## The SEC West and Maximum Likelihood

The upper crust of college football

Eight years ago, Doug Drinen wrote about the Maximum Likelihood rating system, a computer model which one could use to rank college football teams. The short, non-mathy version is this: the probability of Alabama beating Team X is equal to the rating of Alabama divided by the sum of Alabama’s rating plus the rating of Team X. You can use that formula for every game in each season, which would leave you with an enormous series of equations. From there, you would give each team a rating, and keep tinkering with the ratings until the ratings you have for each team provides the system with the maximum possible likelihood of the actual results.

To do this, you would want to give Alabama a high rating, because that would increase the likelihood of the system as a whole reflecting what’s happened on the field. In fact, you might why would we ever limit Alabama’s rating: after all, if we keep jacking up the Tide’s rating, what’s the harm? In this case, there is only one reason not to give Bama an insanely high rating: a loss in Oxford to Ole Miss on October 4th.

Speaking of the Rebels, what should their rating be? A really high one, although it needs to be capped by Mississippi’s losses to both Auburn and LSU. What about Auburn and LSU? Well, both sets of Tigers lost to Mississippi State, Auburn lost to Texas A&M, and LSU lost to both Alabama and Auburn.

You might think “okay, this seems reasonable: all these losses will help control the ratings.” But there’s a problem about to emerge. Sure, LSU and Auburn lost to MSU, but the Bulldogs are undefeated, so there’s no reason not to give Mississippi State a rating of a zillion. And we already know that Alabama is going to get a high rating, so LSU’s loss to the Tide won’t hurt much. LSU lost to Auburn, but isn’t Auburn’s rating really high? The Tigers don’t get dinged for losing to MSU, while the Texas A&M loss doesn’t hurt because A&M’s only losses are to Alabama, Mississippi, and MSU.

As it turns out, the top six teams in the SEC West form what’s known as a closed system: the group is 35-0 when not playing each other. 1 As a result, that is going to cause significant problems with certain computer ratings that are based solely on wins and losses (to the extent people even care about such ratings). Make MSU’s rating a zillion, Alabama’s rating a little less than that, Auburn and Ole Miss just a bit under that, and then LSU and A&M are well, just one level down. But there’s nothing to drag this group of six teams down compared to the rest of college football if you are only looking at wins and losses.

• You might think this isn’t that big of a deal, or that going 35-0 isn’t that impressive. The group beat Kansas State, Wisconsin, and West Virginia out of conference, has four wins against Arkansas, and four more against Florida and Tennessee combined. That’s pretty impressive, but what’s even more interesting about it is that you can’t do this with any other set of teams.
• We can’t include the entire SEC West, because Arkansas lost to Georgia, and Georgia lost to South Carolina and Florida, and both of those teams lost to Missouri, which lost to Indiana, opening up the system to the rest of college football.2 The SEC West is 39-1 in non-division games, but you need to remove Arkansas to keep it a closed system.
• What about the top teams in the Pac-12? That’s not a closed system, either. Oregon is 9-1, but the Ducks lost to Arizona, who lost to Southern Cal, who lost to Boston College. So we can’t keep raising the Ducks’ rating, because there’s an upper bound (we don’t want to keep increasing BC’s rating).3 Arizona State is 8-1 with a loss to UCLA; the Bruins have lost to Oregon and Utah, though, and both of those schools have indirect nonconference losses (Utah lost to Washington State).
• FSU, of course, is undefeated. Until last week, Notre Dame would have formed a closed system with the Seminoles, but the loss to Arizona State changes that.
• What about the Big 10? Michigan State lost to Oregon, ending that, while 8-1 Nebraska lost to Michigan State; as a result, neither of those teams can form closed systems. Ohio State lost to Virginia Tech, and the Hokies have five losses this year.
• The top of Big 12 nearly forms a closed system, and is the closest to matching the SEC for upper-level competition. TCU and Baylor are knocking on the playoffs’ doorstep, and are a combined 16-2. TCU lost to Baylor, which means the schools are 16-1 in all other competition. But Baylor’s loss came to West Virginia. The Mountaineers have four losses, and two of them are really interesting (a third was to TCU). West Virginia lost to TCU (still closed) and Oklahoma, which lost to Kansas State, which lost to Auburn. In theory, that could have created a large closed system across conferences, as Kansas State’s only losses were to the Tigers and TCU. In addition, Oklahoma’s only losses were to Kansas State, Baylor and TCU.  Similarly, West Virginia lost to Alabama, which also keeps the system closed. But it is West Virginia loss to Texas (33-16 in Austin) last weekend, that opens the system.  The Longhorns have five losses, including to BYU and UCLA.
• Had West Virginia beaten Texas, this would have created a fascinating scenario: the six SEC West teams and Baylor, TCU, Kansas State, Oklahoma, and West Virginia would have gone an incredible 61-0 against the rest of college football. It would have still been easy, if one was so inclined, to tout SEC superiority4 due to Auburn’s win over KSU and Alabama’s win over West Virginia, but that group of 11 teams would have formed a massive and exotic closed system. Instead, as is often the case, Texas ruined everything.
• Among less-heralded 1-loss schools… Duke lost to Miami, and the Hurricanes have losses to Louisville, Georgia Tech, and Nebraska. Colorado State lost to Boise State, and the Broncos lost to Ole Miss (so far, so good) and Air Force. Of course, Marshall is also undefeated, but the third easiest schedule in college football has a lot to do with that.

So let’s say you hate the SEC.  What should be your rooting interest today?

• Rooting interest #1: tonight, root for Missouri to beat Texas A&M. The Tigers lost to Indiana, so an A&M loss to the Tigers would break the system and make things look worse for the SEC West. Rooting for Missouri at all times is the number one rule of SEC hatred in 2014.
• Rooting interest #2: tonight, root for Arkansas to beat LSU.    A Hogs win tonight also breaks the system, albeit slightly less directly. Remember, LSU beat Ole Miss which beat Alabama, so an Arkansas win opens up the whole SEC West (save Mississippi State, pending the result against ‘Bama today) to the Arkansas loss to Georgia.
• Rooting interest #3: tonight, root for Georgia to beat Auburn, maybe.  This also opens up the system, which is good, and Auburn is the team most likely to crash the playoffs with 2 losses. As a result, an SEC hater would want Auburn to get its third loss tonight.
• Why maybe? Because there is also a reason to root for Auburn, particularly if Missouri loses to A&M. That’s because if Auburn beats Georgia, that greatly increases Mizzou’s chances of winning the East, which would not be a good look for the SEC as a whole. And while Auburn could sneak into the playoffs with 2 losses, so could UGA if it wins the SEC Championship Game (and the disaster scenario for SEC haters: an Alabama win over MSU tonight, followed by MSU winning the Egg Bowl and Alabama falling to Georgia in the SECCG: at that point, both UGA and Mississippi State would probably make the playoffs).  Rooting for Missouri to make the SEC Championship Game is pretty important for SEC haters, so much so that you may actually want to root for Auburn tonight.
• Finally, you want to root for MSU over Alabama.  The SRS is not a huge fan of MSU, so there’s a decent chance that if MSU wins, not only does only one SEC team make the playoff, but that the national championship game could also be SEC-free.
1. There are seven remaining chances for that to change during the regular season, including three tonight: Auburn travels to Georgia today, Texas A&M hosts Missouri tonight, and LSU goes to Arkansas. In addition, Ole Miss has Arkansas, MSU plays Vanderbilt, Alabama plays um, Western Carolina, and uh, Auburn plays Samford. []
2. The SEC has just three nonconference losses: Tennessee to Oklahoma, Missouri to Indiana, and Vanderbilt to Temple. The Commodores are winless in SEC play, which would make the rest of the conference a closed system if not for the other two losses. []
3. The Pac-12 has five nonconference losses: Stanford to Notre Dame, Southern Cal to Boston College, Washington State to Nevada and Rutgers, and Colorado to Colorado State. []
4. Default rule: Folks will tout SEC superiority under any circumstances. []
• Bryan

Yes, the SEC has only 3 non-conference losses…but look who they’ve played.
8 games vs. USA and SUN teams
5 games vs. MID-AMERICAN teams
No other conference has that many games versus those conferences.
63% of their games are against “weaker” conference teams. Higher than any other conference.
They are 5-2 against “the big 5” … the Pac-12 is 6-2.
Just a couple things to consider while people debate the SEC’s “superiority”