Recently, Matt Brown posited a question that’s been on this Big Sky alumni’s (shout out to the University of Montana) mind for a while now: Why are some teams still in FBS?

Brown notes:

Attendance has declined all over. With the decline of cable TV, the rise of media fees should slow, especially outside the Power 5 conferences. Many state governments have slowed their support for higher education, leading schools to charge students heavy fees to subsidize athletics.

Many teams aren’t going to win anything significant. They’re often the same ones in financial peril.

To free themselves from that wasteful cycle, an FBS team could consider dropping to FCS. There are a few structural differences between the two levels, the biggest being the different scholarship limits. FBS lets you have 85 full-ride scholarships, while FCS is limited to 63 (and in some leagues, even less than that).

The cost savings over scholarships is suspect (the schools are cutting checks to themselves, after all), but the costs for virtually everything else, from facilities to coaching salaries to support staff, are substantially less. The revenues are smaller too, but for some G5 programs without lucrative TV deals, the future savings may outweigh the costs.

Read the whole thing.

Matt offers a few suggestions about teams moving down and rearranging conferences. We will come back to candidates below, but his reasoning is sound. FBS is a grind for many teams, and despite wanting to compete on the highest level, it’s a tough sell to move down:

This sounds like a lot, but it might prove to be a conservative proposal. Dropping a level is hard. There’s a reason only Idaho has done it in recent memory, and the Vandals dealt with fierce initial backlash from fans. Just about every program, even the most resource-starved, is one good hire away from cracking .500. And there are benefits to FBS that don’t easily show up on a balance sheet.

Matt’s methodology involves some common sense moves - your classic UConn moving down, North Dakota State moving up, and my long-time favorite, The Super Sun Belt Conference. Although Matt’s suggestions make sense, deciding who downgrades is still an inexact science.

That’s where the Melitz Model can help. The basic Melitz framework models trade with heterogenous firms, that is, firms with different levels of productivity. Each firm’s total cost of production consists of a fixed cost, a cost of entry, and a variable cost, based on that firm-specific productivity. In a closed economy, there exists a theoretical productivity threshold - a productivity point below which a firm can no longer cover their fixed costs. If a firm’s productivity lands exactly at the productivity threshold, they make no profit, and they stay in the market, a constraint referred to as the zero profit condition. Above that threshold, firms make a positive profit in proportion to their distance from the threshold. We could go much deeper into the intricacies of the model - in fact, I haven’t scraped the surface of trade and exchange - but at its basic level, Melitz’s framework demonstrates how firms with different productivity levels make decisions to stay in a market.

In college football, 130 teams have entered the market - “employing” players as inputs, coaching them and developing them according to their production function, producing wins dependent on their idiosyncratic productivities. Today, I apply the bones of the Melitz model to college football, examining each FBS team as a heterogenous firm. I will estimate their productivity based on the differences between their recruiting rankings and their S&P+ rankings in recent history, and then impose the zero profit condition to determine which schools are better off dropping down to FCS.

First, the Overachievers:

This group includes teams mostly in the G5, as they are primed to do more with less, so I’ll divide this into two groups.

First, your G5 overachievers:

1. Appalachian State (Recruiting 103rd, S&P+ 53rd, +50 spots)
2. Utah State (112th, 63rd, +49)
3. Air Force (125th, 80th, +45)
4. Boise State (65th, 27th, +38)
5. Memphis (75th, 41st, +34)

Now, your P5 overachievers:

10. Wisconsin (35th recruiting, 9th S&P+, +26 spots)
18. Kansas State (61st, 43rd, +18)
24. Utah (41st, 26th, +15)
25. TCU (33rd, 19th, +14)
27. Oklahoma State (36th, 23rd, +13)
28. Iowa (46th, 34th, +12)

In the G5 list, we see some expected names - Appalachian State and Utah State both just lost their coaches to P5 jobs, as Scott Satterfield and Matt Wells demonstrated their high level of “productivity”, leading the way in turning talent into wins. Boise State, a member of the original BCS buster group, and Memphis are examples of the upstart, always competitive G5 schools. Air Force rounds out the top five; the service academies are known for their success despite a talent disadvantage.

The P5 list becomes more fun - this list is full of teams who don’t care about “your rankings”. We see Wisconsin, the land of cheese and huge linemen, who run as tight a recruiting ship as anyone - the Badgers commit to getting their guys and playing their style. Behind the Badgers, we have the two longest tenured coaches in college football and two coaches who have dug their heels in and made their programs home. Kansas State benefitted from Bill Snyder over the last five years, as he, Gary Patterson, and Kirk Ferentz make their hay recruiting two and three stars and getting them to play like four and five stars. Mike Gundy and Kyle Wittingham are two eerily similar coaches - isolated a bit geographically, in the shadow of their conference, and ready to take on whoever - who both have some of the “highest productivity” in the nation.

These ten teams - five G5, five P5, are at the high end of the distribution. They all feature coaches who think different, who recruit on the margins, who zig where others zag. At all ten programs, even despite coaching changes, development style and investment in facilities have yielded higher marginal productivity.

The Zero Profit Condition:

Before we get to the candidates for drop down, let’s look at the distribution of team productivities and try to determine where exactly is the cutoff for productivity.
First, the graph:

Hey, that’s pretty neat- normally distributed! Now, your instinct might be (and my first instinct was) to set the productivity threshold at zero. Boom, all those schools below are out, problem solved. But that posits a few problems for us, namely the fact that 61 teams sit below the 0 threshold (46.92% of the FBS), and the fact that plenty of profitable and successful programs sit down there. (Oh, hi Georgia, Notre Dame, Northwestern, Texas A&M, Iowa State, and Syracuse.) Clearly, the 0 condition is going to require some fine-turning - we don’t want to punish teams who recruit well and are in the same general place in the production rankings, if a few slots down. Since we don’t have an actual production function, we are going to have to look at distances from the mean to determine the most extreme results. Seven teams had differences more than 1.5 standard deviations below the mean, and 11 had differences more than 1.3 standard deviations below the mean. We’ll call those our drop down candidates, and examine their candidacy below.

And on a down note, your Underachievers:

These are the teams doing the least with the most, the programs with the lowest productivity in the distribution. These teams’ decisions to stay in the market result in a negative profit, and they’re only hurting themselves.

I’m just going to give the bottom 11 teams who should consider dropping down to FCS, given the cost of their inputs (recruiting ranking) and their productivity with those inputs (S&P+ ranking).

128. Kansas (70th recruiting, 119th S&P+, -49 spots)
127. Oregon State (56th, 97th, -41 spots)
126. Rutgers (60th, 100th, -40 spots)
125. Maryland (37th, 73rd, -36 spots)
124. SMU (77th, 110th, -33 spots)
123. San Jose State (85th, 113th, -27 spots)
122. Vanderbilt (50th, 76th, -26 spots)
121. Connecticut (96th, 122nd, -26 spots)
120. Kentucky (30th, 54th, -24 spots)
119. Texas (14th, 38th, -24 spots)
118. FIU (91st, 115th, -24 spots)
*Liberty and Coastal Carolina, the most recent teams to jump up, are excluded from this analysis, as we don’t have five year data on either.

There you have it, the 11 least productive teams of the last five years. According to the Melitz model, by remaining in the market, each of these teams are taking a negative profit, and the rational decision is to drop out of the FBS market and into FCS. Obviously, a few of these teams are not going anywhere (it is fun to laugh at Texas ranked 119, though), but a few names on this list make sense - UConn, with the worst defense in college football history, Kansas, with a thin roster and a basketball-first athletic department. Oregon State, with whatever is going on there. (My prescription for Oregon State is to drop down to FCS, or at least start running the triple.)

I also know what else you’re thinking, and yes, these were obvious and could’ve been done without numbers and models and all that shouting. Well, we all knew this, but now we know it with numbers so it’s proof. Sorry, SMU, you’re gone.