Consequences of Schedule Topologies

© Copyright 2009, Paul Kislanko

One of the most-repeated arguments in favor of a division 1A playoff is that the NCAA sponsors a playoff for every other division. The counter-argument is that in Division 1A the entire season is one 14 week-long playoff. We can see why it is right to have a playoff in all other divisions and why there's no need for one in D1A just by analyzing the schedule graphs.

Div Teams Games CI% Diam APL
3† 228 1092 14.44 10 4.33
2 150 742 19.11 8 3.87
FCS 124 590 24.80 6 3.18
FBS 120 675 46.30 4 2.48

  D3 doesn't include the 10 NESCAA teams who only play each other and do not participate in the playoff.
is the number of teams in the (sub)division (except as noted for D3)
is the number of games in which both teams are from the same (sub)division.
is the percentage of all team pairs in the (sub)division who either play each other or have at least one common opponent.
is the largest number of steps required to connect any team to every other team in the (sub)division with a "team plays B plays … plays Z plays otherteam" chain. This is the diameter of the games graph.
is the Average Path Length for the (sub)division. Smaller values indicate greater connectivity.

All of the (sub)divisions except the FBS need a playoff because their regular-season schedules don't provide enough information to determine the relative order of teams. The only way to "connect" all the teams is to have teams that have no common opponents meet in a single-elimination tournament.

FCS, D2 and D3 just don't have the money for airplane trips and hotel rooms, so their regular seasons end with less than a quarter of the team-pairs even having a common opponent. Their schedules result in weakly-connected "regions" within which it is possible to find the top teams, but to find the best teams over the entire division, they have to arrange for the top teams from different regions to play each other.

Even if money were no object, with more teams and fewer regular-season games than D1, to define a regular-season as meaningful as the FBS portion of D1's would require centralized schedule management and a redistribution of teams across conferences. In other words, it's basically impossible for the other divisions to have a schedule "like" the FBS schedule and without that there isn't enough data to have a "mythical" champion based upon polls or computer rankings (though Wolfe, Massey, and a few others do a credible job for all divisions) so they get to crown real champions.

The Other Side of the Coin

The FBS regular season provides enough data to compare teams based upon head to head and records vs common opponents that we can say the question really is "settled on the field." But it could (and should) be better. It shouldn't require the bowl games to have more than half the possible team-pairs have at least a common opponent. With 12 games/team and only 120 teams we'd probably have a CI greater than 50% without trying if it weren't for a few trends that work against that.

The first is my most common rant, and I don't care if you're tired of reading it, I'll repeat it until the problem goes away. Games against FCS teams eliminate FBS-vs-FBS scheduling opportunities, and once those were allowed to count towards bowl-eligibility every year the number of them became and stayed a bit too large. These games are necessary (the change from counting one every four years to every year was done to provide needed revenue opportunities for the FCS teams) but it would've been better to have gone to a "count it once every two years" instead of every year.

The second was the Pac 10's decision to use the permanent 12th game to add a 9th conference game. Commentators everywhere lauded the Pac 10 and called for other conferences to adopt a round-robin conference schedule. But adding a conference game does nothing to improve the regular-season schedule (just moves one team from the Opponents' Opponents bucket to the Opponents bucket), and by taking 10 potential non-conference matchups out of the games graph they made it worse. When we had the first two seasons of 12-game schedules in 2002 we had things like a home and home between USC and Auburn (a rare regular season matchup of the Pac 10 and SEC) but when the 12-game season was made permanent they added the extra conference game instead.

Conf #Playoff
CAAF 5 12
BSky 2 9
SoCon 2 8
MVC 2 8
MEAC 1 10
OVC 1 10
SLC 1 8
Pat 1 7
GWest 1 5
SWAC 0 10
Pio 0 9
Ivy 0 8
NE 0 8
Ind 0 6
BigS 0 5
Now, if every conference did what the pundits suggest, we'd have the ACC, Big 12, CUSA, MAC and SEC playing 11 conference games and 1 game vs an FCS team, and the FBS field would be completely disconnected and we'd need a playoff. But don't get excited. Those other divisions that all have playoffs? They don't have a guaranteed berth for conference champions. So if we devolved to the D2 or D3 format there'd be no guarantee that Sun Belt, MAC, CUSA, or MWC teams would get to participate.

Conf #Teams BCS
Top 16
B12 12 4 3 7
SEC 12 3 2 8
MW 9 3 2 5
B10 11 2 2 7
ACC 12 1 1 10
BigE 8 1 1 6
WAC 9 1 1 5
P10 10 1 1 5
CUSA 12 0 1 6
MAC 13 0 1 5
SBC 8 0 1 2
ND 1 0 0 1
Ind 3 0 0 1
So, if FBS were to become enough more like the other divisions to need a playoff (which per force would mean devaluing the regular season) what shape would it take? Probably the same as the FCS - the top 16 teams seeded by some process into a 4-week playoff.

The chart to the left shows just how different the post-season would be if there had been a 16-team playoff in 2008. It also shows that every conference - especially the non-AQ conferences - would be less-well represented in a 16-team playoff than in the 68-team bowl season.

The selection criteria might well not be the BCS rankings, but most proposals assume all conference champions would automatically qualify, so last year there would've been at least three teams outside of the top 16 by any standard.

Might there better alternatives? It's easy to see that even if we had a playoff, there'd still be about the same number of disgruntled fans.

Grade < All      AQ ¬AQ
A+ μ+2σ +∞ 1     1 0
A μ+1.5σ μ+2σ 6     5 1
B μ+σ μ+1.5σ 15     12 3
C+ μ+0.5σ μ+σ 19     18 1
C μ-0.5σ μ+0.5σ 39     22 17
C- μ-σ μ-0.5σ 18     5 13
D μ-1.5σ μ-σ 14     2 12
E μ-2σ μ-1.5σ 7     1 6
F -∞ μ-2σ 1     0 1
As I noted at the beginning, for the FBS there is enough data for advanced systems to rate teams (and rank them based upon their rating values.) The methods used in advanced rating systems result in a typical normal ("Bell") curve, so we can divide the field by assigning "grades" based upon how much better or worse than average each team is according to that rating.

The results for one such rating after conference championship weekend are shown at the right. Note that if we had had:

So, no matter how many teams are included in a putative playoff, there will be as many (more, actually) teams fans' with a defensible (if not necessarily legitimate) claim that their team was "unfairly" excluded. And this is the "best case" scenario where "the best x" teams are selected and seeded. Including conference champions automatically could only make the numbers worse.