## Tuesday, December 11, 2012

### Tourney ranking test

Suppose the actual strength of 25 teams that we're trying to rank that will be hidden from the algorithm is:
1.A
2.B
3.C
4.D
5.E
6.F
7.G
8.H
9.I
10.J
11.K
12.L
13.M
14.N
15.O
16.P
17.Q
18.R
19.S
20.T
21.U
22.V
23.W
24.X
25.Y

Because we don't know ahead of time the actual ranking we just have them listed randomly:
1. M
2. V
3. G
4. F
5. L
6. Y
7.R
8.U
9.T
10.W
11.B
12.S
13.P
14.A
15.X
16.C
17.H
18.J
19.N
20.K
21.O
22.E
23.D
24.I
25.Q
Now a matchup grid is made.Every team plays 5 other teams. It actually took a little while to think of a pattern that had 5 x's in each row, each column, where if there was an x in a row, column pair then it was also in the transpose, and that nothing was on the top left to bottom right diagonal which would mean a team was playing itself.

Using the fact that earlier letters in the alphabet beat later ones a 1 is put for every win of a row versus a column.

So after 10 iterations of putting the sum of a rows entries into the non-zero column entries it gives the ranking of:
1. A
2. D
3. F
4. B
5. G
6. H
6. E
7. C
8. O
8.M
9. L
9.K
9.Q
10. C
10. N
11. J
12. P
13. T
14. U
15. R
15. S
16. V
17. Y
18. X

So it recovered most of the original alphabetical order.