Tricia Muldoon Brown, PhD, is a Professor of Mathematical Science at Georgia Southern University in Savannah, GA.  Her research interests include recreational mathematics associated with games and sport.

Andrew M. Heroy is employed by the Metis Foundation.  His area of specialty is data science. Eric B. Kahn, PhD, is a Professor of Mathematics as Commonwealth University of Pennsylvania. His research interests are in mathematics in sport and IBL in mathematics.

Losing Matters: A European Association Football Model for NCAA Men’s Basketball

ABSTRACT

Purpose: The purpose of this study is to examine the impact of applying a European association football model to American men’s college basketball.

Methods: Structures for NCAA men’s basketball and European association football are analyzed, and an Association Football (AF) model is proposed which utilizes features of the European system of promotion and relegation and a mathematical model for tournament bids and seeding.  

Results: Data were collected for NCAA men’s basketball teams from 2010 through 2019 and we identify teams which would be affected by promotion and relegation each year and compare the AF-modeled NCAA tournament to the actual tournament brackets finding 85% similarity.

Conclusions: Geographic conferences and relegation models where losing matters could be applied to men’s college basketball to decrease costs and increase excitement and fairness, while still having strong agreement with data from recent years.

Applications in Sport: American sports should consider adopting some selection and organizational practices from European sports, particularly objective selection and seeding and regional groupings.

Key Words: college basketball, tournament model, relegation, geographic conferences

INTRODUCTION

European and American sports cultures have many dissimilar features, but none are more notable than the disparate consequences for losing. European football associations follow an open model where teams can be moved between tiers based on their performance that season. On the other hand, American sports leagues use a closed model that does not allow for movement between major and minor leagues. An attempt was made in the 2010’s and early 2020’s to apply a more American system to European football, forming a super league that would bypass the Premier League’s current system of promotion, relegation, and championship selection. When asked about this idea, as reported in Sports Illustrated (1) Man City coach Pep Guardiola famously says, “It is not a sport when it doesn’t matter if you lose.” In contrast, the American version of these opinions is fictionalized in the popular television series Ted Lasso (20). Ted is the new head coach of FC Richmond, and one of his players questions what happens to losing teams if there is no relegation in America. Ted says, “You know, they play out the rest of the schedule, go through the motions in meaningless games contested in lifeless, half-empty stadiums, and everyone is pretty much fine with that.” The negative ramification of a poor season is not the only difference in European and American sports. We also wish to apply the regional nature of the clubs and teams in the European system and the objective selection process for both promotion and relegation, and postseason selection and seeding. These features have benefits in cost, transparency, and enthusiasm.

Taking advantage of these three association football characteristics, an open system, objective ranking process, and regional structure, we propose a new model for National Collegiate Athletic Association (NCAA) basketball conferences and tournaments. We begin by describing the current NCAA conference model and tournament selection process as well as that used by the Union of European Football Associations (UEFA) and the English Football League. Then we introduce the Association Football model for men’s basketball which realigns the conferences, creates a system of promotion and relegation, and objectively selects and seeds the NCAA tournament. Finally, we use the proposed model to identify teams for promotion and relegation and retroactively determine the tournament field using data collected for each year from 2010 through 2019.

METHODS

Current NCAA Model

Basketball is the most sanctioned sport in the NCAA with over 350 colleges and universities fielding Division I (DI) men’s basketball teams. While the precise number of participating teams varies slightly from year to year as teams move up from or down to Division II, every Division I school has a men’s basketball team.

Conference geography and alignment

Division I teams are organized into 32 conferences. The first college basketball conferences were developed in the early 20th century in an attempt to standardize rules and regulations and protect student athletes. These were primarily geographic in nature, as evidenced by many of the naming conventions such as the Southern Intercollegiate Athletic Association, the Missouri Valley Intercollegiate Athletic Association, or the Pacific Coast Conference. While versions of these conferences still exist in the SEC, the Big 12, and the PAC 12, the participating schools have expanded to include those outside of the original geographic region. For example, the Big 12, originally covering the Missouri Valley, added West Virginia University in 2012 and expanded in 2023 to include Brigham Young University, University of Houston, and University of Central Florida extending the border of the conference from Utah to the gulf of Texas to Florida to West Virginia. Additionally, the Big 10 added University of California Los Angeles and University of Southern California in 2024, stretching the conference from the coast of Maryland to the coast of California. While more feasible today than in 1915, such expansions have an increased cost in dollars and time for teams traveling longer distances.

Moreover, conference affiliation is not necessarily stable, many of the realignments mentioned above were catalyzed by the University of Texas and University of Oklahoma agreeing to move to the SEC for the 2025 season.  Conference movement causes ripple effects as losing a university (or two) creates a void, leading conferences losing a team to invite teams from other conferences subsequently leaving other holes to be filled. Further, conferences not directly impacted by a team leaving or entering will often feel the need to realign to stay competitive. Moriarty (13) explores how some conferences benefit while others are harmed by this domino effect. Although conference realignment is often spurred by football, the other sports, including basketball, are also impacted. Conference realignment is not a recent or transitory phenomenon, Daughters (5) finds that 78 teams switched conferences during the period 1998-2013. Conference realignment, studied in the context of college football, has varied effects including increased attendance and profits for the athletic department while lessening regional rivalries. (See Hoffer and Pincin (10) or Dennie (6) for example.) The movement of schools from one conference to another has been and will likely remain a part of the landscape of college sports.

Tournament selection and seeding

Men’s basketball teams typically play around 30 regular season games each year in a mix of conference and non-conference games. The outcomes of these games and the conference tournament help determine selection for and seeding in the NCAA Men’s basketball tournament. Since 2011, 68 college basketball teams have participated in the tournament; the selection process includes 32 automatic bids going to the conference tournament winner for each conference, as well as 36 at-large bid which are selected by a committee to participate in the tournament. The NCAA selection committee is composed of 12 members, expanded from 10 in 2022 (24), and consists of collegiate athletic directors, conference commissioners, and other conference officials. The committee uses a mix of metrics, discussion, and balloting to seed the field (14). While the teams’ win/loss record is the first consideration, many other factors are considered including distances to event locations, expected attendance numbers, television viewership, player injuries, and recency of strong wins. While objective metrics are applied, tournament selection and seeding are essentially subjective processes and come under fire when things like the “eye test” are used to determine whether teams should be in or out. Personal bias can creep in, and despite recent attempts to increaase transparency, the process remains secretive.

Studies on bias in the selection process have produced mixed results. Criticism has been levied toward the Ratings Performance Index (RPI) which was used as a major determining factor until 2018. The RPI is a blunt metric solely determined by a team’s wins and losses as well as their opponents’ wins and losses. Research into bias of the RPI includes Sanders (19) who, building on previous work on bias in the RPI, divides teams into four different types according to the performance of the conference and the performance of the team within its conference, finding a bias against lower performing teams in higher ranked conferences compared with higher performing teams in lower ranked conferences. Coleman (3) looked at bias in both selection and seeding, finding bias towards teams with a conference member on the selection committee and against mid-major teams. On the other hand, Paul and Wilson (16) asserted the RPI is inherently biased as it omits the margin of victory in its calculation. When attempting to correct for this, (as the committee has access to the margin of victory data) they found no bias. The NCAA introduced a newer ranking system in the 2018-2019 season, hoping to correct some of these issues. This system, called NET, classifies wins by quadrants and incorporates variables such as the location of the game and margin of victory. Some recent analysis is available on the effectiveness of part of this newer system. Reinig and Horowitz (18) use a linear programming approach to incorporate the use of the quadrant system, finding results more consistent with the actual tournament selection.

Because of these flaws with subjectivity and bias, we argue a better selection and seeding method should be free of personal biases and transparent. It is not a new idea to apply non- subjective models to the NCAA Tournament selection process. For example, Matthews et. al. (12) applied the PageRank algorithm to rank all teams, selecting the top 64 teams for the tournament; this method has the advantage of incorporating more variables than RPI including venue, date, and point margin. Also, Dutta and Jacobson (7) made use of a decision tree with 11 stages to pairwise compare all NCAA teams. Those with the most pairwise wins were selected for the tournament, and this method successfully selects almost all the participating teams from 2012-2016. Both of these methods have an implied rank so seeding could be affected with the traditional S-curve (and possibly a tie-breaking mechanism). Further, Reinig and Horowitz (17) used seven variables such as RPI and BPI but also polling ranks to generate a final ranking of the teams that respects domination, that is, one team being equal or ahead of another team in all seven variables.

We note that other works are attempting to predict the selection committees’ choices, such as Coleman, DuMond, and Lynch (4) and while we compare our selections with the past selections, this is as validation not prediction. Furthermore, it is understandably a popular topic to predict the outcomes of games in the tournament, but that is not the purpose of this work.

To summarize, the current NCAA model is flawed by its subjective and semi-transparent process of tournament seeding and selection, the higher costs of moving away from a regional conference alignment, and the instability of movement within these conferences. To correct these flaws, we will propose a model adapted from European association football.

European association football as a model

Association football or soccer has been played in Europe since the 1800’s. The football clubs are organized regionally, primarily by nation, with a few exceptions. The modern international governing body is the Union of European Football Associations (UEFA) while the clubs in England are regulated by the English Football Association. Here we discuss the promotion and relegation of the English clubs in their national association and selection and seeding for the UEFA tournament.

Promotion and relegation in the English Football League System

The English football league is structured as a pyramid with eleven defined levels where the 20-team Premier League sits on the top tier of the pyramid. At the end of each season, teams are moved between tiers based on their performance. Higher performing teams are promoted up the pyramid to the next level and lower performing teams are relegated down the pyramid to the previous level. In the English system, the number of teams promoted and relegated depends on the level with typically between one and four teams moving into and out of each league. In theory, this system allows any local club the opportunity to move up to the national stage over time. Similar relegation and promotion systems are in place in all the major national football associations. Positive benefits have been seen in the European promotion and relegation systems such as increases in both net attendance and player compensation Noll (15).

In particular, the national teams competing in UEFA Champions League (UCL) or UEFA Europa League (UEL) are almost always selected from the top tier of the pyramid. As we are using the UCL as a model for the NCAA tournament, we also wish to include a series of promotions and relegations. Here we model a shorter pyramid with the so-called “power conferences” above mid-major conferences. Because precedence is given in the tournaments to teams from power conferences in college basketball and premier leagues in association football, the promotion system allows high-performing teams from mid-major conferences the opportunity to move up to play against stronger competition but also have increased opportunity for tournament selection. Next, we look at European tournament selection and seeding.

UEL tournament selection and seeding

The UEFA consists of over 50 members and is composed primarily of national football associations in Europe, with some exceptions for associations formed from groups of nations and nations not having their own association. Each member association falls in one of four categories which determine how many representatives will compete from that association in the UCL and UEL championships. The UCL is considered the premier competition with high-ranking teams failing to qualify for the UCL group stage being selected to compete in the secondary UEL.

We are interested in the UEFA championship as a model for the NCAA tournament because this process is objective. Association representatives for the championship are chosen entirely by mathematical rank within the national championship with between one and four of the top finishing teams chosen from that league (with a rare possibility of five teams if the previous year’s UCL or UEL winner fails to qualify). The number of teams is determined by the association’s five-year club coefficient, a metric that measures the average number of points earned by a qualifying team in UCL and UEL competitions, where points are awarded for wins and ties. Specifically, 2 points are allocated for a win, 1 point for a tie, and 0 points for a loss. Each association is ranked by association coefficient (with a tie-breaking system in place when coefficients are identical). Once these teams enter the field, under typical circumstances 26 teams directly qualify for the group stage. These are the UCL and UEL title holders, the champions from associations ranked 1-10, the second-place teams from members ranked 1-6, and the third and fourth place teams from associations ranked 1-4. (If the UCL or UEL title holder qualifies in one of the other categories, then the champion from the eleventh ranked member or the third placing team from the fifth ranked member association, respectively, is selected for the group stage.) The remaining teams are chosen from two pathways: the Champions path and the League path.

The playoffs allow lower ranking teams a chance to play their way into the UCL group stage. The qualifying phase consists of a preliminary round, and three qualifying rounds along with a final playoff round. Fifty-five teams qualify for the playoffs consisting of 44 champions, 9 runners-up, and 2 third place teams from the remaining highest ranking member associations. The champions play along the Champions path and the second and third place teams play in the League path. The teams earn byes for earlier stages based on their ranking.  For example, the top two ranking champions enter in the final play-off round, but the lowest four must begin play in the preliminary round, and the top three runners-up begin playing in the third qualifying round while the next six begin playing in the second qualifying round. Teams are paired based on seeding (determined by an individual club coefficient) and a draw with (after the preliminary round) each pair playing two matches or legs, one on each home field, with the winner determined by total score differential. Any team eliminated before the UCL group stage gains automatic entry in the UEL with byes determined by progression through the qualifying phase and playoff. Furthermore, seeding in the tournament is also determined by coefficients except in extreme instances. Thus, the European system of seeding and selection is based purely on points and is simple, transparent, and unbiased.  To make use of these advantages, we propose the Association Football (AF) model for NCAA men’s basketball.  Our method provides conference alignments, a tournament selection process, and a promotion and relegation system.

Geographic conference alignment

To create new conference alignments, we classified seven conferences[1] in men’s college basketball (ACC, American, Big East, Big 10, Big 12, SEC, and PAC-12) as top-level basketball conferences, because, although there is variability from year to year, these seven conferences typically have the highest non-conference win percentages. For example, in the 2019-20 season these conferences were each winning over 70-80% of their games outside of their conferences according to Wittry (22). In the AF model, the 87 teams from these conferences will form a league analogous to UEFA’s Premier League and as such, they will receive a higher proportion of automatic bids into the tournament. Our proposal of geographic redistricting condenses these seven conferences down to five (East, Central, Midwest, South, and West), with each conference being sub-divided into two divisions. Figure 1 illustrates the top teams grouped into 10 new divisions within five geographic top conferences which we call the Premier-5 (P5) conferences.  (Table 7 in the Appendix lists the teams by conference and division.)

Figure 1: Premier-5 teams grouped by divisions

The remaining D1 teams are placed in Mid-major (MM) conferences (also named East, Central, Midwest, South, and West) that are also subdivided into divisions. Universities are assigned to conferences and divisions with regional proximity as the main factor, and as a secondary factor we tried to keep teams from the same state in the same division. Figure 2 illustrates the distribution of Mid-major teams into 18 divisions. Full lists of these divisions with additional images can be found Tables 8-12 in the Appendix. (Note, the Ivy League with its differing athletic philosophy is exempt from this realignment.)

As expected, universities are not evenly distributed throughout the United States. A lower density of universities in the western states causes those conferences to be geographically larger while a higher density on the eastern seaboard causes those conferences to be geographically smaller but to consist of a larger number of teams. There is precedence for this variation of size

Figure 2: Mid-major teams grouped by divisions (excluding Hawai’i)

within UEFA’s national associations; for example, Scotland has 12 teams while England has 20 in their top leagues. Current DI conferences averaging about 12 teams: the smallest conference is the Ivy League with 8 teams and largest is the Big 10 with 18 teams. The seven major conferences contributing to the AF realignment have expanded in recent years and now average 14 teams per conference. Our five new Premier-5 conferences are comparable in size, but slightly bigger averaging 17 teams per conference and 9 teams for each division. The 13 new mid-major divisions are larger than current conferences averaging about 14 teams per division with a minimum of 8 teams and a maximum of 21 teams in a division.

NCAA tournament

As in association football, some mechanism of promotion and relegation is needed to help the Premier-5 conferences maintain their premier status and deservedly earn the extra automatic bids in the NCAA tournament. Following the association football model, associated with each conference will be a numerical conference coefficient and with each team a numerical team coefficient. Let team P5 wins be the number of games a team wins against Premier-5 teams, and similarly team MM wins are the number of wins the team had against Mid-major teams. The team games are the total number of games played by the team in the regular season.  We define team coefficient as follows:

Conference coefficients are then the mean of the team coefficients in that conference.  Likewise, division coefficients are the mean of the team coefficients in that division. Mimicking association football, we use a simple 2-1-0 point system. The difference being, as college basketball games do not end ties, we keep track of the typical expected difficulty of the game by awarding 2 points for a Premier-5 win, 1 point for a Mid-major win, and 0 points for a loss.

With the team and division coefficients in place, the NCAA tournament can be restructured into two-tiers where top teams are automatically entered into the final tournament of 64 teams and lower-tier teams are given the opportunity to win a one-game playoff or “play-in” game for entry into the tournament. The teams are ranked within their conference by their team coefficients.  We say TC1 is the team with the highest coefficient, TC2 the team with the second highest coefficient, and so on. Then we rank the Premier- 5 conferences from 1 to 5 based on their conference coefficients, and we rank the Mid-major conferences from 1 to 19 based on their conference coefficients. Similarly, here PC# represents the #th ranked premier conference and MC# represents the #th ranked mid-major conference. Along with a tiebreaker, the coefficients completely determine seeding and region for each team. All teams labeled TC1 get an automatic bid, but teams TC2, TC3, and TC4 in PC1 also get an automatic bid as well as teams TC2 and TC3 from PC2 and PC3. This allocated the first 32 spots in the tournament. Further, the order of the locations may be rotated each year so each part of the country has the option to host the top-ranked team, as is done with the FBS national tournament, or alternately, as has been proposed for the NCAA, the teams given one seeds could choose their region with the PC1 TC1 team choosing first, the PC2 TC2 teams choosing second, and the PC3 TC1 team choosing third. The seeding of the teams with automatic bids is found in Table 1.

Table 1: Tournament Seeding

SEED	EAST	SOUTH	MIDWEST	WEST
1	PC01 TC1	PC02 TC1	PC03 TC1	PC04 TC1
2	PC03 TC2	PC02 TC2	PC01 TC2	PC05 TC1
3	PC01 TC3	PC02 TC3	PC03 TC3	PC01 TC4
4	MC03 TC1	MC02 TC1	MC01 TC1	PC01 TC5
5	MC04 TC1	MC05 TC1	MC06 TC1	MC07 TC1
6	MC11 TC1	MC10 TC1	MC09 TC1	MC08 TC1
7	MC12 TC1	MC13 TC1	MC14 TC1	MC15 TC1
8	MC19 TC1	MC18 TC1	MC17 TC1	MC16 TC1

The remaining 32 teams are determined by play-in games and are seeded by S-curve with the winner of the top-ranked play-in game seeded 9^th in the East to the winner of the lowest-ranked play-in game seeded 16^th in the East. To determine the teams in these play-in games we rank all unseeded premier conference teams by their team coefficients. The top 36 Premier-5 conference teams from any division will play in the preliminary round of the tournament. Here we identify the teams rather than the conferences with P#. Similarly, we rank all unseeded Mid-major conference teams by their team coefficients labeling them M#. Here the top 28 Mid-major teams will get a spot in the play-in round. The play-in games are seeded as shown in Table 2. The choice of 36 Premier-5 conference teams and 28 Mid-major conference teams may seem somewhat arbitrary, but when comparing the team coefficients of the 36th Premier-5 conference team and the 1st Mid-major team we saw consistency and so believe this strikes the correct balance. (See the discussion in Section 5.)

Table 2: Play-in games

Game

1

2

3

4

5

6

7

8

9

10

11

12

Home

P01

P02

P03

P04

P05

P06

P07

P08

P09

P10

P11

P12

Away

M28

M27

M26

M25

M24

M23

M22

M21

M20

M19

M18

M17

Game

13

14

15

16

17

18

19

20

21

22

23

24

Home

P13

P14

P15

P16

P17

P18

P19

P20

P21

P22

P23

P24

Away

M16

M15

M14

M13

M12

M11

M10

M09

M08

M07

M06

M05

Game

25

26

27

28

29

30

31

32

Home

P25

P26

P27

P28

P29

P30

P31

P32

Away

M04

M03

M02

M01

P36

P35

P34

P33

Promotion and relegation

An obvious difficulty with applying the model of promotion and relegation from a professional sports league to a collegiate setting is travel. Professional teams are composed of adults whose primary relationship to the team is that of an employee making extended travel simply a component of the work environment. On the other hand, college athletes have the additional responsibilities of being students, and the negative impact of extensive travel demands on scholastic responsibilities should be minimized if possible. With teams being promoted and relegated between Premier-5 and Mid-major conferences, coordinating geographic regions between the conferences is one way to achieve lower travel costs on the student athletes. There is evidence that geographic redistricting can be advantageous in more ways than the direct savings in time of travel. Lawrence (11) suggests rearranging the divisions around regional competition and rivalries will save in operational costs but also help ease overall inequalities between institutions. Additionally, Featherston (8) argues that geographic conferences are central to a student- centered conference alignment approach over the current model driven by financial incentives of national exposure.

With these coefficients in place, the promotion and regulation are simple processes. At the end of each season, within each conference teams are ranked by their team coefficients. The lowest ranking team in each of the ten Premier-5 divisions is identified. Within each mid-major conference, the divisions with the two highest division coefficients are selected and the team with the largest team coefficient from that division is chosen. Then the premier teams and mid-major teams move down and up respectively. Geography is used to determine how the Premier-5 and Mid-major teams are paired and swapped. A total of four teams will be directly affected by the promotion and relegation process in each of the five conferences.

We note, while it may seem unfair to have almost twice as many team vying for the promotion in the East, very talented winning teams in lower-ranked Mid-major East divisions will still have the option to move up in the next season’s promotion. Further, given the large number of mid-major teams in the West it may make sense to promote without relegation for the first two years to increase the size of the Premier-5 West conference to 16 teams to more closely parallel the other four conferences. Finally, the teams from the Ivy League conference will lie outside of this system and remain at the Mid-major level.

DISCUSSION

We have specified how the geographic AF model has the potential to lower costs for the schools and the athletes in terms of travel time and travel expenses as well as potentially balancing operational expenses. The AF model of promotion and relegation also provides stability. There is still movement and excitement or disappointment among the fan bases, but in a controlled manner, so conferences are not left floundering if a team leaves. Objective tournament selection and seeding also has the advantage of reducing bias by removing subjectivity. It should be acknowledged that the weighting system for wins in Premier-5 versus Mid-major divisions will benefit from further study to evaluate if it unfairly favors certain types of teams. The geographic model also has the advantage of increasing fan attendance and revenue as fans of opposing teams will be more able to travel to see the games. These competitive atmospheres could increase and build regional rivalries leading to higher excitement about the game. Most historic college basketball rivalries are geographic in nature, so there is unlikely to be a net negative effect here as well, for example Duke and North Carolina or Kentucky and Louisville, will either remain in the same conference or division, or switch from being in different conferences to being in the same conference or division.

We also posit an increased incentive to win nearer the end of the season for certain teams. With the current system, teams at the bottom of their league in a premier conference are only incentivized to win regular season games through seeding in the conference tournaments and the seeding in the NCAA should their long shot of winning the conference tournament occur. With the AF model, these lower-performing teams will be fighting against relegation, trying to keep their spot in premiere conferences. For Mid-major teams near the top of the conference, current incentives to win the conference and get top seeding in their conference tournament are already strong. Earning promotion will provide another tangible payout for winning the conference title.

Along with these general advantages, we consider potential impacts to the specific teams who get promoted or relegated at the end of the season. These schools will likely see changes in revenue, especially regarding media contracts and possibly apparel and licensing, depending on whether the team was promoted or relegated, changes could be positive or negative. In either case, schools would have to deal with the logistics of rebranding for their new conference. As discussed, conference realignment is already a frequent process so these impacts likely will not be worse in most cases, but there is the possibility a team could move up and down frequently. (For example, Grimsby Town F.C. has been promoted or relegated at least 30 times among different English club tiers over its 100+ year history (9)). Using data from the English Football League, Wilson (21) finds that 75% of teams survive promotion for at least one year with an average rate of 3.1 years before relegation. The English model has five tiers and thus four possible avenues of promotion and the rates of surviving that first promotion vary widely among the tiers.

There is also uncertainty remaining. One major difference between professional sports leagues and college athletics is the recruitment process and choices to attend or transfer from a school that are made by the college athlete. Would teams on the edge of either promotion or relegation see positive, negative, or neutral net impacts on recruiting and transfer decisions? Another uncertainty is the effect on competitive balance. Regular conference realignment can help balance the power within the conference, but geographical divisions do not consider the strength of the program, currently or historically.

RESULTS

We now retroactively apply the AF model to past NCAA tournaments. Data was collected on regular season wins and losses for NCAA Division I men’s basketball teams for the years 2010 through 2019. These data were collected from the website Basketball Reference (2) during the months of May and June in 2021 and used to calculate the previously described team and conference coefficients for each team, conference, and year.

Retroactive promotion and relegation

First, we recognize the teams who are promoted or relegated by the Association Football model from 2010 to 2019 using the AF model conference and division alignments.  (See Table 3.)

Table 3: Teams Promoted or Relegated under the Model by Year

Year	Relegated	Promoted
2010	Nebraska, Tulane East Carolina, Penn State DePaul, Indiana Auburn, Central Florida UCLA, Utah	Missouri State, Sam Houston State Rhode Island, Richmond Marshall, Northern Iowa Murray State, UAB Gonzaga, UT El Paso
2011	Oklahoma, TCU Providence, Wake Forest DePaul, Indiana Auburn, South Florida Oregon State, Utah	Missouri State, North Texas Fairfield, Richmond Marshall, Northern Iowa Belmont, Coastal Carolina Gonzaga, Brigham Young
2012	Nebraska, Texas Tech Boston College, East Carolina DePaul, Butler Auburn, South Carolina Southern California, Utah	Rice, Saint Louis Davidson, Wagner Dayton, South Dakota State Murray State, Southern Mississippi Gonzaga, New Mexico
2013	TCU, Tulsa Penn State, Virginia Tech DePaul, Xavier Auburn, South Florida Oregon State, Washington State	S. F. Austin, Saint Louis Davidson, Massachusetts Akron, North Dakota State Middle Tennessee, Southern Mississippi Gonzaga, New Mexico
2014	TCU, Tulsa Boston College, Virginia Tech Butler, DePaul Mississippi State, South Florida Southern California, Washington State	S. F. Austin, Saint Louis North Carolina Central, VCU Green Bay, Toledo Middle Tennessee, Southern Mississippi Gonzaga, New Mexico
2015	Missouri, Texas Tech Rutgers, Virginia Tech DePaul, Michigan Auburn, South Florida Southern California, Washington State	Sam Houston State, S. F. Austin Old Dominion, Wofford Dayton, Northern Iowa Georgia Southern, Murray State Colorado State, Gonzaga
2016	Missouri, Tulane Boston College, East Carolina Minnesota, Ohio State Auburn, South Florida UCLA, Washington State	Texas A&M Corpus Christi, S. F. Austin Monmouth, James Madison/VCU Dayton, South Dakota State Chattanooga, UNC Wilmington Gonzaga, Hawai‘i
2017	Tulane, Wichita State Boston College, North Carolina State DePaul, Indiana/Ohio State South Florida, Mississippi State Oregon State, Washington	Louisiana Tech, UT Arlington VCU, Winthrop Dayton, Illinois State Middle Tennessee, UNC Wilmington Gonzaga, Nevada
2018	Oklahoma State, Tulane East Carolina, Pittsburgh DePaul, Indiana Mississippi, South Florida California, Washington State	Louisiana Lafayette, Southern Illinois Saint Bonaventure, UNC Greensboro Loyola (IL), South Dakota State College of Charleston, Middle Tennessee Gonzaga, New Mexico State
2019	Oklahoma State, Tulane East Carolina, Pittsburgh Illinois, Notre Dame Georgia, Vanderbilt California, Washington State	Abilene Christian, Louisiana Lafayette VCU, Wofford South Dakota State, Toledo Belmont, College of Charleston UC Irvine, Nevada

While examining this table, unsurprisingly Gonzaga, a mid-major team who has been a national title contender in multiple tournaments, is predicted to be promoted in each of the years except 2019 and in that year their division coefficient was lower than the other two divisions in their conference. Other often-promoted teams are Dayton, Middle Tennessee, Stephen F. Austin, South Dakota State who were promoted four times. Further, DePaul is outclassed in their proposed division and would be predicted to be relegated in 8 of the 10 years. Auburn, East Carolina, Tulane, and Washington State are also relegated in five of the ten years and USF would have been relegated six times. More remarkably, we note that it is possible for quite good teams to get relegated. The Midwest Great Lakes conference was so strong that either Indiana or Ohio State, with 17-14 records, were relegated in 2017. Finally, there is plenty of variety, 42 different teams had seasons bad enough to earn relegation and 56 different teams were promoted.

Comparison of the Association Football model to past NCAA tournament selections

We can also look at the model through the lens of the seeding of the NCAA tournament. We have chosen the 2016 tournament as an example. Tables 5 and 6 found in the Appendix illustrate how the tournament could have been seeded that year.  Between the 32 automatic bids and the 32 play-in bid winners the AF model allows for 96 teams to make the NCAA tournament field, that is 32 pre-first round play-in games followed by the traditional 63 game single-elimination tournament. Given the on-and-off discussion for expanding the tournament field, we argue that this model increases the satisfaction of teams involved, allowing for more teams to participate as well as improving the selection process. Since the AF model has 28 more teams than the current model for tournaments from 1999 through 2010 and 24 more teams for tournaments after 2011, we examine teams that would not participate in the tournament as determined by the AF models but did receive a bid under the current system. These are the teams that potentially object to the change in system.  Table 4 lists the teams not selected by the AF model from 2010 to 2019. Except for 2011, only one or two premier teams were not selected by our model each of the ten years, with a total of sixteen Premier-5 teams being selected in the actual tournaments, but not by the AF model. There was a wider range of Mid-major teams that were not selected: between six and twelve each year and a total of 83 over the ten years. Therefore, the AF model agrees with 85% of the tournament committees’ selections.

We can also look at a basic analysis of the automatic seeding in the model as compared to the committee’s seeding. We consider 13 top teams automatically seeded from the premier conferences. Because the committee is much more likely to take a top premier conference team that does not win its conference tournament, these are less likely to be affected by upsets in a conference tournament than the remaining 19 teams selected after these top-ranked teams.  Thirty-nine of the 40 number 1 seeds in our model were selected for the tournament by the committee, with the one missing being Oregon in 2012. Seeding by the committee ranged from 1 to 6 with the average seeding over these 39 teams being 2.205. There were also 39 of the 40, number 2 seeds selected for the tournament by the committee. The excluded team being SMU in 2016 that was ineligible for the tournament due to NCAA violations. The range here of actual seeds was from 1 to 9, and the average seeding was 3.000. Regarding number 3 seeds, there were again 39 of 40 teams selected by the committee. (SMU in 2014 is the excluded team in this case.) The range is broader, from 1 to 12, with an average seed of 4.203. Overall, the committee and model seedings for teams selected by both was off by an average of 1.110 in those 13 top-ranked teams.

We also used the data to justify the play-in team ranking of 36 Premier-5 teams followed by 28 Mid-major teams. Over the ten years, the 36th-ranked Premier-5 team had a mean team coefficient of 0.9139 while the following top-ranked Mid-major play-in team had a team coefficient of 0.9246. This is less than one one-hundredth of a point advantage to the premier conference team.

We recall that the committee only chooses the at-large teams, with 32 teams chosen automatically by winning their conference tournament. The AF model is unable to account for the situation where a team that performed poorly in the regular season won their conference tournament and received an automatic bid. In fact, many of the current Mid-major conferences have such weak strength of schedules that even teams with reasonably good records won’t be selected unless they win their conference tournament. So, discounting the teams whose records were not strong, but received and automatic bid by winning their conference tournaments, there were only twelve teams that that the AF model omitted. These are: Penn State (2011), Marquette (2011), Southern California (2011), Xavier (2012), Temple (2013), Texas (2014), Purdue (2015), Wichita State (2016), Vanderbilt (2017), Alabama (2018), and Butler (2018).

CONCLUSIONS

We hypothesize some reasons for these teams being selected by the committee despite their poorer performance in the AF model. First, some teams may have been selected based on the “star-power” of that team. The primary example is the 2011 Marquette team that had both Jae Crowder

Table 4: NCAA Tournament teams not selected by the AF model from 2010 to 2019

Year	Teams	Premier-5	Mid-major	Total
2010	New Mexico State (12), Houston* (13), Ohio (14), Robert Morris (15), UC Santa Barbara (15), East Tennessee (16), UA Pine Bluff (16), Lehigh (16)	1	7	8
2011	Butler* (8), Penn State* (10), Marquette* (11), USC* (11), Indiana State (14), Wofford (14), Saint Peter’s (14), Northern Colorado (15), UC Santa Barbara (15), Akron (15), UT San Antonio (16), Alabama State (16), UNC Asheville (16), UA Little Rock (16), Boston University (16)	4	11	15
2012	Xavier* (10), Saint Bonaventure (14), Detroit Mercy (15), Mississippi Valley State (16), Western Kentucky (16), Vermont (16)	1	6	7
2013	Temple* (9), New Mexico State (13), Pacific (15), Iona (15), Albany (15), James Madison (16), Long Island (16), Western Kentucky (16), Liberty (16), North Carolina A&T (16)	1	9	10
2014	Texas* (7), Tulsa* (13), Lafayette (14), Milwaukee (15), American (15), Wofford (15), Coastal Carolina (16), Weber State (16), Albany (16), Mount Saint Mary’s (16), Cal Poly (16), Texas Southern (16)	2	10	12
2015	Purdue* (9), UC Irving (13), Valparaiso (13), UAB (14), Northeastern (14), Belmont (15), Texas Southern (15), New Mexico State (15), Lafayette (16), North Florida (16), Robert Morris (16), Manhattan (16), Hampton (16)	1	12	13
2016	Wichita State* (11), Florida Gulf Coast (16), Fairleigh Dickinson (16), Holy Cross (16), Southern (16), Austin Peay (16), Hampton (16)	1	6	7
2017	Vanderbilt* (9), Kent State (14), Iona (14), Troy (15), Jacksonville State (15), Mount Saint Mary’s (16), South Dakota State (16), Texas Southern (16), UC Davis (16)	1	8	9
2018	Alabama* (9), Butler* (10), Davidson (12), Marshall (13), CSU Fullerton (15), Iona (15), LIU Brooklyn (16), Radford (16), North Carolina Central (16), Texas Southern (16)	2	8	10
2019	Mississippi State* (5), Mississippi* (8), Saint Mary’s (11), Colgate (15), North Carolina Central (16), North Dakota State (16), Fairleigh Dickinson (16), Prairie View A&M (16), Iona (16)	2	7	9

and Jimmy Butler, two current NBA stars, and Darius Johnson-Odom who were all drafted in 2011 or 2012. Another example, is Colin Sexton on Alabama in 2018 who was the No. 2 ranked point guard coming out of high school and drafted 8^th that year. Other teams with future NBA draft picks include USC in 2011 with Nikola Vusevic, or 2016 Wichita State with Landry Shamet. Even undrafted players can excite notice: for example Fred VanVleet on that same Wichita State team twice won the Missouri Valley Player of the Year and the 2017 Vanderbilt team with Luke Kornet breaking school shot-blocking records. Although impossible to precisely measure the impact these future NBA players had on the national conversation, it is quite natural that committee members, also being fans, would be excited to see what some of these players could do in the tournament.

The committee might have also placed extra weight on runs in the conference tournament even if the team did not end up winning the championship game. Penn State and Xavier lost in their conference championship game while USC, Texas, Purdue, Wichita State, Vanderbilt, Alabama, and Butler all lost in their conference semifinals. In fact, 6 of the 9 lost to the eventual winner of the conference tournament. The AF model does not include data from the conference tournaments, so these wins may have helped propel these teams into the tournament if included.

Another explanation for the omission of some teams is strength of schedule as based on the Premier-5 and Mid-major teams in our model. Take the 2016 Wichita State team as an illustration. Overall, their record of 26-9 is favorable, but Wichita State did not move into the American Athletic Conference until the 2017-18 season. So, while they are considered a Premier-5 conference school in AF rankings, they almost exclusively played Mid-major schools in the 2015-16 season precipitating a low team coefficient. There may also be a recency bias; the committee may have felt that based on the past success of Wichita State in the Missouri Valley Conference the 26-9 record deserved a bid, even though our metric disagrees. Wichita State may not be the only team that was selected because of recent tournament success; a weak 2018 Butler was granted a spot in the tournament after stronger Butler teams had appeared in the previous three tournaments and nine of the last eleven.

Finally, we suggest that the committee composed of humans is fallible and some of these teams simply should not have been selected. Especially since our model selected an additional 28 (31 in 2010) teams, team omissions from our model suggests we ranked them significantly lower than the tournament committee who placed them in the field of 68 (65 in 2010). In particular, we point to the selection of Mississippi in 2019. Mississippi had a mediocre record of 20-12 and exited the SEC tournament in the first round. They had no notable players and no tradition of playing in the tournament with only two appearances (2013, 2015) in the previous 15 years. We see also in this year; Mississippi State was selected by the committee and not by the AF model. This decision is also questionable as Mississippi State had a mediocre record of 23-10 and quickly exited the SEC tournament reaching only the quarterfinals. They did however have some second-round future NBA draft picks in Quinndary Weatherspoon who was drafted 49th overall in the 2019 draft and Robert Woodard and Reggie Parry who were drafted 40th and 57th, respectively, in the 2020 draft.

To conclude, geographic conferences and relegation models where losing matters could be applied to men’s college basketball to decrease costs and increase excitement and fairness, while still having strong agreement with data from recent years.

APPLICATIONS IN SPORT

American sports should consider adopting some selection and organizational practices from European sports, particularly objective selection and seeding and regional groupings.

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[1] Conference membership as of 2023