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Re: More than bracket breaking -Reply

> Gary, what were the assumptions of your out round pairings?  Did your
> simulation assume direct high-high matches or high (8-0 v. 5-3)?  It
> makes a difference.  As I recall, the NFL maintains record against record
> (essentially high-high) matches.  This would, it seems to me, facilitate the
> elimination of teams at the three loss level.  I believe this to be a far
> superior process of producing the National Champion.  My only
> reservation is the impact on the judging pool...it seems to me that NFL has
> to rely on a far larger guest judging pool than we do at CEDA Nationals. 
> Also, I believe that under this system we should employ a six round
> preminary schedule as opposed to our current eight.

In the simulation, I used high/high pairing all the way to the end.  One 
thing that needs to be made clear is that to facilitate a "rapid" 
conclusion to the tournament, you do not want to quickly facilitate three 
loss teams getting their fourth loss.  To do so would be to reduce the 
number of debates that would occur in the next round, thereby slowing the 
progress to the magic number 396-399.  That is why high-high matches get 
you predictably to the most rapid conclusion of the tournament.  If you 
have off-matches (teams with different records debating), you might get 
the desirable result that the team with more losses will win, thereby 
avoiding elimination, thereby increasing the pool of teams for the next 
round, thereby reaching the 796 number more rapidly, thereby shortening 
the tournament.  BUT, it is more likely "statistically" that the team 
with the better record would win, thereby hastening the departure of the 
lower seeded teams, reducing the size of the team pool and lengthening 
the time required to debate 796 rounds.  EVERYONE (but one) eventually 
has to lose four times so you want as many opponents available as possible.

The simulation went as follows:

		Teams elim	No. debates	Cum. total

Round 1		0		100		100
Round 2		0		100		200
Round 3		0		100		300
Round 4		13		100		400
Round 5		25		93		493
Round 6		31		81		574
Round 7		31		65		639
Round 8		27		50		689
Round 9		22		36		725
Round 10	16		25		750
Round 11	11		17		767
Round 12	9		12		779
Round 13	5		7		786
Round 14	4		5		791
Round 15	3		3		794
Round 16	1		1		795
Round 17	1		1		796!!!

This assumes higher seed always win - if 13-3 team in round 17 gets hot, 
it might take 4 rounds to complete the quadruple elimination.  NOTE:  
This model also assumes teams leave after fourth loss.  If you guarantee 
8 rounds, the conclusion is the same UNLESS a team with four losses 
debates a team with less than four losses in rounds 5-8.  The 
implications of such off-matches could be to shorten the tournament but 
would more likely lengthen the tournament.

Sincerely,

GARY

 > > Glen Strickland
> Emporia State
> 
> >>> Gary Larson <g-larson@david.wheaton.edu> 04/10/96 11:09pm >>>
> On Wed, 10 Apr 1996, Gary Larson wrote:
> 
> I haven't been able to find the archive so I ran one quick simulation  that I
> will report on briefly.  If we start with 200 teams and pair every  round
> high-high and always have the higher seed win, the tournament would 
> last 17 rounds with the final round being between a 16-0 team and a 
> 13-3 team (with the additional possibility that all three losses would  have
> come from the team they are now meeting).  This scenario also assumes
>  that teams leave the tournament after being eliminated (as opposed to 
> debating a guaranteed number of rounds - e.g. 8).
> 
> For those who want to test a variety of strategies, some quick guidance.
>   The problem is actually easier than it might appear.  I recall a problem 
> my middle school son was given earlier this year.  He was asked the 
> minimum number of matches that would be required in a double
> elimination  tennis tournament with 45 participants.  He immediately set up
> the  draw complete with byes and tried to figure out after each set of 
> matches how many players would remain and how many would be
> eliminated.
> He ended up with a complicated tournament but the right answer - 88 
> matches.  We then discussed a shortcut.  Since one person wins a
> match  and one loses, if the champion loses none and everyone else
> loses two the  minimum number of matches is (45-1)*2.  As a result, a
> tournament with  200 teams would require a minimum of 796 debates
> (max - 799) to give  everyone but the champion four losses.  In the first
> four rounds of the  tournament 100*4 debates would be completed.  The
> best case scenario (if  one wants the tournament to end quickly) is to
> have teams continue to  debate after being eliminated against the teams
> that are not eliminated  and to then NEVER LOSE AGAIN.  In such a  case
> the tournament could end with all teams eliminated after eight  rounds. 
> Of course if they debate after being eliminated and continue to  lose it
> would take far more than 796 rounds to give everyone 4 losses and 
> their continued presence in the tournament would be detrimental to a 
> rapid conclusion.  If you eliminate teams after four losses the real key  is
> how many remaining rounds you have.  Perhaps counter-intuitively, it  is
> BAD to have teams rapidly eliminated because it would take more 
> scheduled rounds to reach the magic number 796.  If off-matches cause 
> teams to be eliminated early (e.g. my scenario had 73 teams after 8 
> rounds as opposed to the 70 we had at nats) rather than speeding up
> the  tournament it slows it down.  In any case, a 200-team tournament
> would  likely take 17-21 rounds to complete (depending, of course, on
> rules for  dealing with the small number of teams that remain after say 14
> rounds).
> 
> I still don't think such a tournament would serve us well.
> 
> Sincerely,
> 
> GARY
> 
> > On Wed, 10 Apr 1996, Steven Hunt wrote:
> >  > >  > >  > > I am not known for radical ideas by many, but I remind the
> CEDA community  > > of my idea for crowning a national CEDA champion
> sort of modeled after  > > high school NFL nationals.
> > >  > > Everyone debates until they lose 4 rounds. We know that at least
> l30  > > teams are so are eliminated by the end of round 8 leaving us with
> 60-70  > > teams. About 40 of those 60-70 teams already have 3 losses.
> Twenty more  > > teams (minimum) should be eliminated by round 9
> leaving at most 50.
> >  > Actually this "radical" idea was floated a year ago by Bill DeForeest
> and  > others.  At that time I ran a variety of computer simulations testing
> the  > tournament length required to eliminate everyone given various  >
> power-pairing constraints.  I will check to see if it is still archived  > to
> provide an empirical base for the discussion.  In short, the  > tournament
> often ran to over 20 rounds.  In Bill's final defense, he  > eliminated the
> worse case scenario by calling it a winner-take-all final  > round when 2
> teams remained (even if one had 3 losses and the other had  > 0). Other
> negative features to the plan would multiple meetings between  > teams
> (potentially 7 if we took the down 4 idea to its logical  > conclusion), a
> huge number of byes, including teams receiving bye when  > only 3 or 5
> teams remained in tournament, difficulties in bracket  > maintenance and
> others.  While a good thought I have grave doubts that it  > would work. 
> More on this later.
> >  > Sincerely,
> >  > GARY
> >  >  >  > > I would guess that 20 more teams would be eliminated in
> round l0 leaving  > > at most 30.  > >  > > Theoretically l0-l5 more teams
> should be eliminated by round ll leaving  > > l0-l5. Rd l2 ought to eliminate
> 8 more leaving 5-8 teams. Rd l3 ought to  > > eliminate 4 more leaving l-4
> teams. Rd l4 ought to cut it to l-2 and Rd  > > l5 ought top leave the
> national champion.
> > >  > > This all depends on power matching methods utilized.  > >
> Probably there could be 3 judge panels in rds 9 on pressing a few more 
> > > judges to work but not significantly more than triple and double octas
> now.
> > >  > > This system leaves a "true" to my mind national champion based
> on overall  > > performance not just a single round.
> > >  > > I know this is a bit radical but I raise it again merely for  > >
> argumentative purposes and discussion.
> > >  > > Steve Hunt  > >  > 
> 
> 
>
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