[tournament-org] The Bar in general

[TobyManning]

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

-- 
Toby Manning
26 Groby Lane
Newtown Linford
LE6 0HH
01530 245298

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