Thursday, February 7, 2013

Optimizing Conference Scheduling for Tournament Selection: Part I, College Football

This is Part 1 of a two-part post about conference scheduling in college sports. I submitted a version of this for inclusion in this year's Evolution of Sport competition at the Sloan Sports Analytics Conference in March. Since they didn't accept it, I decided to post it here. Part 2 is due Monday.

In 2008, the Boise State Broncos of the Western Athletic Conference were ranked 9th in the final BCS standings. That same year, the TCU Horned Frogs of the Mountain West Conference were ranked 11th. Now, in part because neither school was in one of the power conferences like the SEC, both teams were passed over for the most prestigious bowls, and met in the Poinsettia Bowl. Both teams earned a payout of $750,000.

The next season, Boise State finished 6th in the BCS standings, and TCU finished 4th. This time, they met in the Fiesta Bowl, one of the four games in the Bowl Championship Series, and earned a payout of $18 million each. Same teams, very similar regular seasons, 24 times more money. 24 times! That's the difference between a filet mignon with crab meat on top at Smith and Wollensky, and two cheeseburgers – no fries – at McDonald's.

And that's just the monetary benefits. That doesn't even count the national exposure for recruiting, or the increase in freshman applications that typically follows athletic program success.

So, naturally, if you work for a school like Boise State or a conference like the Mountain West, you want to know, "What can I do to improve my chances to get into the biggest bowl games and get that BCS money?" My talk will describe how conferences can improve their members' chances by stacking their conference strength of schedule.

Before we can get to that, we need to take a look at how the BCS works. The BCS consists of five bowl games – a national championship pitting the top two teams in the country, the Sugar Bowl, the Fiesta Bowl, the Orange Bowl, and the Rose Bowl. Thanks to the TV rights deals the BCS signed with ESPN, each team in a BCS bowl will earn an estimated $18 million this season, split up between itself and the other teams in its conference.

So that means the 120 plus teams in the Football Bowl Subdivision are competing for 1 of 10 total spots. Of those 10 spots, 6 are promised to the champions of the six major conferences. And Notre Dame also has an agreement where, if they finish in the top 8, they're also guaranteed a spot. If a team from one of the other five conferences finishes in the top 12, they're guaranteed a spot, and the remaining spots are filled by teams chosen by the bowls themselves (they tend to take established programs from the bigger conferences, to maximize revenue).

Now, as you've probably heard, this is all changing in the next few years as the NCAA moves to a sort of playoff system, but for now, let's not worry about that, and just focus on the BCS.

In order to objectively determine which teams qualify, the BCS relies on a combination of two human and six computer polls. The people behind the computer polls don't release the exact formulas they use to rank teams, but we know that all of them rely heavily on strength of schedule. So, to improve their place in the BCS standings, teams should win games against the best possible teams. It's not exactly rocket science, but it's also not as easy as it sounds to implement in practice. Each team typically gets 3 or 4 games against non-conference opponents, but these games are usually scheduled years in advance, so you have to get a little lucky: the game you scheduled against (say) Boston College after they went 11-3 in 2007 doesn't look so hot this year after they went 2-10.

The other 9 or so games on your schedule are games against conference opponents. Now those games aren't announced until a few months before the season, but the teams you play are set in stone, and there's not much you can do about those ... or is there? Take a look at this scatter plot comparing a team's rank this season to that team's rank the previous season, according to the Sagarin ratings used in the BCS. There's a pretty strong linear relationship there, with a correlation coefficient of 0.7. That means that, in general, a team's performance last season is a decent indicator of how they're likely to perform this season.

This fits with our intuition, and we can see that it holds with other ranking systems as well. This is the same plot, only this time using the rankings from Sports Reference's Simple Ratings Systems. And again, the correlation coefficient is a little better than 0.7: a pretty strong linear relationship.

Okay, so what? Well, we know that we can estimate teams' performance for this season based on how they did last year. And the BCS money represents a huge incentive for schools and conferences. So I propose that conferences stack their divisions, putting all the stronger teams in one division and the weaker teams in the other. Those of you familiar with European soccer will notice that this looks a lot like the relegation and promotion system: it's supposed to.

The benefits of this system are clear. Since the top teams play each other more often, that means the entire top of your conference will play tougher schedules. During the season, that means more attractive matchups for TV networks to choose from, but it also means better rankings in the computer polls and better public perception to help boost the human polls. Better poll standings, of course, means you give your best teams the best possible chance to play in a BCS bowl. And that means increased bowl revenue and national exposure for your top schools and for the conference as a whole.

Let me give you an example. Conference USA is basically divided into east and west divisions along the Mississippi, and each team plays eight conference games: one against each of the other five teams in its division and three against teams from the other division. This table tells you each team's rank in 2011 according to the Simple Rating System, and the average rating of their 2012 conference opponents by the same system. Larger positive numbers represent better teams and stronger schedules, and larger negative numbers represent worse teams and weaker schedules.

So we can see from this table that the team with the toughest schedule based on last year's results is UTEP, who was eighth in the conference last year by this metric. In fact, the easiest schedules in the conference went to the two best teams: Houston and Southern Miss. It turns out that there's a slight negative correlation: the better you did last year, the easier your schedule will be this year.

But it doesn't have to be like that. Here's that same table under my proposed system for a sample schedule. The first division is made up of the top six teams, and the second division is made up of the bottom six. And now Houston gets to play the top eight teams, while Tulane gets to play the bottom eight, and now there's a very strong correlation between last year's performance and this year's strength of schedule.

But ultimately, it didn't matter for Conference USA this year, because they didn't have anyone in serious contention for a BCS bowl. Let's use a different example from a time when it would have mattered. In 2003 Miami (Ohio) finished the year 11th in the BCS standings, and wasn't selected to play in a BCS bowl. Had they been selected, they would have earned $14 million. Instead, they went to the GMAC Bowl and earned $750,000. Again, huge difference.

You can see from this table that Miami's schedule was somewhere in the middle of the conference that year, in line with their fifth-place ranking from 2002. But they played four games – a third of their schedule – against teams that finished in the bottom 25 by the Simple Rating System.

Now, here's the 2003 MAC using this promotion/relegation system. The correlation between past performance and strength of schedule isn't as strong as it was for Conference USA, especially in the second division, but there's still a strong correlation, especially for the teams near the top. More importantly, we can see Miami in the middle of the first division. Now they only play two games against the bottom 25, and their conference opponents' average rating improves from -7.4 to just over -3.8. Would this extra scheduling boost have been enough to push Ben Roethlisberger and the RedHawks into a BCS bowl?

Part 2 is out now, and can be found here.

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