2016 D1A Schedule Topology Part 2 - Round Robins

July 10, 2016

By the end of the season it will take at least four playeds in an A played B played ... chain to connect the last 291 of the 8,256 team-pairs. The 712 games ( A played B) will have turned into 1,899,566 paths with four playeds in them (plus an additional 69,444 paths four playeds long that begin and end at the same team.)

Technically, there will be 949,783 paths that can be traversed in either direction.
The games graph is formed by establishing a vertex for every team and a game between teams represents an edge. The path length between two teams is the smallest number of edges required to get from one team to the other.

As you can tell from the path counts above, except for length one there are usually more than one "shortest path." For teams connected at length two, the number of paths is just the number of opponents the teams have in common. If you try to draw such a graph (try it!) you'll see you wind up with what looks like a solid mass of spaghetti. Instead of trying to take in the entire games graph at once I like to look at what I call its skeleton.

The general idea is to find the edges (games) that contribute the most to shortening the average path length. A bit of thought suggests that this will be the subset of games between teams that have no common opponents, then the ones that have just one common opponent, and so on. The reason is that each of the teams' opponents would have a pathlength > 2 to each of the teams were it not for the game, so the game contributes about 20 "length 2 shortest paths" (The sum of D1A opponents for each team not counting the other team in the pair. It is 20 if both teams play one game against a non-D1A opponent, 21 if one does, and 22 if neither does.)

To get to the "skeleton" of the games graph I begin by finding all subsets of { teams in D1A } in which every team plays every other team. There are 3,379 of these with the largest being the round-robin played by the Big 12 (10 teams.) The first step in finding the skeleton is to strip away the fat: 3,048 of those are just subsets of larger round-robins. Of the remaining 331, 161 consist of teams from the same conference - they only contribute to the extent that the constituent teams do.

That leaves us with 170 round-robins involving teams from more than one conference. These 255 games of the 712 form the skeleton of the games graph. The 132 games between teams with no common opponents form it's "spine." Start again with the 128 vertexes and connect just these edges to get a feel for how the schedule topology affects relative ratings within the (D1A) field.

Unique Interconference Round-Robins

ConfsSizeMembersConferencesGames
33{ Notre Dame; Navy; Army }{ ND AAC Ind }3
33{ Navy; Army; Air Force }{ AAC Ind MW }3
33{ Duke; Notre Dame; Army }{ ACC ND Ind }3
33{ Mississippi State; BYU; Massachusetts }{ SEC Ind MAC }3
33{ Maryland; UCF; Florida Intl }{ B10 AAC CUSA }3
24{ Duke; Miami-Florida; Virginia Tech; Notre Dame }{ ACC ND }6
24{ North Texas; Rice; UTEP; Army }{ CUSA Ind }6
24{ Arizona; UCLA; Utah; BYU }{ P12 Ind }6
23{ North Carolina State; Miami-Florida; Notre Dame }{ ACC ND }3
23{ Syracuse; Virginia Tech; Notre Dame }{ ACC ND }3
23{ North Carolina State; Syracuse; Notre Dame }{ ACC ND }3
23{ BYU; Boise State; Utah State }{ Ind MW }3
23{ Boston College; Syracuse; Connecticut }{ ACC AAC }3
23{ Syracuse; Connecticut; South Florida }{ ACC AAC }3
23{ Florida State; Syracuse; South Florida }{ ACC AAC }3
23{ Notre Dame; Stanford; Southern California }{ ND P12 }3
23{ Florida Intl; Louisiana Tech; Massachusetts }{ CUSA MAC }3
23{ Florida Intl; Old Dominion; Massachusetts }{ CUSA MAC }3
23{ Georgia Tech; Georgia; Vanderbilt }{ ACC SEC }3
23{ Washington; Washington State; Idaho }{ P12 SBC }3
23{ Vanderbilt; Middle Tenn State; Western Kentucky }{ SEC CUSA }3
23{ Missouri; Vanderbilt; Middle Tenn State }{ SEC CUSA }3
23{ South Carolina; Mississippi State; Massachusetts }{ SEC MAC }3
23{ Maryland; Michigan; UCF }{ B10 AAC }3
23{ Wake Forest; Duke; Army }{ ACC Ind }3
ConfsSizeMembersConferencesGames
23{ Oregon State; Washington State; Boise State }{ P12 MW }3
23{ Baylor; TCU; SMU }{ B12 AAC }3
23{ Auburn; Arkansas State; UL Monroe }{ SEC SBC }3
23{ Northern Illinois; Wyoming; San Diego State }{ MAC MW }3
23{ Eastern Michigan; Northern Illinois; Wyoming }{ MAC MW }3
23{ Tulsa; Fresno State; San Jose State }{ AAC MW }3
23{ Illinois; Northwestern; Western Michigan }{ B10 MAC }3
23{ LSU; Mississippi State; South Alabama }{ SEC SBC }3
23{ Georgia Tech; North Carolina; Georgia }{ ACC SEC }3
23{ Florida; South Carolina; Massachusetts }{ SEC MAC }3
23{ Louisville; UNC-Charlotte; Marshall }{ ACC CUSA }3
23{ Indiana; Maryland; Florida Intl }{ B10 CUSA }3
23{ California; Hawaii; San Diego State }{ P12 MW }3
22{ Rice; Stanford }{ CUSA P12 }1
22{ Kentucky; Louisville }{ SEC ACC }1
22{ Massachusetts; Hawaii }{ MAC MW }1
22{ Florida; Florida State }{ SEC ACC }1
22{ South Carolina; Clemson }{ SEC ACC }1
22{ Texas-San Antonio; Texas A&M }{ CUSA SEC }1
22{ UL Lafayette; Georgia }{ SBC SEC }1
22{ Louisville; Houston }{ ACC AAC }1
22{ Massachusetts; Troy }{ MAC SBC }1
22{ Georgia Southern; Mississippi }{ SBC SEC }1
22{ BYU; Cincinnati }{ Ind AAC }1
22{ New Mexico State; Texas A&M }{ SBC SEC }1
ConfsSizeMembersConferencesGames
22{ UL Monroe; New Mexico }{ SBC MW }1
22{ Southern Miss; LSU }{ CUSA SEC }1
22{ Georgia Southern; Georgia Tech }{ SBC ACC }1
22{ BYU; Michigan State }{ Ind B10 }1
22{ San Diego State; South Alabama }{ MW SBC }1
22{ Marshall; Pittsburgh }{ CUSA ACC }1
22{ Memphis; Mississippi }{ AAC SEC }1
22{ Tulane; Massachusetts }{ AAC MAC }1
22{ Buffalo; Boston College }{ MAC ACC }1
22{ Toledo; BYU }{ MAC Ind }1
22{ Georgia Southern; Western Michigan }{ SBC MAC }1
22{ BYU; West Virginia }{ Ind B12 }1
22{ East Carolina; Virginia Tech }{ AAC ACC }1
22{ Central Michigan; Virginia }{ MAC ACC }1
22{ Idaho; UNLV }{ SBC MW }1
22{ UL Lafayette; Tulane }{ SBC AAC }1
22{ Houston; Texas State }{ AAC SBC }1
22{ UNC-Charlotte; Temple }{ CUSA AAC }1
22{ Nevada; Purdue }{ MW B10 }1
22{ Colorado State; Minnesota }{ MW B10 }1
22{ Bowling Green; Memphis }{ MAC AAC }1
22{ San Jose State; Iowa State }{ MW B12 }1
22{ Wake Forest; Indiana }{ ACC B10 }1
22{ Ball State; Florida Atlantic }{ MAC CUSA }1
22{ Miami-Ohio; Cincinnati }{ MAC AAC }1
ConfsSizeMembersConferencesGames
22{ Army; Buffalo }{ Ind MAC }1
22{ Kent State; Alabama }{ MAC SEC }1
22{ Appalachian State; Akron }{ SBC MAC }1
22{ Georgia State; Wisconsin }{ SBC B10 }1
22{ Eastern Michigan; UNC-Charlotte }{ MAC CUSA }1
22{ Fresno State; Toledo }{ MW MAC }1
22{ Louisiana Tech; Texas Tech }{ CUSA B12 }1
22{ Ohio; Tennessee }{ MAC SEC }1
22{ Troy; Southern Miss }{ SBC CUSA }1
22{ East Carolina; South Carolina }{ AAC SEC }1
22{ Utah; San Jose State }{ P12 MW }1
22{ New Mexico; Rutgers }{ MW B10 }1
22{ Temple; Penn State }{ AAC B10 }1
22{ Pittsburgh; Oklahoma State }{ ACC B12 }1
22{ Ohio State; Oklahoma }{ B10 B12 }1
22{ Michigan State; Notre Dame }{ B10 ND }1
22{ Duke; Northwestern }{ ACC B10 }1
22{ Old Dominion; North Carolina State }{ CUSA ACC }1
22{ Buffalo; Nevada }{ MAC MW }1
22{ Oregon; Nebraska }{ P12 B10 }1
22{ Colorado; Michigan }{ P12 B10 }1
22{ Western Kentucky; Miami-Ohio }{ CUSA MAC }1
22{ Kansas; Memphis }{ B12 AAC }1
22{ Akron; Marshall }{ MAC CUSA }1
22{ New Mexico State; Kentucky }{ SBC SEC }1
ConfsSizeMembersConferencesGames
22{ Florida Atlantic; Kansas State }{ CUSA B12 }1
22{ North Texas; Florida }{ CUSA SEC }1
22{ Virginia; Connecticut }{ ACC AAC }1
22{ UNLV; Central Michigan }{ MW MAC }1
22{ Texas; California }{ B12 P12 }1
22{ Middle Tenn State; Bowling Green }{ CUSA MAC }1
22{ Texas State; Arkansas }{ SBC SEC }1
22{ Hawaii; Arizona }{ MW P12 }1
22{ Miami-Florida; Appalachian State }{ ACC SBC }1
22{ Arkansas State; Utah State }{ SBC MW }1
22{ Arizona State; Texas-San Antonio }{ P12 CUSA }1
22{ Baylor; Rice }{ B12 CUSA }1
22{ Akron; Wisconsin }{ MAC B10 }1
22{ UNLV; UCLA }{ MW P12 }1
22{ UTEP; Texas }{ CUSA B12 }1
22{ Virginia Tech; Tennessee }{ ACC SEC }1
22{ Arkansas; TCU }{ SEC B12 }1
22{ Utah State; Southern California }{ MW P12 }1
22{ Northern Illinois; South Florida }{ MAC AAC }1
22{ Cincinnati; Purdue }{ AAC B10 }1
22{ Penn State; Pittsburgh }{ B10 ACC }1
22{ Virginia; Oregon }{ ACC P12 }1
22{ Central Michigan; Oklahoma State }{ MAC B12 }1
22{ UL Monroe; Oklahoma }{ SBC B12 }1
22{ Tulsa; Ohio State }{ AAC B10 }1
ConfsSizeMembersConferencesGames
22{ Nevada; Notre Dame }{ MW ND }1
22{ New Mexico; New Mexico State }{ MW SBC }1
22{ Wyoming; Nebraska }{ MW B10 }1
22{ Eastern Michigan; Missouri }{ MAC SEC }1
22{ Florida Atlantic; Miami-Florida }{ CUSA ACC }1
22{ Ohio; Kansas }{ MAC B12 }1
22{ Iowa State; Iowa }{ B12 B10 }1
22{ Ball State; Indiana }{ MAC B10 }1
22{ North Carolina; Illinois }{ ACC B10 }1
22{ North Carolina State; East Carolina }{ ACC AAC }1
22{ Texas-San Antonio; Colorado State }{ CUSA MW }1
22{ Troy; Clemson }{ SBC ACC }1
22{ Massachusetts; Boston College }{ MAC ACC }1
22{ Texas Tech; Arizona State }{ B12 P12 }1
22{ Old Dominion; Appalachian State }{ CUSA SBC }1
22{ Western Kentucky; Alabama }{ CUSA SEC }1
22{ Georgia State; Air Force }{ SBC MW }1
22{ Mississippi; Florida State }{ SEC ACC }1
22{ Notre Dame; Texas }{ ND B12 }1
22{ LSU; Wisconsin }{ SEC B10 }1
22{ Missouri; West Virginia }{ SEC B12 }1
22{ Rutgers; Washington }{ B10 P12 }1
22{ New Mexico State; UTEP }{ SBC CUSA }1
22{ UCLA; Texas A&M }{ P12 SEC }1
22{ Kent State; Penn State }{ MAC B10 }1
ConfsSizeMembersConferencesGames
22{ Texas State; Ohio }{ SBC MAC }1
22{ Bowling Green; Ohio State }{ MAC B10 }1
22{ SMU; North Texas }{ AAC CUSA }1
22{ Fresno State; Nebraska }{ MW B10 }1
22{ Hawaii; Michigan }{ MW B10 }1
22{ Boise State; UL Lafayette }{ MW SBC }1
22{ Southern Miss; Kentucky }{ CUSA SEC }1
22{ Miami-Ohio; Iowa }{ MAC B10 }1
22{ Oklahoma; Houston }{ B12 AAC }1
22{ Clemson; Auburn }{ ACC SEC }1
22{ Louisiana Tech; Arkansas }{ CUSA SEC }1
22{ Southern California; Alabama }{ P12 SEC }1
22{ Army; Temple }{ Ind AAC }1
22{ Kansas State; Stanford }{ B12 P12 }1
22{ Ball State; Georgia State }{ MAC SBC }1
22{ Colorado State; Colorado }{ MW P12 }1
22{ Toledo; Arkansas State }{ MAC SBC }1
22{ Tulane; Wake Forest }{ AAC ACC }1
22{ Appalachian State; Tennessee }{ SBC SEC }1
22{ Oregon State; Minnesota }{ P12 B10 }1

All of the unique round-robins (including those due only to conference schedules) are available here - Unique Round-Robins.

© Copyright 2016, Paul Kislanko