Modeling March Madness

By Benjamin Remelius

Photo: Kyle Terada-USA TODAY Sports

Note: This work was written and research conducted on March 16, 2022. The findings are being republished here today for the sake of posterity, as the original host of this blog post has since been shut down.

The National Collegiate Athletic Association’s Division I Men’s Basketball Tournament is a loser machine. 64 teams enter the tournament, putting in a long season of hard work and an immense amount of talent, just for 63 to leave with another loss on their schedule. A single-elimination tournament leaves room for a lot of unpredictability. Just about any team can get red hot at any time, and just about any team can get ice cold at any time. Volatility is the name of the game (just ask Virginia). That is why it is important to identify which strengths show through the most often in March, and which weaknesses are most easily exploited. This is the key to projecting the victor of what may be the most unpredictable tournament in the world.

Armed with the regular season per game statistics for each college basketball team to make any of the last ten tournaments and their seed and performance in said tournaments, I got to work. You can go ahead and skip past this next paragraph if you aren’t concerned with my pencil-pusher mumbo-jumbo, but for the TL;DR crowd, this model should effectively predict March results.

First, I assigned each team to participate in a given game as “Team A” or “Team B”. Team A was not always the winner or the higher seeded team, but rather a randomly assigned team of one of the two participants. Then, I marked whether Team A or Team B won a given game. In order to then use this data to make my predictions, I fit a few models predicting the likelihood that Team A would win the game, using a number of varying methods including logistic regression, classification trees, and random forests. Unsurprisingly, each model varied greatly in their predictions. Due to this, I chose to select the model that could most effectively predict the results of randomly selected tournament games that were held out of the model fitting process. My final algorithm was derived from a logistic model, which accurately predicted 135 of the 201 holdout games from the last ten tournaments. While an accuracy rate of 67% may not sound incredibly promising, a more effective measure of model performance when predicting categorical data like this is cross-entropy loss, which takes into account the confidence with which the model predicts a victor. This metric is on a scale from 0 to 1, and with a value below 0.5, I felt confident taking this model into this season’s tournament and seeing what kinds of predictions it makes. With all that out of the way, let’s get to the predictions!

First Four

Yes, I know the Final Four is already well underway, with a couple of great games resulting in Texas Southern and Indiana heading to the dance. Tonight, we have two more good matchups in store with the South Region 16 seed game between Wright State and Bryant and the West Region 11 seed game between Rutgers and Notre Dame. That said, I do have predictions for these games and will give you the model’s predictions ranked by confidence from most to least, a format I will follow in the remaining sections.

16 Texas Southern def. 16 Texas A&M-Corpus Christi

My model really is not all that high on TAMU-CC, who blocked the fewest shots per game of any team to make the tournament this season.

16 Bryant def. 16 Wright State

Bryant had a markedly better regular season than Wright State and you shouldn’t expect that to end with postseason play. Bryant ranks 11th amongst tournament teams on the defensive glass, where Wright State ranks 59th. Look there for a potential x-factor in this matchup.

12 Indiana def. 12 Wyoming

A battle between two different generations of “remember when they were good?” should be won by the Hoosiers, but that shouldn’t be used to detract from the success of the season the Cowboys are having.

11 Rutgers def. 11 Notre Dame

This game is close to a coin toss. Rutgers should win, but teams that should win lose all the time. The Fighting Irish rebound and shoot the ball better, but Rutgers has beaten a lot of teams that are better than Notre Dame and qualify as an at-large bid in spite of the fact that they sport the second worst win percentage of any team to qualify for the tourney.

The Round of 64

Now here’s where the real fun begins. 32 games that feature everything from David and Goliath to Blazers and Cougars. The dreaded 3 vs. 14 and the “c’mon that’s not a real upset” 7 vs. 10 games will be sure to give most bracket makers trouble, but the points you pick up in this round can be key to winning your pool. Here are some things to look for when making your picks for this round.

 

The Round of 64 is all about weeding out weaker low-seeds and finding the diamonds in the rough.

3 Purdue def. 14 Yale

3 Texas Tech def.  14Montana State

Wow, two dreaded 3 vs. 14 games are the most confident predictions this model has for the entire round of 64? Yes. Yale and Montana State are good teams that have a puncher’s chance at best. Purdue and Texas Tech are in a completely different stratosphere.

1 Gonzaga def. 16 Georgia State

1 Baylor def. 16 Norfolk State

1 Arizona def. 16 Bryant

1 Kansas def. 16 Texas Southern

I’ll go ahead and lump all these games together. No, you will not pick the next UMBC. If you’re right, you get one extra point over all your friends. If you’re wrong, you could be eliminating a potential national champion before they even break a sweat.

2 Villanova def. 15 Delaware

2 Auburn def. 15 Jacksonville State

2 Duke def. 15 Cal State-Fullerton

2 Kentucky def. 15 Saint Peters

If I’m starting to sound like a broken record, I’m sorry. I promise the fun stuff is at the bottom of this section, with some sneaky upset picks and games where you could see some great close matchups. These are not those. Pick the two seeds, even if it’s just because you’ll be losing the same amount of points as your friend who goes chalk every year and always finishes top-3 in the pool.

4 UCLA def. 13 Akron

This is not the 4 vs. 13 to target, either. UCLA proved themselves as some sort of a blue-blood Cinderella on this stage last year as an 11 seed, and are now expected to punch down and not up. They’ll do that and should comfortably handle Akron.

7 Ohio State def. 10 Loyola-Chicago

8 North Carolina def. 9 Marquette

I’m lumping these together because I feel the same way about both of these games: shocked at the relative confidence of these predictions. When taking a cursory glance at the bracket, these were two games that I agonized over. How much magic does Sister Jean have left? Will EJ Liddell and Ohio State have a new level of focus after last year’s embarrassing performance? Are the Shaka Smart Marquette Golden Eagles really this good this fast? Is there a team that UNC can’t beat when they’re at their best? Is there a team that can’t beat UNC when they’re at their worst? In spite of that, my model is sure Ohio State and North Carolina will head to the Round of 32. I appreciate its conviction.

11 Iowa State def. 6 Louisiana State

Here’s our first upset, and it’s a good one. Iowa State dominated non-conference play and LSU could be in shambles after firing Will Wade just days ago, and the model doesn’t even know that. This should confirm any suspicions you had about this game.

7 Murray State def. 10 San Francisco

If you’re a fan of a team who has a head coaching vacancy (hey again LSU fans!), there may not be a better game to watch in the tournament. Murray State should win, though, after dominating all season.

5 UConn def. 12 New Mexico State

Much like Ohio State, Connecticut looks like a bounce-back candidate after a flat performance in last year’s tournament. UConn might get into some trouble but there’s good reason to believe they should be able to shoot the Aggies out of the gym.

4 Arkansas def. 13 Vermont

4 Providence def. 13 South Dakota State

While yes, Arkansas is still predicted to beat Vermont and Providence is still predicted to beat South Dakota State, we are in low-confidence territory here. Arkansas had the worst three point percentage of any team to make the tournament. Vermont absolutely demolished their competition en route to the America East Tournament Championship. Providence has had a good season but South Dakota State led all tournament teams in three point percentage this season while fielding one of the most effective offenses in the country. At least one of these 13s should win, if you’re comfortable deciding which one.

9 Memphis def. 8 Boise State

While Memphis clearly needs a true point guard after a disappointing season in which they led all tournament teams in turnovers per game, Penny Hardaway’s squad has a lot of talent and are still here in spite of their weaknesses. They shoot, rebound, and defend better than the Broncos, so they are predicted to win, but this should be a close game that could quickly get out of hand for the Tigers if they can’t move the ball effectively.

5 Saint Mary’s def. 12 Indiana

First Four teams have a history of finding success later in the tournament, but my model doesn’t expect Indiana to be that team. That doesn’t mean it can’t happen, but Indiana over St. Mary’s is not the hill to die on this year for First Four believers.

11 Rutgers def. 6 Alabama

Now there’s a First Four team I can get behind. The Scarlet Knights have more than enough talent to take down the Crimson Tide, and are more than capable of taking down highly regarded opponents this season. If you want to have the 2021 UCLA on your bracket, it should be Rutgers.

3 Wisconsin def. 14 Colgate

3 Tennessee def. 14 Longwood

Here are those 3 vs. 14 plays you were looking for. At this level of confidence, we think the 3s should win but it is worth poking around at the 14s and seeing what you like. Colgate lost their tournament game last year as a 14 seed, and are facing a Wisconsin team that turns the ball over less than any other team in the tournament, but could end up being the next 14-seed to advance to the Round of 32. Longwood scored more points per game than Tennessee while shooting better from the field, from three, and from the free throw line. Their offense could pick up an early lead against the Volunteers and never look back.

9 Creighton def. 8 San Diego State

San Diego State has one of the best defenses in the country. While defense can win a lot of games, it does not win championships in Division I Men’s Basketball. The Blue Jays should take advantage of the fact that they’re facing a team that simply can’t go bucket for bucket with them.

11 Virginia Tech def. 6 Texas

11 Michigan def. 6 Colorado State

Here are a couple more predicted upsets. This model does not take into account the fact that the Wolverine’s worst basketball has come lately. If it did, it would probably have the Rams winning the game, capitalizing on the absence of Juwan Howard. On the other hand, the fact that the model does not take recent play into account means that it is all the more meaningful that it picks Virginia Tech over Texas. This isn’t an overreaction to one hot conference tournament. This is the model correctly assessing what kinds of teams fare best in winner-takes-all atmospheres.

4 Illinois def. 13 Chattanooga

5 Iowa def. 12 Richmond

Another pair of potential upsets that could hit if the lower seeded team can play some of their best basketball. These should not be expected to hit, but could account for some points that your pool-mates aren’t getting from teams that shouldn’t make deep runs costing you more points later on in the tournament

10 Miami def. 7 USC

9 TCU def. 8 Seton Hall

These might be too close to call for some, so let this be your difference maker. Pick up two free points, on me. Or not. Either way, we’re not looking at contenders here. You probably shouldn’t have any of these four teams in your Sweet 16.

12 UAB def. 5 Houston

I promised Blazers and Cougars, and here I am delivering. The model gives a slight edge to the Blazers, so this could be a worthwhile upset pick, but the Cougars made a deep run last year and should not be counted out of this game or another potential deep run in this year’s tournament.

The Round of 32

Here is where the feel-good stories start to come to a close, and a Cinderella is born. Expect to see lots of high seeded teams win here as they continue their season-long push toward glory, while one or two double digit seeds should surprise you like always. After this, we should have some true idea of how the rest of the tournament should shake out. This is also the hardest round of the tournament to predict by far.

 

The Round of 32 is the round in which the model is least confident in its predictions.

4 UCLA def. 5 Saint Mary’s

Remember what I said about UCLA before? How they’re basically putting last year’s Final 4 team back on the floor this year? That all still applies. Saint Mary’s is way too good to go out as a first weekend team but your fate is often determined by the luck of the draw when you slip to a 5-seed, and their draw was UCLA.

2 Kentucky def. 7 Murray State

These Wildcats are one of the top scoring, rebounding, and passing teams in the country. While the Racers have been dominant, Kentucky isn’t a team that can be buried by an opponent that doesn’t shoot the ball at an elite level.

3 Wisconsin def. 11 Iowa State

Iowa State was a buzzsaw until they opened Big 12 play, where they had to compete night in and night out with their cohabitants in the sport’s top conference. Their out of conference prowess got them this far, but it won’t be enough against a Wisconsin team that protects the ball as well as anybody.

1 Gonzaga def. 9 Memphis

Gonzaga made the title game last year, and anything less than that this year would be considered a massive disappointment. Memphis is already being considered a massive disappointment by some, so they surely won’t be the squad to knock off the Bulldogs.

2 Duke def. 7 Michigan State

Expect to see Duke get revenge for their 2019 Elite Eight defeat at the hands of the Spartans in this year’s Round of 32. Michigan State just hasn’t dominated like Duke has, and even at their best they don’t look like they can knock off the Blue Devils.

3 Texas Tech def. 11 Rutgers

The Red Raiders have proven they can beat anybody this year. While Rutgers is here in large part because they’re incredibly battle-tested, Texas Tech is just as battle-tested, while flexing more recent tournament success and earning a 3-seed with a first-year head coach in Mark Adams.

11 Virginia Tech def. 3 Purdue

Here comes Cinderella. After Purdue spent parts of this season ranked number one in the country, they lost their footing a bit as the season went on 

1 Kansas def. 9 Creighton

Here are three reasons why the Jayhawks shouldn’t have much trouble with the Blue Jays: Ochai Agbaji, Remy Martin, and Christian Braun. Kansas is one of the most talented teams in the country, and that should be enough against a good-not-great Creighton squad.

11 Michigan def. 3 Tennessee

This is the one pick my model will make that I truly can’t endorse. This model does not measure trends, and does not know about Juwan Howard’s absence. That said, Michigan has won tournament games without Juwan Howard. He does not singlehandedly make or break this team, and the talent is there to beat anyone.

7 Ohio State def. 2 Villanova

Villanova has a ton of recent success and dominated the Big East Tournament this year. They’re built for this. That said, Ohio State runs an efficient offense and features one of the top players in college hoops. This should be a great game, but the Buckeyes will head to the Sweet Sixteen.

5 Iowa def. 4 Providence

Providence just got absolutely blown out by Villanova in the Big East Tournament. It’s only right that they go out together here, as the Friars hit their second true test in their last three games and once again come up empty.

4 Illinois def. 12 UAB

The Blazers already knocked off a team who made a deep run last year, and now face a team that got KO’d early last year. While these matchups are often enticing picks, don’t expect Illinois to fall victim to the UAB trap game.

1 Baylor def. 8 North Carolina

Expect the reigning champs to make another deep run here. North Carolina is good but Baylor is just in a different league from the Tar Heels right now. Watch as the Bears turn great ball movement into points in this one as they punch their ticket to the Sweet Sixteen.

5 UConn def. 4 Arkansas

The Arkansas Razorbacks will need to find their jumpers if they want to have a chance in this one. UConn shoots the ball well. Arkansas has the worst three point percentage of any team in the tournament this year. The Hogs won’t win trying to trade 2’s for 3’s.

9 TCU def. 1 Arizona

This is the big upset of the round. TCU looks to knock off one of the top offenses in the country, and they really could do that. Colorado, UCLA, and Tennessee are the only teams to beat Arizona all year. Both teams dominated non-conference play this year, and while the Wildcats beat up on their conference, the Horned Frogs had trouble playing in the toughest league in the sport. Arizona has won a lot of games on the defensive glass, but TCU should test them there as one of the top offensive rebounding teams in the country. Second chance points could end up burying the Wildcats this year.

2 Auburn def. 10 Miami

Miami’s win over Duke proved that they have what it takes to punch up in the tournament. Their conference tournament loss proved that better teams will still usually win basketball games. Auburn is a better team, blocking the most shots of any team in the tournament. This could be a good game but should be a Tigers victory.

Sweet Sixteen

The second weekend kicks off with the Sweet Sixteen, wherein we will usually see a Cinderella take form and high seeds take losses that have them heading home early. The first weekend weeds out the good from the great. The second weekend weeds out the pretenders from the contenders.

2 Duke def. 3 Texas Tech

I was initially surprised by the degree of confidence at which my model makes this prediction, but after digging into the data I see why the Blue Devils are seen as an easy pick in this one. This is a matchup of two great teams, but Duke rebounds better and runs one of the most efficient offenses in the country.

1 Gonzaga def. 5 UConn

Gonzaga scores and rebounds at a higher clip than any other team in this tournament. Connecticut won’t be able to fill in the talent gap against a team that features tournament experience and one of the top NBA draft prospects in college basketball.

1 Kansas def. 5 Iowa

Keegan Murray is very good. He isn’t Ochai Agbaji, at least not right now. The Jayhawks have the offense to go score for score with Iowa and the defense to limit the Hawkeyes more than most of their B1G opponents have this season.

4 Illinois def. 9 TCU

Illinois should thank the Horned Frogs on the floor for knocking out Arizona for them, who the model predicts would have beaten the Illini. They will show their gratitude by starting TCU’s offseason early.

2 Auburn def. 3 Wisconsin

Auburn’s interior presence will be too much for the Badgers. Auburn was first in blocks per game and sixth in steals per game amongst teams to reach the tournament. Wisconsin has the fewest turnovers per game of any team in the tournament. If the Tigers can take the ball away, they shouldn’t struggle very much to take down Wisconsin.

1 Baylor def. 4 UCLA

This matchup between 2021 Final Four teams will see the reigning champs take down UCLA. Baylor has done a much better job of executing this year than the Bruins, and that will continue in their tournament matchup.

7 Ohio State def. 11 Michigan

Finally, Michigan is weeded out. Ohio State benefits from seeing the weakest team projected to reach the Sweet Sixteen and move on to the Elite Eight.

11 Virginia Tech def. 2 Kentucky

Shocked to see Cinderella Tech still holding on? It’s not exactly a well-kept secret that Kentucky hasn’t been doing Kentucky things for a little while, without a single Final Four run over their last 5 tournaments. Don’t expect them to break that trend against a Virginia Tech team that can go far in this tournament.

Elite Eight

A win here is all you need for an all-expenses-paid trip to New Orleans. While every team at this level is elite, only one can win it all. Expect close matchups and plenty of them as every team puts in everything they have with a trip to the Final Four on the line.

7 Ohio State def. 4 Illinois

Ron Johnson-USA TODAY Sports

Ohio State never got a chance to match up with any of the top teams in their conference during tournament play after losing a shocker to Penn State to open tournament play. Illinois should be thankful they didn’t see the Buckeyes in the conference tournament, but they won’t be so lucky in this tournament. Ohio State already beat Illinois once this year. It’ll happen again.

1 Kansas def. 2 Auburn

Kansas is one of the few teams that has the shooting to keep up with Auburn that won’t be overwhelmed by the Tigers’ interior presence. Limiting turnovers will be the key to a Jayhawks victory.

1 Baylor def. 11 Virginia Tech

Down goes Cinderella. The reigning champs are just better, on paper and on the floor. Virginia Tech probably wouldn’t be here if they didn’t automatically qualify. Baylor is a one seed as an at-large bid. Hokies fans will have a nice story for years to come but the Bears are here to ensure that’s all they get out of this – a nice story.

1 Gonzaga def. 2 Duke

This should be one of the best games of the tournament. For what my model predicts to be Coach K’s final game on the bench at Duke, they take on a Gonzaga team that will have probably looked invincible thus far. They will look much more mortal in this one, facing a Duke team that won’t cough the ball up and has everything they need to get buckets, but will ultimately head to the Final Four for the second year in a row.

Final Four

I know, having three one seeds in the Final Four will be seen as chalk, using seed as a predictor rather than each team’s skill level, but there is a reason why these teams are one seeds. They are three of the absolute best teams in the country. If they don’t get here, it will be as much to blame on the format of the tournament not successfully rewarding regular season success as it is on each team’s shortcomings. For those of you that hate me for what my computer just spit out at me, at least the model predicts one under the radar team will be playing in New Orleans in the Ohio State Buckeyes.

1 Kansas def. 7 Ohio State

Ohio State’s deep run will be put to an end by Kansas, who has too much talent and does too many things well to lose to a team that isn’t at the top tier of the sport right now.

1 Gonzaga def. 1 Baylor

This year’s rematch of last year’s title game will have a different result. Both teams went out and got reinforcements, but Gonzaga is returning last year’s tournament hero Drew Timme and putting him next to star freshman Chet Holmgren. Baylor doesn’t have the talent to compete with that, and the model’s prediction reflects that.

National Championship

1 Kansas def. 1 Gonzaga

I’m sorry, Bulldogs fans, but back to back National Championship Game losses seem to be in the cards. The Jayhawks just do too many things, too well, and have too much talent to be beaten this year. If it makes you feel any better, as a Missouri Tiger I hate this as much as you do. Kansas is the best team in the country, and they’ll prove it by coming home from New Orleans as the 2021-2022 NCAA Division I Men’s Basketball Tournament Champions.

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