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Unread 01-05-2013, 17:24
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Re: 2013 Qual Schedule Analysis

Quote:
Originally Posted by MikeE View Post
With only 8 matches and a field of 100 any reasonable optimization algorithm should converge to the same general solution: play with 16 different teams and against 24 other different teams.
That solution will always give the same summary statistics.
...although that's not what the schedule summaries are showing, since a pair of teams do play each other more than once.
So I reverse my conclusion.
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Unread 01-05-2013, 17:59
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Re: 2013 Qual Schedule Analysis

It appears that the match scheduler does not care about multiple opponents/partners in surrogate matches. I checked the Archimedes schedule and the teams that had multiple opponents played each other once in their surrogate match and once in a match that counted.

Here is the scheduler's analysis of the Archimedes schedule, which does not show repeats in matches that count.

Code:
Schedule Statistics
-------------------

          #: number of matches played, a '+' after the number
               indicates one additional round as a surrogate
          d: minimum delta between matches (e.g. '1' means back-to-back)
       part: number of distinct partners followed by most frequent repeat count
        opp: number of distinct opponents followed by most frequent repeat count

       both: number of distinct teams seen as partner or opponent
               followed by most frequent combined repeat count
        r/b: balance between red and blue alliance appearances
               eg, 3b means team appeared as blue 3 times more than as red
 4+ repeats: any teams seen four or more times as partners or opponents

 team   #   d    part    opp    both    r/b   4+ repeats
 ----  --  --   -----   -----   -----   ---   ------------
   11:  8  11 | 16  1 | 24  1 | 40  1 |  0
   20:  8   9 | 16  1 | 24  1 | 40  1 |  0
   33:  8   9 | 16  1 | 24  1 | 40  1 |  0
   51:  8   8 | 16  1 | 24  1 | 40  1 |  0
   71:  8   9 | 16  1 | 24  1 | 40  1 |  2r
   78:  8  11 | 16  1 | 24  1 | 40  1 |  0
  126:  8   9 | 16  1 | 24  1 | 40  1 |  2r
  172:  8  11 | 16  1 | 24  1 | 40  1 |  2r
  236:  8  14 | 16  1 | 24  1 | 40  1 |  0
  254:  8   8 | 16  1 | 24  1 | 40  1 |  2b
  291:  8   9 | 16  1 | 24  1 | 40  1 |  2b
  314:  8  11 | 16  1 | 24  1 | 40  1 |  0
  316:  8   8 | 16  1 | 24  1 | 40  1 |  0
  321:  8   9 | 16  1 | 24  1 | 40  1 |  2r
  326:  8   9 | 16  1 | 24  1 | 40  1 |  2b
  365:  8   8 | 16  1 | 24  1 | 40  1 |  0
  379:  8  10 | 16  1 | 24  1 | 40  1 |  2b
  433:  8+ 11 | 16  1 | 24  1 | 40  1 |  0
  469:  8   8 | 16  1 | 24  1 | 40  1 |  0
  525:  8  11 | 16  1 | 24  1 | 40  1 |  2r
  639:  8   9 | 16  1 | 24  1 | 40  1 |  2b
  694:  8  14 | 16  1 | 24  1 | 40  1 |  0
  701:  8   8 | 16  1 | 24  1 | 40  1 |  2b
  801:  8   9 | 16  1 | 24  1 | 40  1 |  2r
  812:  8   8 | 16  1 | 24  1 | 40  1 |  0
  836:  8   9 | 16  1 | 24  1 | 40  1 |  0
  840:  8   9 | 16  1 | 24  1 | 40  1 |  0
  846:  8  11 | 16  1 | 24  1 | 40  1 |  2r
  868:  8   8 | 16  1 | 24  1 | 40  1 |  2b
  910:  8   8 | 16  1 | 24  1 | 40  1 |  2r
  930:  8+  9 | 16  1 | 24  1 | 40  1 |  0
  948:  8   8 | 16  1 | 24  1 | 40  1 |  0
  955:  8   8 | 16  1 | 24  1 | 40  1 |  0
  973:  8  10 | 16  1 | 24  1 | 40  1 |  0
  987:  8+  8 | 16  1 | 24  1 | 40  1 |  0
 1011:  8  10 | 16  1 | 24  1 | 40  1 |  0
 1071:  8  12 | 16  1 | 24  1 | 40  1 |  0
 1075:  8   9 | 16  1 | 24  1 | 40  1 |  2b
 1100:  8   8 | 16  1 | 24  1 | 40  1 |  2b
 1334:  8  13 | 16  1 | 24  1 | 40  1 |  0
 1448:  8  10 | 16  1 | 24  1 | 40  1 |  0
 1519:  8  10 | 16  1 | 24  1 | 40  1 |  0
 1595:  8   8 | 16  1 | 24  1 | 40  1 |  0
 1610:  8   9 | 16  1 | 24  1 | 40  1 |  2b
 1660:  8   8 | 16  1 | 24  1 | 40  1 |  2r
 1714:  8   9 | 16  1 | 24  1 | 40  1 |  2b
 1747:  8  11 | 16  1 | 24  1 | 40  1 |  0
 1756:  8   8 | 16  1 | 24  1 | 40  1 |  0
 1796:  8  11 | 16  1 | 24  1 | 40  1 |  0
 1836:  8   8 | 16  1 | 24  1 | 40  1 |  2b
 1868:  8  10 | 16  1 | 24  1 | 40  1 |  2b
 1902:  8   8 | 16  1 | 24  1 | 40  1 |  0
 1967:  8   8 | 16  1 | 24  1 | 40  1 |  2b
 2016:  8  10 | 16  1 | 24  1 | 40  1 |  0
 2081:  8  11 | 16  1 | 24  1 | 40  1 |  2r
 2137:  8   8 | 16  1 | 24  1 | 40  1 |  0
 2165:  8   9 | 16  1 | 24  1 | 40  1 |  0
 2408:  8  13 | 16  1 | 24  1 | 40  1 |  0
 2415:  8  12 | 16  1 | 24  1 | 40  1 |  0
 2457:  8   9 | 16  1 | 24  1 | 40  1 |  0
 2468:  8   8 | 16  1 | 24  1 | 40  1 |  2r
 2486:  8   9 | 16  1 | 24  1 | 40  1 |  2r
 2543:  8   8 | 16  1 | 24  1 | 40  1 |  2r
 2590:  8  12 | 16  1 | 24  1 | 40  1 |  0
 2604:  8   9 | 16  1 | 24  1 | 40  1 |  0
 2614:  8   9 | 16  1 | 24  1 | 40  1 |  0
 2704:  8   8 | 16  1 | 24  1 | 40  1 |  0
 2705:  8  12 | 16  1 | 24  1 | 40  1 |  0
 2709:  8  10 | 16  1 | 24  1 | 40  1 |  0
 2959:  8  11 | 16  1 | 24  1 | 40  1 |  2b
 3003:  8   9 | 16  1 | 24  1 | 40  1 |  2r
 3008:  8   9 | 16  1 | 24  1 | 40  1 |  0
 3044:  8+  8 | 16  1 | 24  1 | 40  1 |  0
 3145:  8  14 | 16  1 | 24  1 | 40  1 |  2r
 3242:  8  10 | 16  1 | 24  1 | 40  1 |  0
 3245:  8  12 | 16  1 | 24  1 | 40  1 |  0
 3310:  8  10 | 16  1 | 24  1 | 40  1 |  0
 3314:  8   8 | 16  1 | 24  1 | 40  1 |  0
 3467:  8   9 | 16  1 | 24  1 | 40  1 |  2b
 3478:  8   9 | 16  1 | 24  1 | 40  1 |  0
 3504:  8   8 | 16  1 | 24  1 | 40  1 |  2r
 3612:  8  10 | 16  1 | 24  1 | 40  1 |  2b
 3627:  8   8 | 16  1 | 24  1 | 40  1 |  0
 4067:  8   8 | 16  1 | 24  1 | 40  1 |  0
 4265:  8   8 | 16  1 | 24  1 | 40  1 |  0
 4450:  8   8 | 16  1 | 24  1 | 40  1 |  0
 4466:  8   9 | 16  1 | 24  1 | 40  1 |  0
 4470:  8   9 | 16  1 | 24  1 | 40  1 |  2r
 4471:  8   9 | 16  1 | 24  1 | 40  1 |  2r
 4499:  8  10 | 16  1 | 24  1 | 40  1 |  0
 4501:  8   9 | 16  1 | 24  1 | 40  1 |  0
 4537:  8  10 | 16  1 | 24  1 | 40  1 |  0
 4545:  8  13 | 16  1 | 24  1 | 40  1 |  0
 4585:  8   8 | 16  1 | 24  1 | 40  1 |  0
 4589:  8  11 | 16  1 | 24  1 | 40  1 |  0
 4637:  8   8 | 16  1 | 24  1 | 40  1 |  0
 4673:  8   9 | 16  1 | 24  1 | 40  1 |  2b
 4731:  8   9 | 16  1 | 24  1 | 40  1 |  0
 4753:  8  12 | 16  1 | 24  1 | 40  1 |  2b
 4810:  8   8 | 16  1 | 24  1 | 40  1 |  2r
-------------------------------------
 best:  8  14 | 16  1 | 24  1 | 40  1 |  0
worst:  9   8 | 16  1 | 24  1 | 40  1 |  2  (38)

Last edited by Joe Ross : 01-05-2013 at 18:01.
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Unread 01-05-2013, 18:16
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Re: 2013 Qual Schedule Analysis

Quote:
Originally Posted by Joe Ross View Post
It appears that the match scheduler does not care about multiple opponents/partners in surrogate matches. I checked the Archimedes schedule and the teams that had multiple opponents played each other once in their surrogate match and once in a match that counted.

Here is the scheduler's analysis of the Archimedes schedule, which does not show repeats in matches that count.

Code:
Schedule Statistics
-------------------

          #: number of matches played, a '+' after the number
               indicates one additional round as a surrogate
          d: minimum delta between matches (e.g. '1' means back-to-back)
       part: number of distinct partners followed by most frequent repeat count
        opp: number of distinct opponents followed by most frequent repeat count

       both: number of distinct teams seen as partner or opponent
               followed by most frequent combined repeat count
        r/b: balance between red and blue alliance appearances
               eg, 3b means team appeared as blue 3 times more than as red
 4+ repeats: any teams seen four or more times as partners or opponents

 team   #   d    part    opp    both    r/b   4+ repeats
 ----  --  --   -----   -----   -----   ---   ------------
   11:  8  11 | 16  1 | 24  1 | 40  1 |  0
   20:  8   9 | 16  1 | 24  1 | 40  1 |  0
   33:  8   9 | 16  1 | 24  1 | 40  1 |  0
   51:  8   8 | 16  1 | 24  1 | 40  1 |  0
   71:  8   9 | 16  1 | 24  1 | 40  1 |  2r
   78:  8  11 | 16  1 | 24  1 | 40  1 |  0
  126:  8   9 | 16  1 | 24  1 | 40  1 |  2r
  172:  8  11 | 16  1 | 24  1 | 40  1 |  2r
  236:  8  14 | 16  1 | 24  1 | 40  1 |  0
  254:  8   8 | 16  1 | 24  1 | 40  1 |  2b
  291:  8   9 | 16  1 | 24  1 | 40  1 |  2b
  314:  8  11 | 16  1 | 24  1 | 40  1 |  0
  316:  8   8 | 16  1 | 24  1 | 40  1 |  0
  321:  8   9 | 16  1 | 24  1 | 40  1 |  2r
  326:  8   9 | 16  1 | 24  1 | 40  1 |  2b
  365:  8   8 | 16  1 | 24  1 | 40  1 |  0
  379:  8  10 | 16  1 | 24  1 | 40  1 |  2b
  433:  8+ 11 | 16  1 | 24  1 | 40  1 |  0
  469:  8   8 | 16  1 | 24  1 | 40  1 |  0
  525:  8  11 | 16  1 | 24  1 | 40  1 |  2r
  639:  8   9 | 16  1 | 24  1 | 40  1 |  2b
  694:  8  14 | 16  1 | 24  1 | 40  1 |  0
  701:  8   8 | 16  1 | 24  1 | 40  1 |  2b
  801:  8   9 | 16  1 | 24  1 | 40  1 |  2r
  812:  8   8 | 16  1 | 24  1 | 40  1 |  0
  836:  8   9 | 16  1 | 24  1 | 40  1 |  0
  840:  8   9 | 16  1 | 24  1 | 40  1 |  0
  846:  8  11 | 16  1 | 24  1 | 40  1 |  2r
  868:  8   8 | 16  1 | 24  1 | 40  1 |  2b
  910:  8   8 | 16  1 | 24  1 | 40  1 |  2r
  930:  8+  9 | 16  1 | 24  1 | 40  1 |  0
  948:  8   8 | 16  1 | 24  1 | 40  1 |  0
  955:  8   8 | 16  1 | 24  1 | 40  1 |  0
  973:  8  10 | 16  1 | 24  1 | 40  1 |  0
  987:  8+  8 | 16  1 | 24  1 | 40  1 |  0
 1011:  8  10 | 16  1 | 24  1 | 40  1 |  0
 1071:  8  12 | 16  1 | 24  1 | 40  1 |  0
 1075:  8   9 | 16  1 | 24  1 | 40  1 |  2b
 1100:  8   8 | 16  1 | 24  1 | 40  1 |  2b
 1334:  8  13 | 16  1 | 24  1 | 40  1 |  0
 1448:  8  10 | 16  1 | 24  1 | 40  1 |  0
 1519:  8  10 | 16  1 | 24  1 | 40  1 |  0
 1595:  8   8 | 16  1 | 24  1 | 40  1 |  0
 1610:  8   9 | 16  1 | 24  1 | 40  1 |  2b
 1660:  8   8 | 16  1 | 24  1 | 40  1 |  2r
 1714:  8   9 | 16  1 | 24  1 | 40  1 |  2b
 1747:  8  11 | 16  1 | 24  1 | 40  1 |  0
 1756:  8   8 | 16  1 | 24  1 | 40  1 |  0
 1796:  8  11 | 16  1 | 24  1 | 40  1 |  0
 1836:  8   8 | 16  1 | 24  1 | 40  1 |  2b
 1868:  8  10 | 16  1 | 24  1 | 40  1 |  2b
 1902:  8   8 | 16  1 | 24  1 | 40  1 |  0
 1967:  8   8 | 16  1 | 24  1 | 40  1 |  2b
 2016:  8  10 | 16  1 | 24  1 | 40  1 |  0
 2081:  8  11 | 16  1 | 24  1 | 40  1 |  2r
 2137:  8   8 | 16  1 | 24  1 | 40  1 |  0
 2165:  8   9 | 16  1 | 24  1 | 40  1 |  0
 2408:  8  13 | 16  1 | 24  1 | 40  1 |  0
 2415:  8  12 | 16  1 | 24  1 | 40  1 |  0
 2457:  8   9 | 16  1 | 24  1 | 40  1 |  0
 2468:  8   8 | 16  1 | 24  1 | 40  1 |  2r
 2486:  8   9 | 16  1 | 24  1 | 40  1 |  2r
 2543:  8   8 | 16  1 | 24  1 | 40  1 |  2r
 2590:  8  12 | 16  1 | 24  1 | 40  1 |  0
 2604:  8   9 | 16  1 | 24  1 | 40  1 |  0
 2614:  8   9 | 16  1 | 24  1 | 40  1 |  0
 2704:  8   8 | 16  1 | 24  1 | 40  1 |  0
 2705:  8  12 | 16  1 | 24  1 | 40  1 |  0
 2709:  8  10 | 16  1 | 24  1 | 40  1 |  0
 2959:  8  11 | 16  1 | 24  1 | 40  1 |  2b
 3003:  8   9 | 16  1 | 24  1 | 40  1 |  2r
 3008:  8   9 | 16  1 | 24  1 | 40  1 |  0
 3044:  8+  8 | 16  1 | 24  1 | 40  1 |  0
 3145:  8  14 | 16  1 | 24  1 | 40  1 |  2r
 3242:  8  10 | 16  1 | 24  1 | 40  1 |  0
 3245:  8  12 | 16  1 | 24  1 | 40  1 |  0
 3310:  8  10 | 16  1 | 24  1 | 40  1 |  0
 3314:  8   8 | 16  1 | 24  1 | 40  1 |  0
 3467:  8   9 | 16  1 | 24  1 | 40  1 |  2b
 3478:  8   9 | 16  1 | 24  1 | 40  1 |  0
 3504:  8   8 | 16  1 | 24  1 | 40  1 |  2r
 3612:  8  10 | 16  1 | 24  1 | 40  1 |  2b
 3627:  8   8 | 16  1 | 24  1 | 40  1 |  0
 4067:  8   8 | 16  1 | 24  1 | 40  1 |  0
 4265:  8   8 | 16  1 | 24  1 | 40  1 |  0
 4450:  8   8 | 16  1 | 24  1 | 40  1 |  0
 4466:  8   9 | 16  1 | 24  1 | 40  1 |  0
 4470:  8   9 | 16  1 | 24  1 | 40  1 |  2r
 4471:  8   9 | 16  1 | 24  1 | 40  1 |  2r
 4499:  8  10 | 16  1 | 24  1 | 40  1 |  0
 4501:  8   9 | 16  1 | 24  1 | 40  1 |  0
 4537:  8  10 | 16  1 | 24  1 | 40  1 |  0
 4545:  8  13 | 16  1 | 24  1 | 40  1 |  0
 4585:  8   8 | 16  1 | 24  1 | 40  1 |  0
 4589:  8  11 | 16  1 | 24  1 | 40  1 |  0
 4637:  8   8 | 16  1 | 24  1 | 40  1 |  0
 4673:  8   9 | 16  1 | 24  1 | 40  1 |  2b
 4731:  8   9 | 16  1 | 24  1 | 40  1 |  0
 4753:  8  12 | 16  1 | 24  1 | 40  1 |  2b
 4810:  8   8 | 16  1 | 24  1 | 40  1 |  2r
-------------------------------------
 best:  8  14 | 16  1 | 24  1 | 40  1 |  0
worst:  9   8 | 16  1 | 24  1 | 40  1 |  2  (38)
That pattern continues in all 4 divisions and several other schedules based on 8 matches from 100 teams. The surrogate teams also appear in the last match in all cases I've looked at, so I suspect that's an artifact of the initial population of the matches.

So I think we're back to there being no evidence that the matches were not generated randomly with the standard scheduling algorithm.
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Unread 01-05-2013, 18:44
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Re: 2013 Qual Schedule Analysis


At Razorback, there were 101 pairs of teams who played against each other twice.

There were 17 pairs of teams who played against each other 3 times.

There were 217 pairs of team who did not play against each other.

Each team played exactly 12 matches, so I assume there were no surrogates (or am I misunderstanding what a surrogate is, in this context?).


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