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Sports leagues and playoff systems

Sports teams tend to organize themselves into "power leagues" to exclude competition. We could all the members of the power leagues "oligarchs" and the nonmembers "plebes". Leagues also tend to chose poor tournament structures that limit a team's individual choices about who they play and they prevent interesting matchups from happening. Two especially weak formats are single elimination and pools.
Power leagues
                   Number of
                   power leagues

College basketball       8   Big 10, ACC, Big East, SEC, Big 12, Pac 10, MAC, Mountain West
College football         5   Big 10, SEC, Pac 10, Big 12, ACC
College rugby            2   Varsity Club Championship,  Division 1-A rugby
World rugby              2   South Hemisphere 4-Nations, North Hemisphere 6-Nations
College hockey           2   Big 10, National Collegiate Hockey Conference
College wrestling        2   Big 10, Big 12
English club soccer      1   Premiere League
American pro basketball  1
American pro football    1
American pro baseball    1
Professional hockey      1
Formula-1                1
NASCAR                   1
Pro Golf Association     1

Tournament format
                         Regular  Teams  Post-   Postseason format
                         season          season
                         games           teams
National Football League   16      32     12     single elimination
Professional Basketball    82      30     16     single elimination
National Hockey League     82      30     16     single elimination
Major League Baseball     162      31     10     single elimination
College football           12    >100      2     single elimination
Big Ten football            8      12      2     single elimination
College Basketball         27    >300     64     single elimination
Men's college hockey       35      59     16     single elimination
English Premier League     38      20      -     none
Soccer World Cup            -       -     32     pools, single elimination
England Soccer FA Cup       -       -    763     single elimination
The Rugby Championship      6       4      -     none
6 Nations Rugby             5       6      -     none
Rugby Pacific Nations Cup   3       4      -     none
Rugby World Cup             -       -     20     pools, single elimination
Professional Sumo          90      42      0     matches determined each round by judges
Mongolian Wrestling                    >1000     single elimination
NASCAR                     36      59     16     chase
Formula-1                  20      24      -     none
The Rugby Championship is a double round robin between New Zealand, Australia, S. Africa, and Argentina.

6 Nations Rugby is a round robin between England, France, Wales, Scotland, Ireland, and Italy.

The Rugby Pacific Nations Cup is a round robin between Fiji, Japan, Samoa, and Tonga.

The three rugby leagues are rare examples where there is no postseason.


Pools

The world cup is the most prominent example of pools.


World Cup 2014 qualification
                     Teams   Teams   Teams   Games   Quality  Max
                     in 1st  in 2nd  that    played  games    Losses
                     stage   stage   qualify

Europe      UEFA        -     48     13       10       1       3
S. America  Conmebol    -     10      4.5     18       9       5
Africa      CAF        40     10      5        8       0       2
Asia        AFC        20     10      4.5     14       3       5
N. America  Concacaf   12      6      3.5     16       5       7
Pacific     OFC         8      4       .5      9       0       2
Brazil, a member of Conmebol, automatically qualifies, giving Conmebol effectively 5.5 spots.

Two finalists are determined by playoffs. One is determined by a playoff between 5th place Conmebol team and the 5th place AFC team, and another between the 4th place Concacaf team and the 1st place OFC team.

"Games played" is the number of qualifying games played by a team that qualifies as a finalist.

If a team qualifies for the World Cup. The number of "quality games" is the average number of games played against teams that also qualified.

"Max Losses" is the average number of losses incurred by a team that barely qualifies.

Among all 32 finalists:

Average number of games played against finalists during qualifying  ~  2.6
Average number of games played during qualifying                    ~ 12
Average number of games played during finals                        ~  4.0
Average number of losses by a team barely qualifying for the finals ~  4
In Conmebol qualifying, teams get lots of experience playing worthy competition, and a team can afford to lose several times and still qualify.

For CAF, qualification is largely luck and teams don't get a chance to play other finalists.


World Cup history
           Win  Final  Semifinal

Brazil      5     7     11
Germany     4     8     13
Italy       4     6      8
Argentina   2     5      5
Uruguay     2     2      5
France      1     2      5
England     1     1      2
Spain       1     1      2
Netherlands 0     3      5
Czech.      0     2      2
Hungary     0     2      2
Sweden      0     1      3
Teams that usually qualify:
Europe       Germany, Italy,    Spain,  Netherlands,  France,  England,  Portugal
Conmebol     Brazil,  Argentina
Concacaf     U.S.,    Mexico
Asia         Japan,   South Korea
Germany and Brazil are the most sucessful teams and they have only played one World Cup game.
Conmebol 2014 qualifying
           Pts  W  D  L 
Argentina   32  9  5  2
Colombia    30  9  3  4
Chile       28  9  1  6
Ecuador     25  7  4  5
Uruguay     25  7  4  5    Defeated Jordan in a playoff
Venezuela   20  5  5  6
Peru        15  4  3  9
Bolivia     12  2  6  8
Paraguay    12  3  3 10
Brazil plus the top 4 teams qualify. The 5th-place team plays a playoff game against a team from another federation to qualify.
CONCACAF qualifying
           Points  Win  Draw  Loss
U.S.         22     7    1     2
Costa Rica   18     5    3     2
Honduras     15     4    3     3
Mexico       11     2    5     3
Panama        8     1    5     4
Jamaica       5     0    5     5

UEFA 2014 qualifying
Group    Pot 1        Pot 2         Pot 3        Pot 4        Pot 5       Pot 6
  A    + Croatia      Serbia      * Belgium      Scotland     Macedon     Wales
  B    * Italy        Denmark       Czech.       Bulgaria     Armenia     Malta
  C    * Germany    + Sweden        Ireland      Austria      Faroe.      Kazakhstan
  D    * Nether.      Turkey        Hungary    + Romania      Estonia     Andorra
  E      Norway       Slovenia    * Switzer.     Albania      Cyp       + Iceland
  F    + Portugal   * Russia        Israel       N.Ireland    Azerbai.    Luxembourg
  G    + Greece       Slovakia    * B+H          Lithuan.     Latvia      Leich
  H    * Eng land     Monteneg.   + Ukraine      Poland       Moldova     San Marino
  I    * Spain      + France        Belarus      Georgia      Finland

Pot 1 consists of the top 9 seeds, pot 2 consists of the next 9 seeds, etc.
"*" = pool winner
"+" = pool 2nd place
Each pool is a double round robin.

The winner of each pool qualifies for the World Cup. The best 8 2nd-place teams play head-to-head matchups, with the winner of each matchup qualifying.

          Agg
Portugal  4-2   Sweeden
France    3-2   Ukraine
Greece    4-2   Romania
Croatia   2-0   Iceland

Pools

In the World Cup, teams that advance from the pool round to the round of 16

Pools tend to feature many games that have no outcome on qualifying. The Conmebol pool, consisting of 10 teams of which 5.5 advance, features the largest fraction of games that impact qualifying.

A UEFA pool consists of 6 teams, of which 1.5 advance. This pool features the greatest potential for a premier team to not qualify. For example, one of the 2014 pools consists of both Spain and France.


American football playoffs

In American football, the regular season matters. Each regular season win tends to increase the playoff seed by 1, and the playoff seed matters because it determines home field advantage and wildcard byes.

The following table gives the average number of regular season wins for each seed, using data from 2007-2016. The regular season has 16 games.

Seed   Wins   Privilege

  1    13.3   Home field advantage for the semifinal and quarterfinal. Wildcard game bye.
  2    12.1   Home field advantage for the quarterfinal. Wildcard game bye.
  3    10.9   Home field advantage for the wildcard game.
  4     9.2   Home field advantage for the wildcard game.
  5    11.0
  6    10.0
Seeds 1-4 go to division winners and seeds 5-6 go to the best records among the remaining teams.

The frozen tundra of Lambeau Field, Green Bay, Wisconsin


National Basketball Association playoffs

In the NBA, the regular season has little impact on the playoffs. For example, suppose the Milwaukee Bucks are the best team and they win the conference and gain the #1 seed. In the conference playoffs they can expect to face the 8th, 4th, and 2nd seeds. If the Bucks decide to slack and place 8th, they can expect to face the 1st, 2nd, and 3rd seeds in the playoffs. But since the Bucks are the best team the 1st seed is the 2nd best team, the 2nd seed is the 3rd best team, etc.

                                                      Rank of teams played in playoffs

If the Bucks play hard and place 1st in the conference:   2nd, 4th, and 8th
If the Bucks slack and place 8th in the conference:       2nd, 4rd, and 3rd
No matter what the Bucks will face the 2nd and 4th ranked team. The only difference between playing hard and slacking is that they have to play the 3rd ranked team instead of the 8th ranked team.

The following table gives the average number of games won by each seed, using data from 2009-2016. The regular season has 82 games. The difference between the 1st and 8th seeds is typically 20 games. That's a lot of slack.

Seed   Wins

  1    60.8
  2    55.9
  3    52.2
  4    49.9
  5    47.6
  6    45.2
  7    43.7
  8    41.9

NCAA Basketball
Division  Conferences  Teams
   1          32        351
   2          23
   3          45
Power conferences: Big Ten, ACC, Big East, Pac 10, Big 12, SEC, MAC, Mountain West

College Wrestling
            Championships

Oklahoma State  34
Iowa            23
Iowa State       8
Oklahoma         7
Penn State       5
Minnesota        3
Ohio State       1
Arizona State    1
Michigan State   1
Northern Iowa    1
Cornell College  1
Indiana          1


Big Twelve      49
Big Ten         33
Other            3
Few schools outside of the Midwest have won championships.

NCAA hockey

Big Ten
ECAC Hockey

USA Hockey
Hockey East

Men's hockey:

            Championships   Frozen Four

Michigan             9       24
North Dakota         7       21
Denver               7       14
Wisconsin            6       12
Boston College       5       24
Boston University    5       22
Minnesota            5       21
Lake Superior State  3        4
Michigan State       3       11
Michigan Tech        3       10
Cornell              2        8
Maine                2       11
Colorado College     2       10
RPI                  2        5
Minnesota-Duluth     1        4
Harvard              1       12
Providence           1        4
Bowling Green        1
Northern Michigan    1
Union                1
Yale                 1
St Lawrence                   9
Clarkson                      7
New Hampshire                 7
Dartmouth                     4
Women's hockey:
               Championships   Final

Minnesota-Duluth     5          6
Minnesota            5          7
Wisconsin            4          6
Clarkson             1          1
Harvard                         4

NCAA rugby

Varsity Club Championship:
Air Force
Arizona State
Arkansas State
BYU
California
Central Washington
Clemson
Dartmouth
Navy
Notre Dame
Oklahoma
Texas
UCLA
UTAH


Division 1-A Rugby:
East:        Army,  Delaware,  Kutztown,  Penn State,  Wheeling Jesuit
             St. Bonaventure,  Iona,  University at Buffalo
Mid-South:   Lindenwood,  Life University,  Davenport University
California:  Cal Poly,  Saint Mary's,  UC Davis,  San Diego State,
             UC Santa Barbara,  Santa Clara,  Sacramento State,  Stanford
West:        Colorado,  Colorado State,  Wyoming  Northern Colerado,  New Mexico


            Championships

California       25
BYU               4
Air Force         3
Harvard           1
San Diego State   1
The Varsity Club conference was formed in 2013.

http://en.wikipedia.org/wiki/Varsity_Cup_Championship
http://en.wikipedia.org/wiki/Division_1-A_Rugby


UFC

               Mir  Mioc  Werd  Over  Lesn  Vela  Sant  Hunt  Arlo  Silv  Cout  Carw  Nogu

Frank Mir                        -     +-          -     -     -     +           +     ++
Stipe Miocic               +     +                 -     +     +
F. Werdum            -           +-          +     -     +     -     +                 +-
A. Overeem     +     -     +-          +           +     +     +     -                 --
Brock Lesnar   +-                -           -                             +     +
Cain Velasquez             -           +           ++-               ++                +
J. dos Santos  +     +     +     -           +--         +                       +
Mark Hunt      +     -     -     -                 -                 +o
A. Arlovski    +     -     +     -                                   ++
Antonio Silva  -           -     +           --          -     +-
Randy Couture                          -                                               -
Shane Carwin   +                       -           -
A. Nogueira    --          +-                -                             +

+: Victory
-: Defeat
o: Draw
For example, Miocic defeated Werdum


               Holm  Tate  Rousey  Zing  Nunes  Penn  Pena  McMann  Eye  Kaufman  Shev  Davis
Holly Holm            -      +                   +                                 -     f
Miesha Tate      +           -      -      -     -            +      +     -
Ronda Rousey     -    +             +      -                  +            +             +
Cat Zingano           +      -             +     +     -
Amanda Nunes          +      +      -                         +                    +     -
Raq. Pennington  -    +             -
Julianna Pena                       +                                +             -
Sarah McMann          -      -             -                         +                   +
Jessica Eye           -                                -      -                          -
Sarah Kaufman         +      -                                                     -     +-
Val. Shevchenko  +                         -           +                   +
Alexis Davis                 -             +                  -      +     +-
Ger. de Randamie +                         -

Go

Tournament victories
               Honinbo  Meijin  Kisei  Tengen  Oza  Gosei  Judan   Birth

Cho Chikun       12       9       8      2      2     2      6     1956
Iyama Yuta        5       5       5      5      4     5      4     1989
Cho U             2       4       3      1      7     4      2     1980
Yamashita Keigo   2       2       5      2      2     1            1978
Takao Shinji      3       2              1                   2     1976
Yoda Norimoto             4                           6      2     1966
O Rissei                          3             4            4     1972
Hane Naoki        2               2      3            1            1976
O Meien           2                             1                  1961

Goratings.org
               ELO

Ke Jie         3620
Park Junghwan  3593
Mi Yuting      3571
Shin Jinseo    3537
Iyama Yuta     3525
Lian Xiao      3524
Lee Sedol      3516

World cup history

6: Win    5: Final    4: Semifinal    3: Quarterfinal    2: Round 16    1: Round 32
W: Wins
F: Finals
S: Semiinals
Q: Quarterfinals
Z: Sum of the columns from 1950 to 2014

          3 3 3 5 5 5 6 6 7 7 7 8 8 9 9 9 0 0 1 1   W  F  S  Q    Z
          0 4 8 0 4 8 2 6 0 4 8 2 6 0 4 8 2 6 0 4

Brazil    3 2 4 5 3 6 6 2 6 4 4 3 2 3 6 5 6 3 3 4   5  2  4  5   80
Germany     4 2   6 4 3 5 4 6 3 5 5 6 3 3 5 4 4 6   4  4  5  4   78
Italy       6 6 3 2   2 2 5 2 4 6 2 4 5 3 2 6 1 1   4  2  2  2   62
Argentina 5 2       2 2     3 6 3 6 5 2 3 1 3 3 5   2  3     5   51
France    3 2 3 3 2 4   2     2 4 4     6 1 5 1 3   1  1  3  4   45
England         3 3 2 3 6 3     3 3 4   2 3 3 2 1   1     1  8   41
Uruguay   6     6 4   2 3 4 2     2 2     1   4 2   2     3  1   38
Spain       3   4     2 2     2 3 3 2 3 1 3 2 6 1   1     1  5   37
Neth.       2 2             5 5     2 3 4   2 5 4      3  2  1   34
Sweden      3 4 4   5     2 3 2     1 4   2 2          1  3  2   32
Mexico    3     3 2 2 2 2 3   2   3   2 2 2 2   2            4   32
Hungary     3 5   5 2 3 3     2 2 1                    2     3   31
Serbia    4     3 3 3 4     3   2   3   2   1 1           2  5   29
Czech       5 3   2 2 5   2     2   3       1          2     2   29
Belgium   3 2 2   2       2     3 4 2 2 1 2     3         1  3   28
Switz.      3 3 3 3   2 2             2     2 1 2            4   27
USA       4 2   3                   1 2 1 3 1 2 2         1  2   24
Austria     4 2   4 2         3 3   1   1                 2  2   24
Poland        2           3 4 3 4 2       1 1             1  2   23
Chile     3     3     4 2   2   2       2     2 2         1  2   22
Russia              3 3 4 3     3 2 1 1   1     1         1  4   22
Paraguay  3     3   2             2     2 2 1 3              3   18
Bulgaria              2 2 2 2     2   4 1                 1      15
S. Korea          2               1 1 1 1 4 1 2 1         1      14
Scotland          2 2       2 2 2 1 1   1                        13
Portugal                4         1       1 4 2 1         2      13
Cameroon                        2   3 1 1 1   1 1            1   11
Denmark                           2     3 2   1              1    9
Japan                                   1 2 1 2 1        1        8
Costa Rica                          2     1 1   3            1    8
Croatia                                 4 1 1   1                 7


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