Tips for picking a winning bracket from Badger Bracketology

These tips for winning your March Madness bracket pool is reblogged from Punk Rock Operations Research.

1 Ignore RPI, use math based rankings instead to take strength of schedule into account.

Ken Massey has a rankings clearinghouse here: I’m happy to say that I’m the only women contributor to this list :) My rankings are posted there and can be found here.

2 Pay attention to the seeds

The seeds matter because they determine a team’s path to the Final Four. Some seeds generate more upsets than others, such as 7-10 seeds and 5-12 seeds. Historically, 6-11 seeds go the longest before facing a 1 or 2 seed. Teams with an 8 seed face a tough Round-of-64 opponent and have to face a 1 seed next (sorry Badgers).

However, there are plenty of upsets. The Final Four has been composed of all 1 seeds only once. See BracketOdds at Illinois for more information on how the seeds have fared.

Having said that, the committee doesn’t always get it right. There are Some teams like SMU, Wichita State, and Xavier are underseeded and are poised to upset. Also, Villanova is the overall #1 seed and has a 15% chance of winning the entire tournament, which is low, meaning that there isn’t a strong favorite this year.

3 Don’t pick Kansas to win it all

Be strategic. The point is NOT to maximize your points, it’s to get more points than your opponents. I’ve been getting in the habit of picking my Final Four first and filling in the rest later.  You can pick the eventual winner (say, Villanova) and still lose your pool if everyone else picks Villanova. FiveThirtyEight estimates that Villanova has a 15% chance of winning the tournament, meaning that another team is probably going to win.

One way to be strategic is to pick an undervalued top team to win the tournament. For example, last year Kansas was selected as the overall winner in 27% of brackets on ESPN and in 62% of Final Fours) despite having an overall 19% chance of winning (538). On the other hand, UNC was selected as the overall winner in 8% of brackets (with a 15% win probability). Getting UNC right last year helped vault past those who picked Kansas.

4 It’s random

The way brackets are scored means that randomness rules. It’s easy to forget that a good process does not guarantee the best outcome in any give year. A good process yields better outcomes on average but your mileage may vary any given year (at least that what I tell myself when I don’t win my pool!)

Small pools are better if you have a good process. The more people in a pool, the higher chance that someone will accidentally make a good bracket with a bad process. It’s like stormtroopers shooting at a target. They’re terrible, but if they take enough shots they’ll hit the target once. 

For more reading:

hear a talk about Badger Bracketology on 3/1 @ 12:05 at UW-Madison

I will be giving a talk tomorrow on bracketology.

Chaos and Complex Systems Seminar:
Tuesday, March 1
12:05-1:00 p.m.
4274 Chamberlin Hall,

How to rank sports teams and forecast game outcomes using math models.

Laura Albert McLay, Industrial and Systems Engineering

Selecting the teams for the College Football Playoff for NCAA men’s football is a controversial process performed by the selection committee. We present a method for forecasting the four team playoff weeks before the selection committee makes this decision. Our method uses a modified logistic regression/Markov chain model for rating the teams, predicting the outcomes of the unplayed games, and simulating the unplayed games in the remainder of the season to forecast the teams that will be selected for the four team playoff. We will discuss how the method can be applied to rank NCAA basketball teams and fill out a bracket in the tournament.

Refreshments will be served.


hear a talk about Badger Bracketology on 12/9 @ 12:30 at UW-Madison

I will be talking about Badger Bracketology this week.

Time: Wednesday, December 9th, 12:30pm.

Location: Wisconsin Institute for Discovery, room 3280.

Speaker: Laura Albert McLay, Associate Professor, Department of Industrial and Systems Engineering, UW-Madison.

Title: A Modified Logistic Regression Markov Chain Model for Forecasting the College Football Playoff.

Abstract: Selecting the teams for the College Football Playoff for NCAA Division IA men’s football is a controversial process performed by the selection committee. We present a method for forecasting the four team playoff weeks before the selection committee makes this decision. Our method uses a modified logistic regression/Markov chain model for rating the teams, predicting the outcomes of the unplayed games, and simulating the unplayed games in the remainder of the season to forecast the teams that will be selected for the four team playoff. 

Things I will discuss:

  • Did the College Football Playoff committee get it right?
  • Can math get it right?
  • Was Iowa really overrated?

I’ll answer these questions and more. And yes, there will be lots of badger pictures!


final NCAA football rankings

Here are the final Badger Bracketology rankings. We think the committee got it right.

mLRMC rankings:

  1. Alabama
  2. Clemson
  3. Michigan State
  4. Oklahoma
  5. Ohio State
  6. Stanford
  7. Houston
  8. Iowa
  9. Notre Dame
  10. Florida State
  11. North Carolina
  12. Western Kentucky
  13. Mississippi
  14. Texas Christian
  15. Michigan
  16. Oklahoma State
  17. Oregon
  18. Florida
  19. Bowling Green
  20. Temple
  21. Navy
  22. Northwestern
  23. Utah
  24. Baylor
  25. Memphis

ln(mLRMC) rankings:

  1. Alabama
  2. Clemson
  3. Michigan State
  4. Oklahoma
  5. Stanford
  6. Ohio State
  7. Iowa
  8. Houston
  9. Notre Dame
  10. Michigan
  11. North Carolina
  12. Mississippi
  13. Florida
  14. Florida State
  15. Northwestern
  16. Texas Christian
  17. Oregon
  18. Western Kentucky
  19. Oklahoma State
  20. Louisiana State
  21. Temple
  22. Bowling Green
  23. Memphis
  24. Utah
  25. Baylor


Rankings vs. forecasts

The Playoff Selection Committee’s rankings yield the ranking right now, which only gives insights into who would be in a playoff if it were held today. Our method simulates the rest of the season to forecast who might be in the playoff at the end of the season by taking the remaining schedule (and strength of schedule) into account.

Here are the mLRMC rankings and forecasts

Rankings right now Forecasted rankings at the end of the season
1. Clemson 1. Clemson
2. Alabama 2. Alabama
3. Oklahoma 3. Oklahoma
4. Notre Dame 4. Michigan State
5. Michigan State 5. Iowa
6. Ohio State 6. Notre Dame
7. Iowa 7. Stanford
8. Florida 8. Florida
9. Michigan 9. Ohio State
10. Stanford (no other teams have >1% chance of making the playoff)

First, I would note that the rankings right now are close to the forecasted rankings. This makes sense because the season is almost over. Two teams–Notre Dame and Ohio State–have a lower forecast than their current rankings suggest because they have a tough path to the playoff. Notre Dame has to play Stanford and Ohio State can only make the B1G championship game if Michigan State loses (and then OSU will likely have to win the playoff).

Other teams have a better forecast than their current rankings suggest because they have an easier path to the playoff. Iowa has to play Nebraska and then just has to win the B1G championship game. They will be underdogs, but they still will have a chance. Likewise, Stanford has a tough final game against Notre Dame but will then play in the PAC 12 championship game, where another win will boost their chances.

The differences between the current and final rankings is accentuated earlier in the season when there are more future games to play. I like the focus on the future because this is something industrial engineers do. We don’t just study the past using statistical methods, we build models to guide decisions in the future.

final thoughts on our NCAA football playoff forecasting model

Here are some final thoughts on our model and methodology. First, the pros.

  1. Our models worked really well considering how little information they use. Really well. I thought 12-13 games would not be enough to provide a reasonable forecast, but we ended up being very close to the committee rankings.
  2. All three versions of the model converged on the same results, which wasn’t too surprising given that they all use the same underlying network to gauge quality. But not having agreement would have pointed to a problem.

Now the cons.

  1. There is always that team that clearly doesn’t belong in the rankings, especially early on (I’m looking at you, Minnesota!)
  2. I would want to use additional information next year to instead give teams a fraction of a win based on the point differential in played games. This could help connect our network and provide more refined forecasts.
  3. We don’t use any human and/or crowdsourced information, like point spreads or some of the polls. This can help make the most sense of games that have already been played. There is no need to entirely rely on math models as we did this past year, but I do want to give the math to add value over more traditional models that only rely on human evaluation (like the polls).
  4. It looks like we will need to do some manual tweaking of the results to account for teams from non-major conferences like Marshall. We weren’t sure what to do with them, but it seems like a team like Boise State or Northern Illinois could get invited so long as their schedule passes the sniff test for difficulty (Marshall’s did not) and the team goes undefeated.
  5. We need a better testing and validation plan for selecting model parameters. What we did didn’t work well. We tried to choose the parameters that forecasted the most games “correctly,” but ultimately this ended up yielding nonsensical parameters. In the paper we used, the authors selected parameters based on predicting the outcomes of the most bowl games, and the parameters were pretty nonsensical. For example, home games counted for 3x more than away games, meaning that a team with 6 away wins would be ranked about the same as another team with 2 home wins. I selected parameters that made the most sense and “worked.” For example, home wins/losses counted 15-20% more than away wins/losses to account for the higher expectations associated with home field advantage. But I think we can improve this.

In sum, it sounds like there are a few directions to improve the basic model. We will try to clean up our code and post it in the relatively near future.

Nate Silver wrote a nice post summarizing final thoughts for FiveThirtyEight’s college football model. Their model was based on the previous week’s polls, which injected the human element into the rankings. And this introduced a bias into the rankings. Michael Lopez has a nice post on voter bias and how this affects rankings. I’m not saying that using information from humans shouldn’t play a role, but think math deserves some credit.

will the best teams make the playoff?

Our methodology uses math to consistently rank teams based on game outcomes and strength of schedule. The method implicitly assume that the “best” teams–those that are ranked the highest–will make the playoff.

It’s worth noting that the committee may not be interested in selecting the best teams. In reality, a committee of humans ranks the teams to determine who is invited to the playoff. The committee members are subject to biases that enter the process. They also may be interested in selecting the most deserving teams rather than the best teams. This is a key issue. The most deserving teams generally have the best records (teams in weak conferences like Marshall are an exception), whereas the best teams may have a non-embarrassing loss or two and a very strong strength of schedule. In the past, undefeated teams are almost always selected over arguably better teams with a single loss.

At present the Selection Committee’s current top teams are actually underdogs or weak favorites to teams that are ranked much lower. This is evidence that the committee is ranking teams according to who is most deserving rather than according to who is best.

To be sure, our method is biased by the outcomes of the games, and game outcomes are an imperfect way to capture which team is “best.” Teams that lose on a fluke play (such as Alabama last year) are dinged in the rankings. But in general, our method will try to rank the teams from best to worst, not from most deserving to least deserving. This is one reason why our end of the season rankings will differ from those of the committee.