To Matrix or not to Matrix

[Ron Van Putte]

On Nov 13, 2004, at 3:54 PM, George Kennie wrote:

>
> <<<BTW, the way the matrix system is implemented now, the top eight 
> entrants are seeded, based on the previous Nats, and the
> top four are distributed among groups 1, 2, 3, 4, and the next four 
> are distributed among groups 1, 2, 3, 4.>>>
>
> This is confusing to me. To say that the top 4 are distributed in 
> groups 1,2,3&4 and the next 4 are distributed in groups 1,2,3&4 sounds 
> the same as the top 8 are distributed in groups 1,2,3&4 ?????? Please 
> clarify.

Pilots are seeded 1 thru 8.  Pilots seeded 1 and 5 are in group 1, 
pilots seeded 2 and 6 are in group 2, pilots seeded 3 and 7 are in 
group 3 and pilots seeded 4 and 8 are in group 4.  First day is group 1 
vs 2 and group 3 vs 4.  Second day is group 1 vs 3 and group 2 vs 4.  
Third day is group 1 vs 4 and group 2 vs 3.  If things go according to 
the seeding, at the end of the third day, pilots  1 thru 3 should each 
have won at least two rounds.  Pilot 1 will have won six times, pilot 2 
will have won four times and pilot 3 will have won twice.  Pilot 4 will 
not have won a round, but should be close for the day against pilot 3.  
We keep the best score from each day, plus the next best score not 
previously used, so pilot 1 has a 4,000 normalized score, pilot 2 also 
has a 4,000 normalized score and pilot 3 has a score of 2,000, plus his 
third daily score and the next highest score not used previously.  
Pilot 4 has his three best daily scores, plus the highest score not 
previously used.

I have run simulated contests for 32 pilots using this seeding and, 
unless pilot 1 is vastly superior to pilot 2, even the worst case 
scenario of having pilots who are ranked 1, 5, 9, 10, 11, 12, 13, 14 in 
group 1, pilots  who are ranked 2, 6,  15, 16, 17, 18, 19, 20 in group 
2, pilots  who are ranked 3, 7, 21, 22, 23, 24, 25, 26 in group  3 and 
pilots  who are ranked 4, 8, 27, 28, 29, 30, 31, 32 in group 4, the 
matrix system will get EVERY finishing place correct.  Try it yourself 
if you don't believe it.  Frankly, I am tired of having people who have 
not "done the numbers" claim otherwise.  I had a lively discussion and 
exchange of data with Dave Lockhart on this subject and he could 
demonstrate situations where the matrix system did not get the right 
order, but it required that the best pilot had to be far superior to 
all the other pilots for the matrix system to get it wrong.  That 
hasn't happened in real life so far.

I'll be honest in agreeing that the problem of a good pilot having an 
unlucky day (flameouts, equipment problems, etc) causing a pair of low 
scores on one day that would keep him from the finals, is not right, 
but I don't see a fair way around it.

Ron Van Putte
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