.
>
> The outcome confirms that you cannot set the bar on the basis of
> number of rounds alone, but it depends on the nature of the
> distribution of top grades. It leads to the following table which is
> a rough linear representation of the extremes of the bar populations
> in the simulations:
>
> rounds 2 3 4 5 6 7 8 9 10
> low 2 3 4 5 6 7 8 9 10
> high 11 12 14 15 16 18 19 21 22
>
> In these simulations the bar was calculated by a Monte Carlo
> algorithm. The bar depth never exceeded 3 and was very rarely equal to 3.
>
> Toby said:
> >Of course, the statement on bar depth being less than 3 assumes that
> >the grades are "correct" in some ill-defined way.
>
> The McMahon system relies on players entering with realistic grades,
> and so in all my discussions I always assume that grades are
> consistent with player strengths as found on our rating page.
>
>
> Geoff
>
> 33 Ashbury Close, Cambridge CB1 3RW 01223 710582
>
> On 06/11/2018 13:27, TobyManning via tournament-org wrote:
>> Further issues with the Bar at the 3 Peaks...
>>
>> *Background*
>>
>> The 3 peaks is a 5 round tournament. The entry was 5d 5d 2d 1d 1d 1k
>> 1k 1k 2k.... and Bob Bagot wanted to put the bar at 1 kyu. However,
>> the software (Go Draw) put it at 5 dan, so in the first round the 2 5
>> dans played each other (and the 2d played a 1 d). With advice from
>> Geoff - for which many thanks - the bar was restrospectively changed
>> to 1 kyu for rounds 2-5.
>>
>> Incidentally one of the 5 dans lost to a 1 dan - it can happen.
>>
>> *Analysis*
>>
>> The BGA Tournament Handbook
>> (http://www.britgo.org/organisers/handbook/tournament4) states (my
>> added emphasis):
>>
>>
>> /4.2////The Bar/
>>
>> /Because a player's starting score is determined by their grade, a
>> player who was 7 dan would have a massive advantage and the best
>> chance to win the tournament, as such a player would start with a
>> very high MMS. To counteract this, and to give as many people as
>> possible a reasonable chance of winning the tournament, players at or
>> above a certain rank all begin at the same MMS. This rank is called
>> the McMahon bar. For example, if the bar is set at 3 dan (which is an
>> MMS of 2) then no player can start at an MMS of more than 2, no
>> matter what his or her grade: 3-dans, and all players stronger than
>> 3-dan, also start with an MMS of 2, and are said to start "above the
>> bar". The position for the bar depends on the number of rounds to be
>> played and also the entry at each of the higher grades. BGA
>> recommended guidelines are as follows:/
>>
>> /3 rounds/ /4-8 players/
>> /4 rounds/ /5-10 players/
>> /5 rounds/ /6-12 players/
>> /6 rounds/ /7-15 players/
>> /7 rounds/ /8-18 players/
>> /8 rounds/ /9-22 players/
>> /9 rounds/ /10-26 players/
>> /10 rounds/ /11-30 players/
>>
>> /These figures attempt to meet the following conditions:/
>>
>> * /There must be a unique winner. This sets an absolute upper limit,
>> of 2//^r ////players above the bar, where r is the number of
>> rounds./
>> * /If there are too many above the bar, the tournament will end
>> without all of the top players having played each other./
>> * /If there are too few above the bar, these receive an unfair (and
>> unnecessary) disadvantage./
>> * /Higher graded players should not run out of even game opponents./
>>
>> /The McMahon System imposes two quite severe constraints on the
>> pairing of players at each round. The first is the rule that there
>> are no repeat games. This increasingly restricts the opponents of the
>> stronger players in the later rounds. The second is the aim of
>> pairing players on the same MMS, which provides the main pairing
>> diversity in the early rounds.////
>> //
>> //These two pairing rules, together with the nature of the winning
>> probability between players of different grades, provides quite an
>> important ingredient in determining the position of the bar. //*It
>> turns out that players in the bar group have at least some chance of
>> winning the tournament if the difference between the maximum grade
>> and the bar grade (the bar-depth) is less than 3*//, whatever the
>> number of rounds [See BGJ 173 Finding The Bar]./
>>
>> /If you are using Geoff Kaniuk's GoDraw to create the draw,//*it will
>> automatically set the bar according to the above table taking into
>> acount the restriction on the bar depth*//. This is particularly
>> effective in tournaments where the dan entry is very fragmented with
>> possible gaps in the higher grades./
>>
>>
>> Of course, the statement on bar depth being less than 3 assumes that
>> the grades are "correct" in some ill-defined way.
>>
>> It is clear that what is happening is the restriction on bar depth is
>> over-riding the recommended nuimbers in the Table. I believe that
>> this is wrong, and that the Table should have supremacy.
>>
>> The Table is constructed on 2 simple principles:-
>>
>> a) The total should be less than 2**n (where n is the number of
>> rounds - this ensures a unique winner
>>
>> b) The Tournament winner's opponents should all have started above
>> the Bar (although one appreciates that this may not have been the
>> case if the number above the bar is odd and the eventual winner is
>> drawn down in their first game).
>>
>> In the 3 Peaks example,each 5 dan will play 5 opponents, of strength
>> (probably) 5d 2d 1d 1d 1k, and if (for example) one of the 1 dans
>> wins all 5 games, including beating both 5 dans, they shdol win the
>> Tournament.
>>
>> Of course one can always play handicap games at the top end.... but
>> that is a different debate.
>>
>> Toby
>>
>>
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>
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--
Toby Manning
26 Groby Lane
Newtown Linford
LE6 0HH
01530 245298
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