In schedule analysis Part 2 I said
There are a lot of fun things to find out just using the set of team-pairs who play each other such as the sets of teams who play every other team in the set (I'll get to that in a later column)and this is that later column.
Begin with the 716 games that pair one D1A team with another D1A team and find all of the subsets of D1A where every team in the subset plays every other team. There are 3308 of those (including the 716 two-team "round robins".)
That's a bit misleading, though. For instance all of the round-robin subsets of sizes 9 and 8 are just themselves subsets of the single 10-team round robin that the Big 12 plays. There are 336 unique round-robins in the 2015 schedule. 164 of those are purely due to conference schedules.
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Here's the complete list of unique round-robins in the 2015 1A schedules. Those with representation from more than one conference are flagged with ∗.
Size | Members | |
10 | { Baylor; Iowa State; Kansas; Kansas State; Oklahoma; Oklahoma State; Texas; TCU; Texas Tech; West Virginia } | |
7 | { Illinois; Iowa; Minnesota; Nebraska; Northwestern; Purdue; Wisconsin } | |
7 | { Duke; Georgia Tech; Miami-Florida; North Carolina; Pittsburgh; Virginia; Virginia Tech } | |
7 | { Indiana; Maryland; Michigan; Michigan State; Ohio State; Penn State; Rutgers } | |
7 | { Boston College; Clemson; Florida State; Louisville; North Carolina State; Syracuse; Wake Forest } | |
7 | { Florida; Georgia; Kentucky; Missouri; South Carolina; Tennessee; Vanderbilt } | |
7 | { Alabama; Arkansas; Auburn; LSU; Mississippi; Mississippi State; Texas A&M } | |
6 | { Houston; Memphis; Navy; SMU; Tulane; Tulsa } | |
6 | { Air Force; Boise State; Colorado State; New Mexico; Utah State; Wyoming } | |
6 | { Fresno State; Hawaii; Nevada; San Diego State; San Jose State; UNLV } | |
6 | { California; Oregon; Washington; Arizona State; Southern California; Utah } | |
6 | { Arizona; Arizona State; Colorado; Southern California; UCLA; Utah } | |
6 | { Oregon State; Stanford; Washington State; Arizona; Colorado; UCLA } | |
6 | { California; Oregon; Oregon State; Stanford; Washington; Washington State } | |
6 | { Louisiana Tech; North Texas; Rice; Southern Miss; Texas-San Antonio; UTEP } | |
6 | { Ball State; Central Michigan; Eastern Michigan; Northern Illinois; Toledo; Western Michigan } | |
6 | { UCF; Cincinnati; Connecticut; East Carolina; South Florida; Temple } | |
5 | { Florida Atlantic; Florida Intl; Marshall; Middle Tenn State; Western Kentucky } | |
5 | { Arkansas State; New Mexico State; Texas State; UL Lafayette; UL Monroe } | |
5 | { Arkansas State; Georgia State; South Alabama; Texas State; UL Lafayette } | |
5 | { Appalachian State; Arkansas State; Georgia State; South Alabama; UL Lafayette } | |
5 | { Appalachian State; Georgia State; South Alabama; Troy; UL Lafayette } | |
5 | { Appalachian State; Georgia Southern; Georgia State; South Alabama; Troy } | |
5 | { Florida Atlantic; Florida Intl; Marshall; Old Dominion; Western Kentucky } | |
5 | { Akron; Buffalo; Kent State; Massachusetts; Miami-Ohio } | |
Size | Members | |
5 | { Akron; Bowling Green; Buffalo; Kent State; Massachusetts } | |
5 | { Arkansas State; Idaho; New Mexico State; Texas State; UL Monroe } | |
5 | { Akron; Buffalo; Kent State; Miami-Ohio; Ohio } | |
5 | { Akron; Bowling Green; Buffalo; Kent State; Ohio } | |
5 | { California; Oregon; Washington; Washington State; Arizona State } | |
5 | { UNC-Charlotte; Florida Atlantic; Florida Intl; Marshall; Old Dominion } | |
5 | { California; Oregon; Oregon State; Washington; Utah } | |
5 | { Georgia Southern; Idaho; New Mexico State; Troy; UL Monroe } | |
5 | { Georgia Southern; Idaho; New Mexico State; Texas State; UL Monroe } | |
5 | { Appalachian State; Georgia Southern; Idaho; Troy; UL Monroe } | |
5 | { Appalachian State; Georgia Southern; Idaho; South Alabama; Troy } | |
5 | { Washington; Arizona; Arizona State; Southern California; Utah } | |
5 | { Oregon; Arizona State; Colorado; Southern California; Utah } | |
5 | { California; Arizona State; Southern California; UCLA; Utah } | |
5 | { Washington State; Arizona; Arizona State; Colorado; UCLA } | |
5 | { Oregon State; Arizona; Colorado; UCLA; Utah } | |
5 | { Oregon State; Stanford; Washington; Washington State; Arizona } | |
5 | { Oregon; Oregon State; Stanford; Washington State; Colorado } | |
5 | { California; Oregon State; Stanford; Washington State; UCLA } | |
5 | { Stanford; Arizona; Colorado; Southern California; UCLA } | |
5 | { California; Oregon; Stanford; Washington; Southern California } | |
5 | { UNC-Charlotte; Florida Atlantic; Florida Intl; Marshall; Middle Tenn State } | |
5 | { Arkansas State; Georgia State; New Mexico State; Texas State; UL Lafayette } | |
5 | { Air Force; Boise State; New Mexico; Hawaii; San Jose State } | |
4 | { Colorado State; Wyoming; San Diego State; UNLV } | |
Size | Members | |
4 | { Georgia Southern; Georgia State; South Alabama; Texas State } | |
4 | { New Mexico State; Troy; UL Lafayette; UL Monroe } | |
4 | { Washington; Washington State; Arizona; Arizona State } | |
4 | { Utah State; Wyoming; Nevada; San Diego State } | |
4 | { UNC-Charlotte; Rice; Southern Miss; Texas-San Antonio } | |
4 | { UNC-Charlotte; Old Dominion; Southern Miss; Texas-San Antonio } | |
4 | { Bowling Green; Ohio; Ball State; Western Michigan } | |
4 | { Miami-Ohio; Eastern Michigan; Northern Illinois; Western Michigan } | |
4 | { Appalachian State; Troy; UL Lafayette; UL Monroe } | |
4 | { Appalachian State; Arkansas State; UL Lafayette; UL Monroe } | |
4 | { UCF; Cincinnati; East Carolina; Tulsa } | |
4 | { Akron; Buffalo; Kent State; Central Michigan } | |
4 | { Marshall; Middle Tenn State; Western Kentucky; North Texas } | |
4 | { California; Oregon State; UCLA; Utah } | |
4 | { Middle Tenn State; Louisiana Tech; North Texas; Texas-San Antonio } | |
4 | { Temple; Memphis; SMU; Tulane } | |
4 | { Louisville; Syracuse; Pittsburgh; Virginia } | |
4 | { Miami-Ohio; Ohio; Northern Illinois; Western Michigan } | |
4 | { Buffalo; Miami-Ohio; Ohio; Northern Illinois } | |
4 | { Ohio; Ball State; Northern Illinois; Western Michigan } | |
4 | { New Mexico; Hawaii; Nevada; San Jose State } | |
4 | { Florida Atlantic; Florida Intl; Old Dominion; UTEP } | |
4 | { Akron; Massachusetts; Miami-Ohio; Eastern Michigan } | |
4 | { Boise State; Colorado State; Wyoming; UNLV } | |
4 | { Clemson; Florida State; Georgia Tech; Miami-Florida } | |
Size | Members | |
4 | { UCF; Cincinnati; Connecticut; Houston } | |
4 | { Bowling Green; Kent State; Massachusetts; Toledo } | |
4 | { Oregon State; Washington; Arizona; Utah } | |
4 | { Old Dominion; Southern Miss; Texas-San Antonio; UTEP } | |
4 | { Colorado State; Utah State; Wyoming; San Diego State } | |
4 | { Air Force; Colorado State; Utah State; Fresno State } | |
4 | { UCF; Cincinnati; Houston; Tulsa } | |
4 | { UCF; Houston; Tulane; Tulsa } | |
4 | { UCF; Connecticut; Houston; Tulane } | |
4 | { UCF; Connecticut; Temple; Tulane } | |
4 | { East Carolina; South Florida; Temple; SMU } | |
4 | { Utah State; Fresno State; Nevada; San Diego State } | |
4 | { Colorado State; Fresno State; San Diego State; UNLV } | |
4 | { Colorado State; Utah State; Fresno State; San Diego State } | |
4 | { Wyoming; Nevada; San Diego State; UNLV } | |
4 | { UNC-Charlotte; Marshall; Old Dominion; Southern Miss } | |
4 | { Oregon; Washington State; Arizona State; Colorado } | |
* | 4 | { Boston College; Clemson; Wake Forest; Notre Dame } |
4 | { California; Washington State; Arizona State; UCLA } | |
4 | { Boise State; Hawaii; San Jose State; UNLV } | |
4 | { Bowling Green; Ball State; Toledo; Western Michigan } | |
4 | { Bowling Green; Massachusetts; Ball State; Toledo } | |
4 | { Arkansas State; Idaho; South Alabama; Texas State } | |
4 | { Appalachian State; Arkansas State; Idaho; UL Monroe } | |
4 | { Appalachian State; Arkansas State; Idaho; South Alabama } | |
Size | Members | |
4 | { South Florida; Memphis; Navy; SMU } | |
4 | { South Florida; Temple; Memphis; SMU } | |
* | 4 | { Cincinnati; Connecticut; East Carolina; BYU } |
4 | { New Mexico; Utah State; Wyoming; Nevada } | |
4 | { Oregon; Oregon State; Colorado; Utah } | |
4 | { Georgia Southern; Idaho; South Alabama; Texas State } | |
4 | { Connecticut; Houston; Navy; Tulane } | |
4 | { Cincinnati; Houston; Memphis; Tulsa } | |
4 | { Stanford; Washington; Arizona; Southern California } | |
4 | { Oregon; Stanford; Colorado; Southern California } | |
4 | { California; Stanford; Southern California; UCLA } | |
4 | { East Carolina; Navy; SMU; Tulsa } | |
4 | { East Carolina; South Florida; Navy; SMU } | |
4 | { Connecticut; East Carolina; South Florida; Navy } | |
4 | { Massachusetts; Ball State; Eastern Michigan; Toledo } | |
* | 4 | { Georgia Tech; Pittsburgh; Virginia; Notre Dame } |
4 | { Georgia State; New Mexico State; Troy; UL Lafayette } | |
4 | { Georgia Southern; Georgia State; New Mexico State; Troy } | |
4 | { Georgia Southern; Georgia State; New Mexico State; Texas State } | |
* | 4 | { Connecticut; Navy; Tulane; Army } |
4 | { Cincinnati; South Florida; Temple; Memphis } | |
4 | { Air Force; Fresno State; Hawaii; San Jose State } | |
4 | { Western Kentucky; Louisiana Tech; North Texas; Rice } | |
4 | { Middle Tenn State; Western Kentucky; Louisiana Tech; North Texas } | |
4 | { Florida Intl; Middle Tenn State; Western Kentucky; Louisiana Tech } | |
Size | Members | |
3 | { Ohio State; Illinois; Minnesota } | |
3 | { Indiana; Iowa; Purdue } | |
3 | { Missouri; Arkansas; Mississippi State } | |
3 | { Maryland; Rutgers; Wisconsin } | |
3 | { Penn State; Illinois; Northwestern } | |
3 | { Michigan; Ohio State; Minnesota } | |
3 | { Indiana; Maryland; Iowa } | |
3 | { South Carolina; Vanderbilt; Texas A&M } | |
3 | { Ohio State; Penn State; Illinois } | |
3 | { Wake Forest; Duke; North Carolina } | |
3 | { North Carolina State; Wake Forest; North Carolina } | |
3 | { Georgia; Kentucky; Auburn } | |
3 | { Kent State; Central Michigan; Toledo } | |
3 | { South Carolina; LSU; Texas A&M } | |
3 | { Florida; South Carolina; LSU } | |
3 | { Michigan State; Rutgers; Nebraska } | |
3 | { Rutgers; Nebraska; Wisconsin } | |
3 | { Michigan; Penn State; Northwestern } | |
* | 3 | { BYU; Utah State; Fresno State } |
3 | { Florida Atlantic; Rice; UTEP } | |
3 | { Akron; Central Michigan; Eastern Michigan } | |
3 | { North Carolina State; North Carolina; Virginia Tech } | |
3 | { Boston College; North Carolina State; Virginia Tech } | |
3 | { Maryland; Iowa; Wisconsin } | |
3 | { Tennessee; Alabama; Arkansas } | |
Size | Members | |
3 | { Missouri; Tennessee; Arkansas } | |
3 | { Marshall; North Texas; Southern Miss } | |
3 | { Florida Atlantic; Western Kentucky; Rice } | |
3 | { Michigan; Minnesota; Northwestern } | |
* | 3 | { Navy; Army; Air Force } |
3 | { Michigan State; Nebraska; Purdue } | |
3 | { Indiana; Michigan State; Purdue } | |
3 | { Georgia; Alabama; Auburn } | |
3 | { Georgia; Tennessee; Alabama } | |
3 | { Florida; LSU; Mississippi } | |
3 | { Boston College; Duke; Virginia Tech } | |
3 | { Boston College; Wake Forest; Duke } | |
3 | { Buffalo; Central Michigan; Northern Illinois } | |
3 | { UNC-Charlotte; Florida Atlantic; Rice } | |
* | 3 | { BYU; Fresno State; San Jose State } |
3 | { Vanderbilt; Mississippi; Texas A&M } | |
3 | { Florida; Vanderbilt; Mississippi } | |
3 | { Florida Intl; Louisiana Tech; UTEP } | |
3 | { Kentucky; Missouri; Mississippi State } | |
3 | { Kentucky; Auburn; Mississippi State } | |
* | 3 | { Notre Dame; Stanford; Southern California } |
* | 3 | { Penn State; Rutgers; Army } |
* | 3 | { Ohio State; Northern Illinois; Western Michigan } |
* | 3 | { Clemson; Georgia Tech; Notre Dame } |
* | 3 | { Missouri; Connecticut; BYU } |
Size | Members | |
* | 3 | { Minnesota; Kent State; Ohio } |
3 | { UNC-Charlotte; Middle Tenn State; Texas-San Antonio } | |
* | 3 | { Notre Dame; Temple; Massachusetts } |
* | 3 | { Wake Forest; Duke; Army } |
* | 3 | { Kansas State; Louisiana Tech; Texas-San Antonio } |
* | 3 | { Kansas State; Oklahoma State; Texas-San Antonio } |
* | 3 | { Baylor; Texas; Rice } |
* | 3 | { Marshall; Kent State; Ohio } |
* | 3 | { Indiana; Florida Intl; Western Kentucky } |
* | 3 | { Florida State; Syracuse; South Florida } |
* | 3 | { BYU; Boise State; San Jose State } |
* | 3 | { BYU; Boise State; Utah State } |
* | 3 | { Utah; Utah State; Fresno State } |
* | 3 | { Washington; Utah; Utah State } |
* | 3 | { Mississippi State; Louisiana Tech; Southern Miss } |
* | 3 | { Southern California; Arkansas State; Idaho } |
* | 3 | { North Carolina State; South Alabama; Troy } |
* | 3 | { Georgia; Georgia Southern; UL Monroe } |
* | 3 | { Georgia; Alabama; UL Monroe } |
* | 3 | { Florida; Mississippi; New Mexico State } |
* | 3 | { Louisville; Kentucky; Auburn } |
* | 3 | { Texas Tech; Arkansas; UTEP } |
* | 3 | { Michigan State; Central Michigan; Western Michigan } |
* | 3 | { Michigan State; Ohio State; Western Michigan } |
* | 3 | { Baylor; TCU; SMU } |
Size | Members | |
* | 3 | { Illinois; Minnesota; Kent State } |
* | 3 | { Washington; Boise State; Utah State } |
* | 3 | { Vanderbilt; Middle Tenn State; Western Kentucky } |
* | 3 | { Michigan; Oregon State; Utah } |
* | 3 | { Duke; Tulane; Army } |
* | 3 | { Duke; Georgia Tech; Tulane } |
* | 2 | { Clemson; South Carolina } |
* | 2 | { UL Monroe; Hawaii } |
* | 2 | { Georgia; Georgia Tech } |
* | 2 | { Florida State; Florida } |
* | 2 | { UNC-Charlotte; Kentucky } |
* | 2 | { Florida Atlantic; Florida } |
* | 2 | { Idaho; Auburn } |
* | 2 | { North Texas; Tennessee } |
* | 2 | { Vanderbilt; Houston } |
* | 2 | { Army; Rice } |
* | 2 | { Western Kentucky; LSU } |
* | 2 | { Mississippi; Memphis } |
* | 2 | { Georgia State; Ball State } |
* | 2 | { UL Monroe; Tulsa } |
* | 2 | { Navy; Notre Dame } |
* | 2 | { Troy; Mississippi State } |
* | 2 | { New Mexico State; New Mexico } |
* | 2 | { Florida Intl; Massachusetts } |
* | 2 | { Eastern Michigan; LSU } |
Size | Members | |
* | 2 | { UL Lafayette; Louisiana Tech } |
* | 2 | { San Jose State; Auburn } |
* | 2 | { Wyoming; Appalachian State } |
* | 2 | { Temple; UNC-Charlotte } |
* | 2 | { Miami-Florida; Cincinnati } |
* | 2 | { Hawaii; Wisconsin } |
* | 2 | { Miami-Ohio; Western Kentucky } |
* | 2 | { Maryland; West Virginia } |
* | 2 | { Indiana; Wake Forest } |
* | 2 | { Arkansas State; Toledo } |
* | 2 | { Colorado State; Texas-San Antonio } |
* | 2 | { LSU; Syracuse } |
* | 2 | { UCF; South Carolina } |
* | 2 | { Kansas; Rutgers } |
* | 2 | { Bowling Green; Purdue } |
* | 2 | { San Diego State; Penn State } |
* | 2 | { Appalachian State; Old Dominion } |
* | 2 | { Ball State; Northwestern } |
* | 2 | { Southern Miss; Nebraska } |
* | 2 | { BYU; Michigan } |
* | 2 | { Akron; UL Lafayette } |
* | 2 | { North Texas; Iowa } |
* | 2 | { Middle Tenn State; Illinois } |
* | 2 | { Texas State; Houston } |
* | 2 | { Army; Eastern Michigan } |
Size | Members | |
* | 2 | { Virginia Tech; East Carolina } |
* | 2 | { Nevada; Buffalo } |
* | 2 | { Northern Illinois; Boston College } |
* | 2 | { Boise State; Virginia } |
* | 2 | { Troy; Wisconsin } |
* | 2 | { Wyoming; Washington State } |
* | 2 | { BYU; UCLA } |
* | 2 | { Iowa State; Toledo } |
* | 2 | { Southern Miss; Texas State } |
* | 2 | { Nevada; Texas A&M } |
* | 2 | { California; Texas } |
* | 2 | { Central Michigan; Syracuse } |
* | 2 | { South Alabama; San Diego State } |
* | 2 | { Virginia Tech; Purdue } |
* | 2 | { San Jose State; Oregon State } |
* | 2 | { Georgia State; Oregon } |
* | 2 | { North Carolina State; Old Dominion } |
* | 2 | { Tulsa; Oklahoma } |
* | 2 | { Illinois; North Carolina } |
* | 2 | { UTEP; New Mexico State } |
* | 2 | { Air Force; Michigan State } |
* | 2 | { UNLV; Michigan } |
* | 2 | { Cincinnati; Miami-Ohio } |
* | 2 | { Nebraska; Miami-Florida } |
* | 2 | { South Florida; Maryland } |
Size | Members | |
* | 2 | { Pittsburgh; Iowa } |
* | 2 | { Buffalo; Florida Atlantic } |
* | 2 | { Northwestern; Duke } |
* | 2 | { Colorado State; Colorado } |
* | 2 | { Memphis; Bowling Green } |
* | 2 | { New Mexico; Arizona State } |
* | 2 | { Eastern Michigan; Wyoming } |
* | 2 | { Miami-Ohio; Wisconsin } |
* | 2 | { UCLA; UNLV } |
* | 2 | { Ball State; Texas A&M } |
* | 2 | { Oklahoma; Tennessee } |
* | 2 | { UCF; Stanford } |
* | 2 | { North Texas; SMU } |
* | 2 | { Washington State; Rutgers } |
* | 2 | { Buffalo; Penn State } |
* | 2 | { Hawaii; Ohio State } |
* | 2 | { Tulsa; New Mexico } |
* | 2 | { Arizona; Nevada } |
* | 2 | { South Alabama; Nebraska } |
* | 2 | { Fresno State; Mississippi } |
* | 2 | { Oregon; Michigan State } |
* | 2 | { Bowling Green; Maryland } |
* | 2 | { Houston; Louisville } |
* | 2 | { Memphis; Kansas } |
* | 2 | { Iowa; Iowa State } |
Size | Members | |
* | 2 | { Western Michigan; Georgia Southern } |
* | 2 | { East Carolina; Florida } |
* | 2 | { Minnesota; Colorado State } |
* | 2 | { Massachusetts; Colorado } |
* | 2 | { Appalachian State; Clemson } |
* | 2 | { San Diego State; California } |
* | 2 | { Missouri; Arkansas State } |
* | 2 | { Toledo; Arkansas } |
* | 2 | { Middle Tenn State; Alabama } |
* | 2 | { Pittsburgh; Akron } |
* | 2 | { Miami-Florida; Florida Atlantic } |
* | 2 | { Ohio State; Virginia Tech } |
* | 2 | { Purdue; Marshall } |
* | 2 | { Georgia Southern; West Virginia } |
* | 2 | { Virginia; UCLA } |
* | 2 | { Florida Atlantic; Tulsa } |
* | 2 | { Arizona State; Texas A&M } |
* | 2 | { Bowling Green; Tennessee } |
* | 2 | { Penn State; Temple } |
* | 2 | { Akron; Oklahoma } |
* | 2 | { Texas; Notre Dame } |
* | 2 | { Stanford; Northwestern } |
* | 2 | { UNLV; Northern Illinois } |
* | 2 | { BYU; Nebraska } |
* | 2 | { UL Lafayette; Kentucky } |
Size | Members | |
* | 2 | { Texas State; Florida State } |
* | 2 | { Old Dominion; Eastern Michigan } |
* | 2 | { Wisconsin; Alabama } |
* | 2 | { UNC-Charlotte; Georgia State } |
* | 2 | { North Carolina; South Carolina } |
* | 2 | { TCU; Minnesota } |
* | 2 | { Ohio; Idaho } |
* | 2 | { Colorado; Hawaii } |
* | 2 | { Oklahoma State; Central Michigan } |
* | 2 | { Florida Intl; UCF } |
* | 2 | { Texas-San Antonio; Arizona } |
The interconference games between teams that have no common opponents contribute the most to the connectivity of the 1A field. Each team obtains the maximum number of opponents' opponents from those matchups. (This is easy to see: each common opponent combines with the team-pair to form an order-three round robin. Since these pairs are not part of a larger one, they have no opponents in common.)
So the three-team multi-conference round robins contribute less to connectivity than the two-team but more than the four-team. We can order the teams by how many opponents' opponents are obtained from each of the round-robins in which they participate to give another measure of team schedule contribution to connectivity/
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Again, it's no surprise that the independent teams top the list. This makes even more visible though the problem of 9-game conference schedules. The conference teams who play them and teams who schedule non-conference games against them are less connected than teams who play three or four nonconference 1A games instead of two or three.
© Copyright 2015, Paul Kislanko