THE POWER RANK

The injustice of schedule in college football – how analytics can determine conference win probabilities

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Brass Scales Of Justice Off Balance, Symbolizing Injustice, Over WhiteCollege football has a short season. Eight or nine games determine whether your teams wins its division or conference.

This conference schedule used to include all other teams in the conference, a round robin format. Then SEC commissioner Roy Kramer added Arkansas and South Carolina so his 12 team conference could hold a championship game. The Big Ten added Penn State to grow to 11 teams.

When conferences get bigger and separate into divisions, your team can no longer play every other team in the conference. While each team plays a round robin in its division, the cross division schedule can vary greatly.

For example, consider the Big Ten Legends division. Michigan plays Ohio State, a national title contender for most people, Penn State and Indiana from the other division. Michigan State plays Indiana, Purdue and Illinois, arguably the worst 3 teams in the conference.

The schedule imbalance is worse for LSU in the SEC West, as they face Georgia and Florida, two national championship contenders, from the other division. Alabama faces Tennessee and Kentucky instead.

This imbalance in schedule greatly affects your team’s chance to win its division.

Let’s put some numbers behind this injustice.

How to determine win probabilities for a conference

The game of football is inherently random. A fumble or a tipped pass can flip the results of a game in a single play. It can even derail Nick Saban’s Alabama dynasty for a few weeks, as AJ McCarron thew a goal line interception to seal their loss to Texas A&M last season.

To account for this randomness, I use the Monte Carlo method to simulate the 2013 college football season. This method employs random numbers to sample the many outcomes that can happen during the season.

Monte Carlo is the same technique Ed Thorpe used to test how his black jack strategy would perform in a casino. He did pretty well in those casinos, inspiring a generation of kids like Jeff Ma to win millions in Las Vegas.

How does this work for college football? Suppose Michigan has a 53% chance to beat Nebraska at home this season, as my preseason rankings predict. In a simulation, Michigan wins this game with 53% probability. Just like an actual football game, the simulation takes the uncertainty heading into the game and turns into the certainty of a win or loss. The simulation repeats this random picking of game winners for each game.

Flipping coins is the easy part of simulating the college football season. The computer then calculates the win loss record from the game results to determine the winner of the division. In the case of a tie, this gets complicated. The computer looks at head to head records and division records to determine a champion.

This simulation is repeated many times, and the win probability for a team is the fraction of simulations that it wins its division or conference.

The win probabilities for each game come from my preseason rankings. These are based on a regression model that considers a team’s rating in The Power Rank, turnovers and returning starters.

SEC West

This is the toughest division in college football. In my preseason rankings, three of the top 5 teams in the nation come from the SEC West. LSU brings up the rear behind Alabama and Texas A&M at 5th in the nation.

The schedule will make life even more difficult for the Tigers this season. Here are the cross division games for the top 3 teams; the first team is a rivalry game played every year.

  • Alabama – Tennessee, at Kentucky
  • Texas A&M – at Missouri, Vanderbilt
  • LSU – Florida, at Georgia

LSU faces Florida and Georgia, two teams that could contend not just for the SEC East title but also the national championship. Instead, Alabama faces two struggling programs in Tennessee and Kentucky with first year head coaches. This discrepancy surfaces in the win probabilities for the SEC West.

The Power Rank's preseason prediction for SEC WestAlabama has a 62% chance of winning the SEC West, while LSU has only a 9% chance. LSU coach Les Miles has complained about the schedule before, even suggesting that a “random computer draw” pick the cross division games. You know something is wrong when a football coach suggests using computers.

Big Ten Legends Division

Each Big Ten team also plays a fixed cross division game each year. For the three teams expected to contend for the Legends division, this game is first in these lists of cross division games in 2013.

  • Nebraska – at Penn State, Illinois, at Purdue
  • Michigan – Ohio State, at Penn State, Indiana
  • Michigan State – Indiana, Purdue, at Illinois

Michigan plays Ohio State, a potential national title contender, while Nebraska and Michigan State duck the Buckeyes this year. Michigan and Nebraska both play at Penn State, a program still in good shape despite the devastating sanctions from the Jerry Sandusky scandal. Instead, Michigan State gets arguably the 3 worst teams in the conference.

The Power Rank's preseason prediction for the Big Ten Legends Division.This division is an interesting case study for schedule imbalance since my preseason rankings rate these 3 teams so closely. Only a point and a half separate Nebraska from Michigan State, with Michigan in between.

In my simulations, Michigan State has a 34% chance to win the division. Michigan has a 19% chance despite a higher rating than the Michigan State. Nebraska, which has a home game against Michigan State, has 38% chance. The schedule does no favors for Michigan.

These odds are calculated from my preseason rankings, which rank Ohio State 16th in the nation. This is contrary to the national consensus that the Buckeyes will contend for the national title. If the Buckeyes are actually one of the top 3 teams in the country, the gap in win probability between Michigan and Michigan State will get larger.

Pac-12 North

Out west, teams play a nine game conference schedule. This includes the 5 teams from within the division and 4 of 6 teams from the other division. The California schools (Stanford, California in the North, USC and UCLA in the South) play each other each season.

These schools insisted on keeping these rivalries intact when the conference grew from 10 to 12 teams. And no one will argue against playing a historic rival every year, especially with the ticket sales these games generate. However, these games will have an impact on the Pac-12 North division.

Here are the cross division games for Oregon and Stanford, two highly ranked teams expected to contend for the division.

  • Oregon – at Colorado, UCLA, Utah, at Arizona
  • Stanford – Arizona State, at Utah, UCLA, at USC

In essence, Oregon plays at Colorado, the worst team in the South, while Stanford plays at USC, the best team in the South. As a result, Oregon has a 73% chance to win the division, while Stanford has a 19% chance.

The Power Rank's preseason projection for the Pac-12 NorthA big part of this discrepancy is that the preseason rankings have Oregon rated a touchdown better than Stanford. Whether this holds up depends on how well new Oregon coach Mark Helfrich does after Chip Kelly left for the Philadelphia Eagles. However, schedule also plays a role in these odds.

How to fix the imbalance in schedule

With today’s mega conferences in college football, your team no longer plays every other team in the conference. This can lead to an imbalance of schedule across teams in a division, as you can see in SEC West, Big Ten Legends and Pac-12 North this 2013 season. This imbalance will affect your team’s odds of winning the division.

In my next blog post, I’ll suggest how to fix this problem. There’s no perfect solution, except for going back to 1991 and convincing Roy Kramer not to add to additional teams to the SEC. But fans deserve better.

Do you have any suggestions for how to fix the imbalance in conference schedule? Let me know in the comments.

How did Amy Nelson’s bracket do in the SB Nation pool?

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When the field for the NCAA tournament was announced this year, The Power Rank unveiled its interactive bracket. The bracket exemplifies our mission in sports analytics. At its core, the bracket shows the 416 win probabilities for each team in each game. Will your team win? This is our answer. Moreover, the bracket displayed the tournament structure in an elegant, symmetric tree structure that could only come from the mind of graphic designer, Angi Chau, that doesn’t follow sports. Hover over the nodes to get win probabilities for a game. Hover over team names to get the probabilities for advancing to each round.

Fortunately, sports fans also seem to like advanced analytics and data visualization. The bracket spread rapidly through social media, and I soon got a call from Amy Nelson at SB Nation. She just launched Full Nelson, a series of weekly sports documentaries, and wanted to do one on our March Madness analytics. Of course, we were thrilled. She asked me to fill out a bracket for her pool based on our numbers.

How Amy’s bracket was picked. Winning a NCAA tournament pool goes far beyond the probabilities in our interactive bracket. Consider a bracket in which the higher ranked team in The Power Rank won each game. This year, our numbers had Kentucky as the highest ranked team. A bracket with Kentucky as champion would fare well in the pool but not win. People like Grandma Feng, who doesn’t know that a basketball is round, also picked Kentucky to win but also had Ohio and North Carolina State making the Sweet Sixteen. She wins the pool based on shear luck. The larger the number of entrants in a pool, the more likely someone makes some startling picks that win the pool.

In a big pool, one needs to look for undervalued teams. The Power Rank gave Ohio State almost a 12% chance to win the tourney, the second highest likelihood after Kentucky. If you pick Ohio State and they actually win, your bracket picks up 63 points (1 for the first round, 2 for the second round, all the way up to 32 for winning the championship game). More importantly, it’s unlikely that many other people picked Ohio State as the champion. On Yahoo, only 4.5% of brackets did this. In a pool with 100 entrants, 4 people will pick Ohio State on average. Your bracket only has to do better that 4 other people in the early rounds.

For more details about picking an optimal bracket, see this excellent article by Galen Hall. I used these concepts to pick Ohio State for Amy, a scene that shows up in the documentary (see below). However, picking the bracket in general was a frustrating experience. Ideally, one should put some math behind these concepts and optimally pick a bracket based on pool size. For example, an optimal bracket probably would not have Michigan State in the Elite Eight, simply because of the four other top 20 teams (Memphis, Saint Louis, New Mexico and Louisville) in that part of the bracket. But this additional analytics will have to wait until next year.

The roller coaster ride of following a bracket. Amy’s bracket did pretty poorly after the first weekend. For example, it had Kentucky, Wichita State, UNLV and Duke in the Sweet Sixteen from the South region. Only one team, Kentucky, made it that far. When we shot the final scenes for the documentary, we knew the bracket was suffering. I even mention that we didn’t pick the bracket to win the first weekend. A week later, the bracket surged, sporting 3 (Kentucky, Ohio State and Kansas) Final Four teams. Amy would pick up another 64 points, the total points available in the first two rounds, if Ohio State beat Kentucky in the national championship game. With the only bracket with Ohio State as champion, she would easily win the SB Nation pool. However, this scenario had only a 18% chance based on our numbers. Even after picking 3 Final Four teams, the odds of winning a competitive bracket are still rather small.

In the semifinal game in New Orleans, Ohio State faced off against Kansas. While the Jayhawks were down most of the game, their defense took Ohio State out of their half court offense. Kansas coach Bill Self might be the next Coach K, a leader that can motivate his players to a higher intensity level. A late game surge, capped with an off balanced layup that 6′ Elijah Johnson somehow got over 6’8″ Jared Sullinger with a minute to go, sealed the victory for Kansas. Amy wasn’t winning the pool with this bracket. She finished 10th out of 23 people. However, picking Ohio State was still the best strategy for this pool with 23 participants. Had she picked Kentucky over Ohio State in the championship game, she would have finished 4th at best. The top seven brackets all had Kentucky as the winner, and the winning bracket had Ohio and North Carolina State in the Sweet Sixteen. Go Grandma.

Why March Madness is like counting cards. But does that mean The Power Rank is worthless? No. Using our win probabilities, or maybe even those of Ken Pomeroy or Nate Silver, gives you an edge against the competition. It’s like counting cards in black jack. In the long run, people like Jeff Ma made a lot of money in Vegas based on a small edge against the dealer. Does that mean he won every hand? No. Did he win every time he doubled down on 11 against a 6 up card from the dealer? As he details in his book The House Advantage, no. You’re not going to win every March Madness pool using The Power Rank. And for those that believe in the power of numbers in the long run, the NCAA tournament is particularly frustrating since the opportunity arises once a year. But do you want to be Jeff Ma and have a movie made about you? Or do you want to be the person who keeps hitting on 17 expecting that 4?

Check out the Full Nelson episode on The Power Rank.

For more content, follow The Power Rank on Twitter.

Related Posts:

—About The Power Rank.
—Interactive bracket for NCAA Tournament.
—College basketball rankings.

The Power Rank featured on Full Nelson, SBNation’s YouTube Channel

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At last year’s Sloan Sports Analytics conference, I met Jeff Ma, the inspiration behind Bringing Down the House and 21, the movie. More than any other person at the conference, Jeff was interested in my academic approach towards ranking teams and projecting future outcomes. So when Angi Chau and I posted this interactive bracket for the NCAA tournament last week, I emailed Jeff about it. He was kind enough to post it Twitter, which brought it to Amy Nelson’s attention. Amy works at SBNation and just launched a YouTube channel. We got in touch by phone last Wednesday, and in less than 24 hours after that, she was in San Francisco to do a short documentary on The Power Rank and our web of win probabilities. This episode of Full Nelson is the result.

For more content, follow The Power Rank on Twitter.

Related Posts:

—About The Power Rank.
—Interactive bracket for NCAA Tournament.
—College basketball rankings.