Round Robins and Elmer's

February 7, 2016

I noted last time that over 57 per cent of all team-pairs will end the season as either opponents or opponents' opponents. This means computer rankings will in general be useful by the time they're needed. In this article I'll look deeper at how schedules contribute to connecting the field using different a fun metric I call the "glue factor."

There are 15 weekends for the 2016 regular season, and the average team will face 21 different opponents. The matchups that do the most to connect the two teams to the rest of the field are those with no common opponents. As of this writing there are 135 of those, with the largest contribution to opponents' opponent counts being Richmond vs Miami (Ohio), who have a combined 55 other opponents. The smallest is contribution from these pairs is 29 (Northern Kentucky/Western Illinois.)

I call the teams who are opponents of either team in a pair with no common opponents "glued" by the pair. Team A becomes an opponents' opponent for each of team B's opponents and team B becomes an Os O for each of team A's opponents, and without this A-B pair they would be no better than an Os-Os-O, except for those opponents of A who play an opponent of B but not B, and vice versa for those opponents of B.

To take the deeper look we find all of the subsets of the games graph where every team in the subset plays every other team in it.

As you can see from the table at the right, there are 24,106 subsets of the D1 schedule graph wherein every team plays every other team in the subset, but only 1800 that are not members of a larger subset. In general we need only look at the unique subsets for those that glue the games graph into a connected whole.

Notice that there are no round-robins with more than seven teams that have representatives from more than one conference. The 13 largest are all determined by conference schedules:

82{ UCF; Cincinnati; UConn; ECU; Houston; Memphis; S Florida; Tulane }1{ AAC }113199465882.3
81{ FGC; Jacksonville; Kennesaw; Lipscomb; NJIT; UNF; SC Upstate; Stetson }1{ ASUN }92256746958.6
113{ App St; Arkansas St; Ark-Little Rock; Georgia Sthrn; Georgia St; Louisiana; La-Monroe; USA; Texas St; UTA; Troy }1{ SBC }98356363057.3
91{ C of Charleston; Delaware; Elon; Hofstra; JMU; NC-Wilmington; Northeastern; Towson; William & Mary }1{ CAA }95346148854.2
93{ ETSU; Furman; Mercer; NC-Greensboro; Samford; Citadel; VMI; W Carolina; Wofford }1{ SoCon }87295846451.6
102{ Bakersfield; Sacramento; Chicago St; G Canyon; New Mex St; N Dakota; N Colorado; Seattle; UTRGV; Utah Valley }1{ WAC }80235751351.3
84{ Bradley; DBU; Evansville; Illinois St; Indiana St; Missouri St; S Illinois; Wichita St }1{ MVC }88315739949.9
92{ Baylor; Kansas; Kansas St; Oklahoma; Oklahoma St; Texas; TCU; Texas Tech; W Virginia }1{ B12 }83335040044.4
112{ Austin Peay; Belmont; E Illinois; E Kentucky; Jacksonville St; Morehead; Murray St; SE Missouri St; SIU-E; Tenn Tech; UT-Martin }1{ OVC }71294242038.2
111{ Arizona; Arizona St; California; Oregon; Oregon St; USC; Stanford; UCLA; Utah; Washington; Wash St }1{ P12 }67274040036.4
83{ Columbia; Cornell; Penn; Princeton; Brown; Dartmouth; Harvard; Yale }1{ Ivy }57223524530.6
94{ Cal Poly; Fullerton; Northridge; Hawaii; LBSU; UC Davis; UC Irvine; UC Riverside; UCSB }1{ BigW }57243326429.3
101{ BYU; Gonzaga; LMU; Pacific; Pepperdine; Portland; San Diego; USF; Santa Clara; St Mary's }1{ WCC }62303228828.8

As one would expect, multiconference round robins in general contribute more to how well-connected the field is. Not all are equally efficient in that regard, though. We can measure efficiency a couple of ways. The number of Opponents' Opponent pairs contributed by a round robin of size N (Cont) is

(GluedDupe) × (N-1)
Considering only the round robins involving three or more teams not all from the same conference, here are those that contribute at least 200 or at most 60:
7{ Clemson; Charleston So; Presbyterian; Winthrop; S Carolina; Citadel; Wofford }4{ ACC BigS SEC SoCon }782631244.6
7{ Richmond; C of Charleston; Elon; JMU; NC-Wilmington; Towson; William & Mary }2{ A10 CAA }772829442.0
6{ Notre Dame; Michigan; Michigan St; C Michigan; E Michigan; Toledo }3{ ACC B10 MAC }873028547.5
5{ UMass-Lowell; UConn; Boston Coll; Northeastern; Bryant }5{ AE AAC ACC CAA NE }841428056.0
5{ Notre Dame; Bradley; Inc Word; Texas So; Gonzaga }5{ ACC MVC SLC SWAC WCC }821327655.2
6{ Iowa; Bradley; DBU; Indiana St; Missouri St; S Illinois }2{ B10 MVC }752226544.2
5{ UConn; Rhode Island; Boston Coll; Northeastern; Bryant }5{ AAC A10 ACC CAA NE }821626452.8
6{ Michigan St; Oakland; C Michigan; E Michigan; Toledo; W Michigan }3{ B10 Hor MAC }752326043.3
6{ Clemson; Presbyterian; S Carolina; Furman; Citadel; Wofford }4{ ACC BigS SEC SoCon }722026043.3
6{ NC-Asheville; ETSU; Furman; NC-Greensboro; W Carolina; Wofford }2{ BigS SoCon }722125542.5
6{ Bradley; Evansville; Illinois St; Indiana St; Missouri St; SIU-E }2{ MVC OVC }752425542.5
5{ Dayton; George Mason; SC Upstate; Kentucky; Wofford }4{ A10 ASUN SEC SoCon }852225250.4
7{ Lipscomb; Austin Peay; Belmont; E Illinois; E Kentucky; Tenn Tech; UT-Martin }2{ ASUN OVC }632224635.1
6{ Nebraska; Kansas; Kansas St; Creighton; Wichita St; Neb-Omaha }5{ B10 B12 BigE MVC Summ }732424540.8
6{ Hartford; UConn; Rhode Island; Northeastern; Bryant; Cent Conn St }5{ AE AAC A10 CAA NE }742524540.8
6{ Clemson; Presbyterian; Furman; Citadel; W Carolina; Wofford }3{ ACC BigS SoCon }692124040.0
4{ C Michigan; Tennessee; St Mary's; G Canyon }4{ MAC SEC WCC WAC }86624060.0
5{ UConn; UMass; Rhode Island; Boston Coll; Northeastern }4{ AAC A10 ACC CAA }781923647.2
6{ Oklahoma St; DBU; Indiana St; Missouri St; Wichita St; ORU }3{ B12 MVC Summ }692223539.2
4{ Boston Coll; Villanova; Indiana St; Chicago St }4{ ACC BigE MVC WAC }881023458.5
6{ NC St; Duke; Georgia Tech; UNC; Virginia; Coastal Car }2{ ACC BigS }752923038.3
6{ SC Upstate; Presbyterian; S Carolina; Furman; Citadel; Wofford }4{ ASUN BigS SEC SoCon }702423038.3
4{ Stony Brook; Elon; Bowling Green; App St }4{ AE CAA MAC SBC }81522857.0
4{ ECU; Maryland; Tennessee; SE Louisiana }4{ AAC B10 SEC SLC }82722556.3
5{ Georgia Tech; Kennesaw; Georgia; Mercer; Georgia Sthrn }5{ ACC ASUN SEC SoCon SBC }701522044.0
7{ Evansville; Austin Peay; Belmont; E Kentucky; Murray St; SIU-E; UT-Martin }2{ MVC OVC }602421630.9
4{ Davidson; Rhode Island; Campbell; Indiana St }3{ A10 BigS MVC }821021654.0
5{ Cincinnati; Louisville; Indiana; Xavier; Kentucky }5{ AAC ACC B10 BigE SEC }752121643.2
6{ Fordham; LaSalle; St Joseph's; Villanova; Canisius; St Peter's }3{ A10 BigE MAAC }763321535.8
6{ SC Upstate; Charleston So; Presbyterian; S Carolina; Citadel; Wofford }4{ ASUN BigS SEC SoCon }712821535.8
5{ W Kentucky; Georgia; Kentucky; Tennessee; Vanderbilt }2{ CUSA SEC }732021242.4
5{ Clemson; Charleston So; C of Charleston; S Carolina; Citadel }5{ ACC BigS CAA SEC SoCon }671421242.4
7{ TAMU; Ab Christian; Houst Bap; Inc Word; Sam Houston; S.F. Austin; TAMU-CC }2{ SEC SLC }582321030.0
6{ Albany; Binghamton; Maine; UMass-Lowell; Stony Brook; NY Tech }2{ AE Ind }642221035.0
7{ LSU; McNeese St; New Orleans; Nicholls St; Nrthwstrn St; SE Louisiana; Louisiana }3{ SEC SLC SBC }612621030.0
4{ UConn; Missouri St; Austin Peay; Alcorn St }4{ AAC MVC OVC SWAC }77721052.5
5{ Cincinnati; W Kentucky; Georgia; Kentucky; Tennessee }3{ AAC CUSA SEC }752320841.6
5{ LaSalle; St Bonaventure; St Joseph's; Villanova; Canisius }3{ A10 BigE MAAC }732120841.6
4{ St Louis; Morehead; Neb-Omaha; Arkansas St }4{ A10 OVC Summ SBC }77820751.8
4{ Cincinnati; Coastal Car; Ball St; Ole Miss }4{ AAC BigS MAC SEC }801120751.8
6{ La Tech; LSU; McNeese St; New Orleans; Nrthwstrn St; Louisiana }4{ CUSA SEC SLC SBC }662520534.2
6{ ECU; UNC; Campbell; High Point; Elon; NC-Wilmington }4{ AAC ACC BigS CAA }723120534.2
7{ S Illinois; Austin Peay; Belmont; E Illinois; Jacksonville St; Murray St; SE Missouri St }2{ MVC OVC }572320429.1
5{ Virginia Tech; ETSU; Citadel; VMI; W Carolina }2{ ACC SoCon }681720440.8
5{ Lipscomb; MTSU; Miami OH; W Michigan; Belmont }4{ ASUN CUSA MAC OVC }722120440.8
4{ VCU; NC-Wilmington; E Kentucky; S Dakota St }4{ A10 CAA OVC Summ }75720451.0
4{ Fordham; Michigan St; Presbyterian; Furman }4{ A10 B10 BigS SoCon }801320150.3
6{ Tulane; LSU; New Orleans; Nicholls St; SE Louisiana; Louisiana }4{ AAC SEC SLC SBC }642420033.3
6{ Albany; Stony Brook; Fordham; NY Tech; Fairfield; Manhattan }4{ AE A10 Ind MAAC }672720033.3
6{ Hartford; Rhode Island; Northeastern; Quinnipiac; Bryant; Cent Conn St }5{ AE A10 CAA MAAC NE }682820033.3
↑ 200 or more pairs; 60 or fewer pairs ↓
5{ Cal Poly; San Jose St; Pacific; USF; Santa Clara }3{ BigW MW WCC }38236012.0
4{ Oklahoma St; S.F. Austin; Ark-Little Rock; UTA }3{ B12 SLC SBC }46266015.0
3{ TAMU-CC; Chicago St; UTRGV }2{ SLC WAC }44146020.0
3{ UCF; Cornell; Brown }2{ AAC Ivy }3996020.0
3{ Harvard; Yale; Fairfield }2{ Ivy MAAC }44146020.0
3{ Maine; NY Tech; Lehigh }3{ AE Ind Pat }44146020.0
3{ Binghamton; NY Tech; Penn }3{ AE Ind Ivy }40106020.0
3{ Georgia; Georgia Sthrn; USA }2{ SEC SBC }46175819.3
3{ High Point; NC-Asheville; NC-Greensboro }2{ BigS SoCon }47185819.3
3{ UT-Martin; Ala A&M; Jackson St }2{ OVC SWAC }3785819.3
3{ Clemson; Florida St; C of Charleston }2{ ACC CAA }44155819.3
3{ Northwestern; Illinois-Chi; N Kentucky }2{ B10 Hor }3895819.3
3{ Hofstra; Towson; Coppin St }2{ CAA MEAC }44155819.3
3{ C Arkansas; S.F. Austin; Ark-Little Rock }2{ SLC SBC }44155819.3
3{ Ole Miss; Ark-Pine Bluff; Grambling }2{ SEC SWAC }3895819.3
3{ N Dakota St; S Dakota St; N Dakota }2{ Summ WAC }3785819.3
3{ Cal Poly; California; USF }3{ BigW P12 WCC }43145819.3
4{ Oregon St; Wash St; Seattle; Utah Valley }2{ P12 WAC }40215714.3
4{ Hawaii; LMU; USF; Santa Clara }2{ BigW WCC }39205714.3
4{ UC Riverside; LMU; Portland; San Diego }2{ BigW WCC }39205714.3
4{ LBSU; UC Irvine; San Jose St; LMU }3{ BigW MW WCC }39205714.3
4{ Cal Poly; Fresno St; Bakersfield; Sacramento }3{ BigW MW WAC }43245714.3
3{ SIU-E; Tenn Tech; W Illinois }2{ OVC Summ }39115618.7
3{ Florida A&M; Alabama St; Jackson St }2{ MEAC SWAC }3245618.7
3{ UW-Milwaukee; Youngstown; Kent St }2{ Hor MAC }40125618.7
3{ Rider; Lafayette; Lehigh }2{ MAAC Pat }44165618.7
3{ Ark-Pine Bluff; Arkansas St; Ark-Little Rock }2{ SWAC SBC }42145618.7
3{ Coastal Car; NC-Greensboro; Citadel }2{ BigS SoCon }48205618.7
3{ Manhattan; St Peter's; Lehigh }2{ MAAC Pat }46185618.7
3{ Albany; UMass-Lowell; Harvard }2{ AE Ivy }43155618.7
3{ Oklahoma St; Texas; Prairie View }2{ B12 SWAC }41135618.7
3{ UCSB; St Mary's; Bakersfield }3{ BigW WCC WAC }45175618.7
3{ UC Davis; Nevada; Arizona St }3{ BigW MW P12 }41135618.7
2{ Richmond; Miami OH }2{ A10 MAC }5505527.5
4{ Cal Poly; LBSU; UC Irvine; San Jose St }2{ BigW MW }37195413.5
4{ Baylor; Inc Word; Lamar; Sam Houston }2{ B12 SLC }43255413.5
4{ UC Irvine; UC Riverside; LMU; San Diego }2{ BigW WCC }41235413.5
4{ Oregon St; Portland; Seattle; Utah Valley }3{ P12 WCC WAC }40225413.5
3{ NJIT; Coppin St; Norfolk St }2{ ASUN MEAC }3695418.0
3{ MVSU; Arkansas St; Ark-Little Rock }2{ SWAC SBC }40135418.0
3{ LMU; St Mary's; Bakersfield }2{ WCC WAC }44175418.0
3{ UNF; Penn; Dartmouth }2{ ASUN Ivy }40135418.0
3{ Xavier; N Kentucky; Wright St }2{ BigE Hor }39125418.0
5{ Nevada; New Mexico; San Jose St; USF; Santa Clara }2{ MW WCC }37245210.4
3{ Northridge; Bakersfield; N Colorado }2{ BigW WAC }39135217.3
3{ Utah; Wash St; Houst Bap }2{ P12 SLC }39135217.3
3{ La Tech; UTSA; TAMU-CC }2{ CUSA SLC }44185217.3
3{ UC Irvine; Bakersfield; Seattle }2{ BigW WAC }41155217.3
3{ Oakland; Pepperdine; Portland }2{ Hor WCC }35105016.7
3{ Auburn; LSU; Southern }2{ SEC SWAC }42175016.7
3{ Delaware; Towson; Delaware St }2{ CAA MEAC }41165016.7
3{ UC Davis; Air Force; Nevada }2{ BigW MW }38135016.7
3{ Washington; Wash St; Gonzaga }2{ P12 WCC }38135016.7
5{ Cal Poly; Hawaii; UC Davis; USF; Santa Clara }2{ BigW WCC }3826489.6
4{ Cal Poly; UCSB; Pepperdine; USF }2{ BigW WCC }40244812.0
3{ La Tech; UTSA; McNeese St }2{ CUSA SLC }43194816.0
3{ NY Tech; Penn; Princeton }2{ Ind Ivy }37134816.0
3{ Binghamton; Cornell; Penn }2{ AE Ivy }3394816.0
4{ Coppin St; UMES; Fairleigh Dickinson; Mt St Marys }2{ MEAC NE }31164511.3
4{ USC; UCLA; LMU; Pepperdine }2{ P12 WCC }41264511.3
3{ Missouri St; ORU; W Illinois }2{ MVC Summ }35134414.7
3{ Washington; N Colorado; Seattle }2{ P12 WAC }35134414.7
3{ Northridge; Pepperdine; Portland }2{ BigW WCC }34144013.3
4{ Cal Poly; LBSU; Fresno St; San Jose St }2{ BigW MW }3623399.8
3{ Cal Poly; California; UCLA }2{ BigW P12 }37183812.7
5{ Cal Poly; UC Davis; Pacific; USF; Santa Clara }2{ BigW WCC }3728367.2

You can get a feel for the skeleton of the games graph by browsing 2016 Scheduled Round Robins where you will find all 1704 sorted in decreasing per-team contribution to O-Os for all round robins.

The interconference game-count matrix I included last time is symmetrical - the same number appears in the (confA,confB) position and (confB,confA). You can't tell from the number of games how many teams from confA play at least one team in confB, which usually is not the same as the number of teams in confB that play teams in confA. Here is a breakdown that does:

Interconference Pairings by Team


In memory of

Paul Kislanko