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<p>Geoff:</p>
<p>Thanks for the extra information.</p>
<p>However, I revert to my intiial question:</p>
<p>Which is more inportant, to<b> restrict the bar depth</b> or to
have the<b> number of people above the bar compliant with the
Table</b> in the handbook
(<a class="moz-txt-link-freetext" href="http://www.britgo.org/organisers/handbook/tournament4">http://www.britgo.org/organisers/handbook/tournament4</a>).</p>
<p>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.</p>
<p>I have re-read your article in BGJ #173, which discusses how
effectively the MacMahon system gives people an even spread of
opponents.</p>
<p>We need to recognise that, <b>irrespective of where the bar</b>
is set:-</p>
<p>a) those at the very top (the 4 dans) will have more "easy" games
and we expect them to have an above-average result</p>
<p>b) those well below the bar (the 5 kyus, say) will have a 50:50
result on average</p>
<p>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.** <br>
</p>
<p>So placement of the bar cannot prevent this disadvantagement; it
merely alters the make up of the cohort in my group (c) above.</p>
<p>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.</p>
<p>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).</p>
<p>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.</p>
<p><b>Manual Overrides</b></p>
<p>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. <br>
</p>
<p>I think this emphasises the importance of getting the GoDraw
defaults as good as we can.<br>
</p>
<p>Toby</p>
<p>**I speak from (not really bitter) experience.<br>
</p>
<br>
<br>
<br>
<div class="moz-cite-prefix">On 07/11/2018 13:31, Geoff Kaniuk via
tournament-org wrote:<br>
</div>
<blockquote type="cite"
cite="mid:ad005c2f-f467-5843-1d76-758ff48c03f9@kaniuk.co.uk">A.
THREE PEAKS
<br>
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.
<br>
<br>
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.
<br>
<br>
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.
<br>
<br>
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.
<br>
<br>
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:
<br>
<br>
After closing the register,
<br>
If you do not like the bar,
<br>
Just change it!
<br>
<br>
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!
<br>
<br>
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!
<br>
<br>
B. THE BGA BAR TABLE CONDITIONS
<br>
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
<br>
<br>
C. THE BGA BAR TABLE VALUES
<br>
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.
<br>
<br>
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.
<br>
<br>
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:
<br>
<br>
rounds 2 3 4 5 6 7 8 9 10
<br>
low 2 3 4 5 6 7 8 9 10
<br>
high 11 12 14 15 16 18 19 21 22
<br>
<br>
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.
<br>
<br>
Toby said:
<br>
>Of course, the statement on bar depth being less than 3
assumes that >the grades are "correct" in some ill-defined way.
<br>
<br>
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.
<br>
<br>
<br>
Geoff
<br>
<br>
33 Ashbury Close, Cambridge CB1 3RW 01223 710582
<br>
<br>
On 06/11/2018 13:27, TobyManning via tournament-org wrote:
<br>
<blockquote type="cite">Further issues with the Bar at the 3
Peaks...
<br>
<br>
*Background*
<br>
<br>
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.
<br>
<br>
Incidentally one of the 5 dans lost to a 1 dan - it can happen.
<br>
<br>
*Analysis*
<br>
<br>
The BGA Tournament Handbook
(<a class="moz-txt-link-freetext" href="http://www.britgo.org/organisers/handbook/tournament4">http://www.britgo.org/organisers/handbook/tournament4</a>) states
(my added emphasis):
<br>
<br>
<br>
/4.2////The Bar/
<br>
<br>
/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:/
<br>
<br>
/3 rounds/ /4-8 players/
<br>
/4 rounds/ /5-10 players/
<br>
/5 rounds/ /6-12 players/
<br>
/6 rounds/ /7-15 players/
<br>
/7 rounds/ /8-18 players/
<br>
/8 rounds/ /9-22 players/
<br>
/9 rounds/ /10-26 players/
<br>
/10 rounds/ /11-30 players/
<br>
<br>
/These figures attempt to meet the following conditions:/
<br>
<br>
* /There must be a unique winner. This sets an absolute upper
limit,
<br>
of 2//^r ////players above the bar, where r is the number of
rounds./
<br>
* /If there are too many above the bar, the tournament will
end
<br>
without all of the top players having played each other./
<br>
* /If there are too few above the bar, these receive an unfair
(and
<br>
unnecessary) disadvantage./
<br>
* /Higher graded players should not run out of even game
opponents./
<br>
<br>
/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.////
<br>
//
<br>
//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]./
<br>
<br>
/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./
<br>
<br>
<br>
Of course, the statement on bar depth being less than 3 assumes
that the grades are "correct" in some ill-defined way.
<br>
<br>
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.
<br>
<br>
The Table is constructed on 2 simple principles:-
<br>
<br>
a) The total should be less than 2**n (where n is the number of
rounds - this ensures a unique winner
<br>
<br>
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).
<br>
<br>
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.
<br>
<br>
Of course one can always play handicap games at the top end....
but that is a different debate.
<br>
<br>
Toby
<br>
<br>
<br>
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<br>
<br>
</blockquote>
<br>
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<br>
<pre class="moz-signature" cols="72">--
Toby Manning
26 Groby Lane
Newtown Linford
LE6 0HH
01530 245298</pre>
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