In my last article, I posted this year’s iteration of my annual model for predicting the outcome of the NCAA Division I Men’s Basketball Tournament. I provided the modeled win probability of all 2278 possible matchups along with an “expected” bracket representing the outcome if the modeled favorite wins every game. Check that out here.

That bracket isn’t terribly practical, though. Just because the model gives Team A a 55% chance of winning doesn’t mean they’re going to win. That’s not much different from a coinflip! Furthermore, it doesn’t really reflect the other matchups that a team may have to go through. If Team A has a win probability of 20% against Team B in the second round, that doesn’t look too good for them. However, what if Team B’s win probability in the first round against Team C is only 51% and Team A’s win probability against Team C would be 80%? The “expected” bracket doesn’t show this, but that suddenly makes Team A’s outlook much better.

That’s where simulations come in. We can use the modeled win probabilities to simulate the entire tournament. We can run this simulation any number of times and compile the results to see how likely each time is to reach each round of the tournament assuming that the modeled win probabilities are accurate. I ran 10,000 simulations of the tournament – here are the results.

South Region

The top overall seed Alabama Crimson Tide are unsurprisingly the favorites to make it to the Final Four and win the region. Furthermore, their 12.5% probability of winning the tournament tops the region with No. 2 Arizona being the next best at 5.2%. Arizona looks to be a formidable team in their own right with a solid 20% likelihood of making the Final Four.

Afterwards, there’s a drop-off before the next tier of teams: No. 3 Baylor and No. 5 San Diego State. Their odds of making the Final Four, National Championship, and winning it all are all virtually the same. Everyone else is a long way down and not really worth a mention.

Midwest Region

Well, this one looks like a two man show.

There’s a lot to say about the Houston Cougars. They’re the favorites in Vegas to win the tournament and they boast one of the most stifling defenses in the country. With star Marcus Sasser set to return from injury shortly, the Cougars are poised to show off their best team in years. That’s saying a lot, given that they’re coming off of a Final Four appearance in 2021 and an Elite Eight loss in 2022.

Then we have the No. 2 Texas Longhorns. Texas is ranked 18th in offensive efficiency in 11th in defensive efficiency according to KenPom.com – with a 26-8 record and a recent Big 12 title, this balanced roster is coming into the tournament with some positive momentum.

The Cougars have an astonishing 44.6% likelihood of making the Final Four according to our model, with Texas following them up at 23.0%. The two favorites have 20.8% and 5.5% respective probabilities to win the entire tournament. No one else in the region is over one percent. It’s clear that one of these teams should be the ones to make it out of the Midwest.

East Region

No. 1 Purdue leads the East with a 5.7% probability of winning the tournament, followed closely behind by No. 2 Marquette at 4.9%. Spoiler alert, but this is the lowest mark for a region’s top team. Of all four regions, our model has the East as the least likely to field the tournament’s eventual champion.

Purdue and Marquette and virtually neck-and-neck for Final Four odds. Marquette is viewed as having a more favorable path to the Elite Eight, while Purdue is favored in a matchup between the two teams.

Afterwards, we have No. 4 Tennessee and No. 5 Duke – sleepers to steal the region and sneak into the Final Four, but not really viewed as massive title contenders (2.0% and 1.2% championship odds respectively).

West Region

Finally, we’ve got the West. Here’s a fun one – take a look at how much this model hates the No. 1 Kansas Jayhawks. It has the remaining top five seeds as more likely to make it to the Final Four – even No. 5 Saint Mary’s! If you want a one seed to fade, the Jayhawks may be the one for you.

At the top, we have the No. 2 UCLA Bruins with a fantastic 36.2% probability to win the region and a very nice 13.5% mark of winning the tournament. That’s behind Houston but slightly ahead of Alabama for the 2nd best overall. In order, they’re followed up by No. 3 Gonzaga, No. 4 Connecticut, No. 5 Saint Mary’s, and No. 1 Kansas.

Commentary

I think simulation analysis has a lot of value in revealing details in how the bracket shaped paths for the top teams. Last year, my simulations revealed that Kansas had the highest probability of making it to the Final Four. They weren’t viewed as the best team in the tournament and were not favored to win it, but the simulations demonstrated that they had the easiest path to the Final Four. Picking the Final Four teams correctly is a huge boost, so knowing which teams have easy/hard paths is immensely important.

This time around, Kansas isn’t so fortunate. They look like a fade candidate rather than a team poised to win their region. On the other hand, Houston has the highest Final Four probability in the tournament – if you want a safe Final Four pick, they might be your best bet!

Unfortunately, these margins are very small. We’re just playing the numbers here – anything can happen once these teams step on the court. There’s a reason no human has selected a perfect bracket yet, and there’s a reason it’s called March Madness. Don’t put too much stock on the statistics – there’s a lot that they can’t quantify. Most pre-tournament analyses like this one did not foresee the No. 8 North Carolina Tar Heels embarking on a miraculous Final Four run last season. We’re guaranteed to see more unexpected results this March, so don’t expect perfection. If you want to win your bracket pool, all you can do is play the numbers and hope for the best.

The post March Madness 2023: Tournament Simulation Results appeared first on The Spax.

For the fourth time in this website’s history, I’ll be training a model to predict the outcome of March Madness, the annual postseason tournament to crown a champion of men’s Division I college basketball.

Over the past four years, The Spax’s modeled bracket has varied in performance. Since a hot debut in 2019 where our model correctly predicted three of the Final Four teams (including five-seed Auburn) and the national champion Virginia Cavaliers, it has certainly cooled down.

Of course, scoring a lot of points is generally going to be difficult if you don’t predict the champion correctly. In two straight years of picking Gonzaga to win it all, the Bulldogs were not able to finish the job. Granted, most models in both years had Gonzaga winning it – they were the national favorites for a reason. That’s why an optimal bracket strategy would not be to simply pick the team with the highest probability to win each game like I do for the purpose of this analysis – rather, you should consider each team’s win probability relative to the public’s assessment of their win probability. Maybe some one-seed is modeled as the favorite to win their region, but not by that much, so you choose to pick the five-seed that has a solid 40% modeled probability to beat them head-to-head.

Anyway, let’s get to this year’s picks:

First Four

I slacked off this year and didn’t get this article out before the play-in games occurred, so all four of these games have actually ended by now. The forecast winner ended up going 3-1, the sole error being in Pittsburgh’s 60-59 win over Mississippi State.

South Region

Top Team: The top overall seed in the country is the University of Alabama, and they’re unsurprisingly the clear top dogs in their region as well. It would be a shock to see them fall prior to the Elite Eight, and they would also be favored to beat the two-seed Arizona Wildcats in that matchup. With top NBA Draft prospect Brandon Miller leading the way, Alabama has a chance to make a transformational run.

Potential Disappointment: There’s not a whole lot to say here – both No. 2 Arizona and No. 3 Baylor are forecast to make it to the Sweet Sixteen, and losing to one another wouldn’t really be a huge disappointment. However, it’s certainly possible that one of them falls in the Round of 32 – failing to make it to Sweet Sixteen because they suffered a loss to No. 6 Creighton or No. 10 Utah State would certainly be a slap in the face for either program.

Sleeper Pick: This is probably the least interesting region, to be frank. I don’t think there’s a great sleeper pick, but if I had to pick one I would probably go with No. 6 Creighton. I think there’s a chance that they snag a couple of early wins to find themselves in a Sweet Sixteen matchup against No. 2 Arizona.

Most Probable First-Round Upsets: No. 10 Utah State over No. 7 Missouri (70.70 percent chance)

Midwest Region

Top Team: The Alabama Crimson Tide are the top overall seed in the tournament, but according to sportsbooks, the Houston Cougars are the favorites to win it all. The Cougars have had a great run over the past five or so years, with coach Kelvin Sampson leading them to the Elite Eight in 2022, the Final Four in 2021, and the Sweet Sixteen in 2019. That’s a fantastic run, especially considering the injuries they endured (missing their most talented player in Marcus Sasser in 2022). They’ve already had postseason success, but the 2023 Cougars are even better than past iterations of the team and now all eyes are on a title. Sasser is entering the tournament with an injury and is questionable to play in the first round, but with a healthy lineup, the Cougars should be the safest Final Four pick in the tournament.

Potential Disappointment: The model has a Round of 32 match up between No. 3 Xavier and No. 6 Iowa State as a virtual coinflip. That early of a loss would be a let down for the Musketeers, and with a tough potential outing against Texas in the next round anyway, expectations shouldn’t be too high for Xavier.

Sleeper Pick: I’ll go with another six-seed here, this time the Iowa State Cyclones. Like I said, they’ve a shot to knock off Xavier if they can get past the first round. However, something interesting I noticed is that Mississippi State would’ve been forecast to beat Iowa State in the Round of 64. As you know, they lost to Pittsburgh in the First Four. Pittsburgh, on the other hand, are not at all favored to beat Iowa State. These sort of discrepancies are unsurprisingly common because the transitive property doesn’t apply to sports, but I wouldn’t be shocked to see Pittsburgh upset Iowa State.

Most Probable First-Round Upsets: No. 10 Penn State over No. 7 Texas A&M (37.73 percent chance), No. 13 Kent State over No. 4 Indiana (38.82 percent chance), No. 14 Kennesaw State over No. 3 Xavier (31.85 percent chance)

East Region

Best Team: The No. 1 Purdue Boilermakers enter the tournament with high expectations after 7’4 superstar Zach Edey led them to a 29-5 record and a Big Ten title. They’re tied with the Jayhawks for the 3rd best odds (Houston, Alabama) of winning the tournament per Bovada, and both our model and sportsbooks view them as the favorite to win the East.

Potential Disappointment: … but it’s not necessarily going to be a walk in the park. After the first round, the “easiest” predicted matchup for Purdue is in the Sweet Sixteen against Duke. In that affair, the Blue Devils are given a 34.87% win probability. Memphis has a modeled win probability of 37.74% in the Round of 32, and Marquette pose a threat of their own in the Elite Eight. It’s clear that the two candidates for disappointing one-seed are Purdue and Kansas this year.

Sleeper Pick: Watch out for the No. 8 Memphis Tigers. They’re coming off of a win over the Houston Cougars (albeit sans Sasser) to win the AAC Tournament as they enter the Big Dance with some good momentum. The same is true for Purdue, of course, who will undoubtedly be favored to win a potential matchup between the two teams in the Round of 32, but I wouldn’t write off the Tigers completely.

Most Probable First-Round Upsets: No. 10 USC over No. 7 Michigan State (40.47 percent chance), No. 11 Providence over No. 6 Kentucky (49.33 percent chance), No. 14 Montana State over No. 3 Kansas State (31.37 percent chance)

West Region

Top Team: The forecast winners of this region are the two-seed UCLA Bruins. While it’s always sticks out when we don’t pick a one-seed to advance, this result isn’t actually an upset – the Bruins are currently the favorites in Vegas to win the West region at +275, followed by Kansas at +350. The Bruins’ program has had a modern resurgence, with a Final Four appearance in 2021 and a Sweet Sixteen run in 2022. They’ll almost certainly make that three straight Sweet Sixteen appearances this year, with a key potential matchup against Gonzaga testing their ability to go the distance.

Potential Disappointment: Whenever a one-seed doesn’t get out of their region, it can be considered a disappointing tournament for them. The defending champion Kansas Jayhawks enter the West as the top seed, but as I mentioned before, they are not favored to come out on top. Furthermore, they’re actually forecast to fall to four-seed Connecticut in the Sweet Sixteen. It is clear that the Jayhawks will not have an easy road to the Final Four.

Sleeper Pick: Well, Connecticut’s a four-seed predicted to make the Elite Eight, so it suffices to say that they’re a solid sleeper pick to throw into your bracket. There’s not much else I’d buy into – I think picking Arkansas or Arizona State to get into the Sweet Sixteen would be a little too risky.

Most Probable First-Round Upsets: No. 11 Arizona State over No. 6 TCU (52.59 percent chance), No. 10 Boise State over No. 7 Northwestern (55.78 percent chance)

Final Four

The model forecasts the Final Four matchups to beat Houston v. UCLA and Alabama v. Purdue, with the favorites winning and moving onto the National Championship Game. The Cougars and the Crimson Tide are the clear two favorites to win the tournament, so it’s only fitting that they’d meet in the title game. If they do, we predict Houston to have the edge.

Needless to say, this is a pretty chalky Final Four. Just because this is viewed as the most likely outcome does not mean that it’s going to happen – it almost certainly won’t! Maybe Kansas will make it in over UCLA. Maybe Connecticut will get in over either. Perhaps Purdue falls in the Sweet Sixteen and Marquette takes their place. Or maybe some random double-digit seed comes in and takes a spot. Who knows? A good bracket probably shouldn’t pick these four teams in the end.

I’ve only shown a fraction of the possible matchups that can occur in March Madness. I’ll provide the win probabilities for every single one of them, though! If you’d like to see the model’s projections for matchups not listed above, you can search for them in table below which consists of 2,278 rows, one for every possible matchup. Just type the name of the two teams separated by a space. For instance, if you want to search for the Houston-Kansas matchup, type “Houston Kansas” into the search bar to get the win probability (69.34% for Houston).

In the next article, we’ll take a look at simulation results using these win probabilities.

The post March Madness 2023: Forecasting the NCAA Division I Men’s Basketball Tournament appeared first on The Spax.

In yesterday’s article, I described our annual logistic regression model for predicting the outcome of the NCAA Division I Men’s Basketball Tournament. I applied it to this year’s tournament to get the model’s “expected” bracket and the win probability for each team in every possible matchup. You can click the link here to see all of that good stuff.

Another good way to show the results is through a simulation – we can use the modeled win probabilities to simulate the entire tournament in less than a second. For example, I just ran a simulation of the tournament and in this hypothetical scenario, the Final Four teams are Gonzaga, Villanova, Kentucky, and Kansas. The Jayhawks went on to top the Gonzaga in the championship game. Not at all difficult to imagine that playing out.

We can run this simulation any number of times and compile the results to see how likely each time is to reach each round of the tournament assuming that the modeled win probabilities are accurate. We’ll go through each region to see the results.

West Region

Gonzaga won the West in 34.0% of our simulations, ahead of Duke at 26.1% and Texas Tech at 16.9%. There’s a drop-off afterwards before we get No. 4 Arkansas at 5.2% and No. 5 Connecticut at 6.2%. In terms of who can actually win the tournament, we see the same pattern of a “Big 3” with Gonzaga at 14.3%, Duke at 7.8%, and Texas Tech at 3.5%.

South Region

Despite the previous article having Houston in the Final Four in the situation in which the model is perfectly accurate, Arizona does have a substantially higher chance of reaching the Final Four in our simulated runs. The one-seed Wildcats reach the Final Four in 33.9% of simulations versus 20.7% for Houston followed by 15.7% for No. 3 Tennessee and 15.0% for No. 2 Villanova. These are also the only four teams who won the tournament in more than 1% of simulations.

Houston is a super interesting case. Most metrics love them, but there is plenty reason for concern – a weak schedule, two key injuries, and the fact that they’ll probably run into Arizona in the Sweet Sixteen. I would personally wager that the analytics are overrating the Cougars’ chances, so I’d be weary of picking them over Arizona to make the Final Four. Their performance in the tournament is probably the thing I’m most interested in keeping an eye on.

East Region

Now we have the East, the most tightly contested region. Baylor is favored to win it at 27.1% followed by Kentucky, Purdue, and UCLA at 24.8%, 18.7%, and 16.3% respectively. That’s an incredibly tight race between the top four seeds.

It’s worth noting that the Baylor Bears are dealing with injuries right now (not explicitly accounted for in the model) which should give even more reason for you to not pick them in your Final Four. I also do not think any teams outside of the top four seeds in the region are worth picking – I would choose between Kentucky, Purdue, and UCLA.

Midwest Region

Finally, the Kansas Jayhawks won the Midwest in 37.8% of simulations. Auburn represented the region in 21.0% of the iterations followed by the five-seed Iowa Hawkeyes at 15.3%. Impressively, the 11-seed Iowa State Cyclones managed to break into the Final Four in 4.5% of the simulations.

Based on this data, it also seems that the model views the Jayhawks’ path as being the easiest. It’s not easy seeing any other team coming out of the region and winning the entire tournament.

Commentary

The two most important factors in picking a successful March Madness bracket is to have an accurate Final Four and accurately pick the champion. And part of having a strong FInal Four is to be smart with the seeds that you select. On average, 1.7 one seeds make it to the Final Four, so you don’t want to go all “chalk.” Baylor is probably not a one-seed that should be selected, leaving you to pick between Gonzaga/Kansas/Arizona.

It is also fairly common for a seven-seed or lower to make it to the Final Four. A few interesting picks to make it to the Final Four are No. 8 San Diego State (3.0%), No. 9 Memphis (2.5%), and No. 11 Iowa State (4.5%). Or maybe you’d go with slightly higher seeded sleepers like No. 5 Iowa (15.3%), No. 4 UCLA (16.3%), and No. 5 Houston (20.7%). Based on ESPN bracket data, all six of these “sleepers” are picked to advance to the Final Four at a lower rate than they actually do in simulations – perhaps they’re strong values pick in larger pools.

As for who’s going to win… well, that’s a tough question. Gonzaga (14.3%), Kansas (14.0%), and Arizona (12.8%) won the tournament most often during these 10,000 simulations, followed by a drop-off before we get teams like Houston, Duke Baylor, and Kentucky. Gonzaga is actually given a significantly higher chance of winning by sportsbooks (25% implied odds) and the public (27.8% of ESPN brackets picking them to win). Whether it’s rightful or not, the model does not view Gonzaga’s chances as highly as others. In this case, Kansas is an interesting contrarian pick as just 8.5% of brackets have them winning it all.

Unfortunately, these margins are very small. We’re just playing the numbers here – anything can happen once these teams step on the court. There’s a reason no human has selected a perfect bracket yet, and there’s a reason it’s called March Madness. Don’t put too much stock on the statistics – there’s a lot that they can’t quantify. Most pre-tournament analyses like this one did not foresee the No. 11 UCLA Bruins embarking on a miraculous Final Four run last season. We’re guaranteed to see more unexpected results this March, so don’t expect perfection. If you want to win your bracket pool, all you can do is play the numbers and hope for the best.

The post March Madness 2022: Tournament Simulation Results appeared first on The Spax.

Since creating this website in November 2018, I’ve created yearly statistical models for the purpose of predicting the annual NCAA Division I Men’s Basketball Tournament.

The first time was in 2019 when we successfully forecasted the national champion Virginia Cavaliers and three of the four Final Four teams (including the five-seed Auburn Tigers). The predicted bracket finished in the 99th percentile of ESPN’s Tournament Challenge.

The tournament returned in 2021 after the COVID-19 pandemic forced the cancellation of the 2020 edition. We weren’t quite as successful this time around – while the model picked three of the four Final Four teams again (including the two-seed Houston Cougars), the Baylor Bears unexpectedly bested the Gonzaga Bulldogs in the National Championship Game. Not picking the correct champion (which is worth by far the most points) meant the model’s corresponding bracket finished in just the 79th percentile of all brackets submitted to ESPN. Although I did submit a variation of it that had Baylor correctly besting Gonzaga in the national championship and finished in the 99.6th percentile, most bracket pools don’t allow multiple entries so that isn’t particularly relevant.

In any case, I believe the first two iterations of The Spax’s March Madness model have been reasonably successful and I’m glad to bring it back again this year with some changes to its methodology, including a bonus for games previously won in the tournament. For example, if we were predicting the probability of Georgia State (16) beating Boise State (8) in the Round of 32, we’d automatically factor in the fact that Georgia State must have beaten Gonzaga (1) in the first round in order for that matchup to even take place. A few other variables have been added as well, including one for a team’s tournament experience.

With that said, let’s get started by taking a look at the First Four matchups.

First Four

Notre Dame v. Rutgers is viewed as essentially a coinflip while Texas Southern and Indiana winning their respective games seems to be a “safer” bet. Meanwhile, Bryant is predicted to have a ~58% probability of besting Wright State to earn a R64 matchup against Arizona.

Most of these odds roughly line up with sportsbooks’ odds with the exception of Bryant vs. Wright State – Bryant will be entering that game as 3.5 point underdogs.

West Region

Top Team: Gonzaga will be playing their third consecutive tournament as the top seed in their region. While they definitely aren’t as viewed as strongly as they were last year (NCG loss vs. Baylor), they are still considered the favorite to win the tournament and they have the best modeled probability of reaching the Final Four. An upset before then would not be the craziest thing to happen, though – instead of an 88% win probability in the Round of 32 like last season, the Bulldogs have “just” a 75% win probability of beating Memphis in the second round this year. While they should make it out of the region, their path is not the easiest it could be and it’ll definitely be something to watch.

Potential Disappointment: The Duke Blue Devils will be seeking a magical farewell run for the legendary Coach K, but it will not be an easy path for them at all. While their potential Round of 32 matchup against Michigan State isn’t considered as worrisome by the model as some fans & analysts view it, Texas Tech is given a slight edge over them in the Sweet Sixteen matchup. Interestingly, though, if Duke and Gonzaga do matchup in the Elite Eight, the Blue Devils have a respectable modeled win probability of 42.44%. I could realistically see Duke losing at any point after the first round so I’m not sure exactly what to expect.

Sleeper Pick: It’s not obviously looking at the bracket, but the nine-seed Memphis Tigers are an interesting team to watch this year. Given how good Gonzaga is and what Memphis’ seeding is, a 25% win probability is relatively interesting. In a potential Sweet Sixteen matchup against five-seed Connecticut, Memphis has a modeled 43.15% win probability and a 29.05% modeled win probability in an Elite Eight bout against Texas Tech. None of these are even close to guaranteed and obviously even their first round matchup is viewed as a tight one, but I do think Memphis is the most interesting mid-low seed in the region.

Most Probable First-Round Upsets: No. 10 Davidson over No. 7 Michigan State (36.43 percent chance)

South Region

Top Team: According to our model, the five-seed Houston Cougars would represent the South region in the Final Four if the modeled favorite won every game. This may come off as a surprise, but analytics do seem to like the Cougars – they rank 4th in KenPom’s rankings and 2nd in BartTorvik’s. It’s not at all difficult to make the case that Houston may be underseeded. On the other hand, two of their four most important players are likely out for the season (Marcus Sasser and Tramon Mark). The model does not explicitly account for injuries (it does place extra weight on more recent games where Mark and Sasser did not play, though) so this should definitely be something to keep in mind when filling out a bracket. You don’t want to just put one seeds in the Final Four so naturally Houston is a pretty good Final Four pick to go against the grain, but giving them a 51.01% win probability over Arizona is probably unrealistic. They will also have to go through Illinois and Tennessee to reach the Final Four, so there’s no reason for excessive optimism – it’ll be quite the tough path. Hell, UAB is even a popular 12 seed upset pick in the first round.

Potential Disappointment: Anytime a one-seed doesn’t make it out of the Sweet Sixteen, it can be considered a disappointment. And in a hypothetical third round matchup against Houston, the top seed Arizona Wildcats have a modeled win probability of 48.99%. While that’s basically a 50/50, it is an interesting possibility for an early exit for the team with the second-best odds of winning the tournament according to sportsbooks. It’s worth noting that Arizona would have modeled win probabilities of 67.96% and 76.19% in hypothetical Elite Eight matchups against No. 2 Villanvoa and No. 3 Tennessee respectively. If they manage to get past Houston, or escape a matchup against them, they have as good of a chance of making the Final Four as the other one seeds.

Sleeper Pick: This region has the potential to be a bit wild – a couple first round teams to watch are No. 13 Chattanooga and and No. 11 Michigan. The model gives Michigan a 60% probability of pulling off the first round upset while the Chattanooga has a relatively high 33% probability for the massive upset over Illinois.

Most Probable First-Round Upsets: No. 10 Loyola Chicago over No. 7 Ohio State (41.92 percent chance), No. 11 Michigan over No. 6 Colorado State (60.00 percent chance), No. 13 Chattanooga over No. 4 Illinois (32.89 percent chance)

East Region

Top Team: The one-seed Baylor Bears are the modeled favorites to come out of the East. The Bears won the 2021 NCAA Division I Men’s Basketball Tournament (also as the one-seed) with a blowout win over the undefeated Gonzaga Bulldogs in the National Championship Game. While going for back-to-back titles will be an incredibly difficult task, it would not at all be a surprise to see them in the Final Four again …

Potential Disappointment: … but it also wouldn’t be surprising to see an earlier exit for the Baylor Bears. They’re not expected to have an easy time in the East – the very real threat of potential matchups against No. 2 Kentucky, No. 3 Purdue, and No. 4 UCLA pose true danger to the Bears. Baylor would have modeled win probabilities of 62.65%, 60.40%, and 62.49% in these matchups respectively. While that makes them consistent favorites, they’re far from a sure thing. Any of those top four teams could realistically be seen in the Final Four. In particular, the two-seed Kentucky Wildcats are a very formidable threat to win the East and disappoint the Baylor Bears.

Sleeper Pick: In my opinion, the four-seed UCLA Bruins are the most interesting team in the East. I expect them to advance to a Sweet Sixteen matchup against No. 1 Baylor where they have a solid 37.51% modeled win probability. And in hypothetical Elite Eight matchups against No. 2 Kentucky and No. 3 Purdue, the Bruins have modeled win probabilities of 35.77% and 53.65% respectively. In 2020, the No. 11 Bruins unexpectedly made a miraculous run all the way to the Final Four (and went toe-to-toe with Gonzaga) and they look even better in 2021.

Most Probable First-Round Upsets: No. 10 San Francisco over No. 7 Murray State (64.36 percent chance), No. 11 Virginia Tech over No. 6 Texas (36.43 percent chance)

Midwest Region

Top Team: Bill Self has coached the Kansas Jayhawks to the one-seed for the ninth time and after dominating the Big 12 Tournament, they look like a team ready for the big dance. The one-seed Jayhawks should probably not have much of a problem advancing to the Sweet Sixteen (although they’d “only” have a modeled win probability of 71.26% in a R32 matchup against SDSU). Iowa and Auburn may not be walks in the park but Kansas could have a harder path.

Potential Disappointment: The No. 11 Iowa State Cyclones actually have an above 50% modeled win probability in the first round against No. 6 LSU – despite the Tigers being 3.5 point favorites in Vegas, the model really doesn’t like their chances against the Cyclones. And in a potential second round matchup against the No. 3 Wisconsin Badgers, the Cyclones have a modeled win probability of 43.02% – pretty remarkable for an 3 vs. 11 matchup. As such, the three-seed Badgers are a glaring candidate for an early exit according to the model.

Sleeper Pick: The model clearly considers the aforementioned Iowa State Cyclones as a possibility for a surprising run. Looking elsewhere for another sleeper, their in-state rivals serve as an interesting candidate. The Iowa Hawkeyes are expected to get past Richmond and South Dakota State in the first two rounds to meet the one-seed Jayhawks in the Sweet Sixteen. And a 30.58% modeled win probability against Kansas is not at all bad. 42.68% modeled win probability versus No. 2 Auburn in the Elite Eight and a whopping 68.21% win probability against No. 3 Wisconsin. And just for fun, Iowa would have the 60.81% edge in an in-state Elite Eight matchup.

Most Probable First-Round Upsets: No. 11 Iowa State over No. 6 LSU (55.78 percent chance)

Final Four

And we’ve reached the Final Four! We have three one-seeds (Gonzaga, Baylor, Kansas) and a five-seed in the Houston Cougars. Funny enough, it reminds me of last season where the model forecasted Houston beating Baylor in the Final Four to advance to the NCG where they were predicted to lose to Gonzaga.

This time around, Houston is barely favored over the Jayhawks while Gonzaga has a decent edge (as far as you can expect from a 1 vs. 1 matchup) over Baylor in a rematch of last season’s National Championship Game. And once again, the model foresees a Gonzaga vs. Houston matchup in the championship, with Gonzaga coming out on top again.

If we predict the same championship matchup every year, it has to happen eventually. Right?

Jokes aside, it would be odd if Gonzaga wasn’t favored. They are viewed by the favorites by most statistical models, Vegas’ odds, and public opinion. But we play the games for a reason – anything can happen. If Kentucky reaches the Final Four instead of Baylor, Gonzaga’s modeled win probability would drop to 57.65% – a much closer matchup.

Or maybe we get No. 2 Duke vs. No. 1 Baylor (50.86% win probability for Baylor). Or No. 2 Duke vs No. 2 Kentucky (56.76% win probability for Kentucky). Or No. 1 Arizona vs. No. 1 Kansas (58.28% win probability for Kansas).

Needless to say, there’s a lot of possible matchups in March Madness. We’ve only presented a subset of the possibilities so far. If you’d like to see the model’s projections for matchups not listed above, you can search for them in table below which consists of 2,278 rows, one for every possible matchup. Just type the name of the two teams separated by a space. For instance, if you want to search for the Gonzaga-Houston matchup, type “Gonzaga Houston” into the search bar to get the win probability.

In the next article, we’ll take a look at simulation results using these win probabilities.

The post March Madness 2022: Modeling the NCAA Division I Men’s Basketball Tournament appeared first on The Spax.

Last month, I released my modeled predictions for the NCAA Division I men’s basketball tournament. It was the second version of the machine learning model after it performed exceptionally well in 2019. Unfortunately, the bracket had a lot less green this time around.

Despite Gonzaga obviously being favored to win the tournament by every predictive model, they collapsed with an embarrassing performance in the national title game at the hands of the Baylor Bears. While the model correctly picked three of the Final Four teams, it did not pick Baylor to advance to the national title game, let alone win it all. As one-third of the maximum number of points for an ESPN bracket come from the final three games, Baylor’s unexpected success obviously had quite a toll on the model’s final performance. However, we can still evaluate its performance as we did two years ago.

Hits & Misses

Hits

Our model started off with a 3-1 record in the First Four after picking all four of the underdogs. Most of the win probabilities were quite close and all of the First Four games were pretty close too, so it doesn’t really mean much.

In the initial article, I said that “USC and Oregon both have relatively solid odds to make it to the Elite Eight.” The six-seed Trojans had a modeled probability of 45% to beat three-seed Kansas (they did) and the seven-seed Oregon Ducks had a modeled probability of 45% to beat the two-seed Iowa Hawkeyes (they did). The model also favored USC to beat Oregon in their matchup and for Gonzaga to annihilate USC (although that wasn’t a hot take). Not a bad job in the West region.

Houston advancing to the national title game was the surprising pick from the model. While they didn’t, they at least made it to the Final Four instead of the one-seed Illinois Fighting Illini. But they also had a historically easy route to the Final Four, so who knows how good they really were?

Misses

The East region was a bit of a mess. UCLA obviously shook everything up — the model didn’t pick them to advance past the first round and they ended up winning the entire region. Alabama lost early, Texas lost early, Connecticut was a sleeper pick and they lost in the first round, etc.

Alright, I don’t think anyone saw Oral Roberts winning two games. The model’s performance in the South region also wasn’t superb, but it’s at least a bit more understandable. I don’t think anyone saw Oral Roberts winning two games. The model also did not like Arkansas’ chances in the region, and while Arkansas did advance to the Elite Eight, they didn’t make it convincing.

Baylor annihilating Houston in the Final Four cost our bracket 160 points, so it was obviously an impactful miss. It would’ve been more understandable if the game was close (after all, Houston was given a 63% win probability, nowhere near a guarantee), but the Cougars didn’t look like they belonged on the same court as the eventual champion Baylor Bears.

Comparison to Other Models

Compared to the three most prominent March Madness models, The Spax comes in at third ahead of FiveThirtyEight and behind Model284 and SportsLine.

The Spax’s model was the highest performing by a slim margin through the Elite Eight, as it had a good start in the Round of 64 while also correctly picking three of the Final Four teams (unlike FiveThirtyEight, who incorrectly had Illinois in the Final Four instead of Houston).

Model284 and SportsLine pulled ahead in the Final Four where their model forecasted Baylor to move on to the national title game. That one game, being worth 160 points, ended up making the difference. All four models incorrectly predicted that Gonzaga would win the championship.

Conclusion

Every year, I submit a bracket to the ESPN Tournament Challenge which simply follows the model’s pick. Last year’s bracket finished with 1360 points (ranked 138,776th in the world, 99.2 percentile). I created 24 variations of that bracket, none of which performed any better. This time around, the model’s bracket finished with 920 points (ranked 3,115,289th in the world, 78.8 percentile). Not so good. I did create 15 variations, though. Unfortunately, I was overconfident in Houston beating Baylor, so I only made one bracket in which Baylor won the championship. This bracket was fantastic, accumulating 1400 points and ranking 64,554th in the world (99.6 percentile). Of course, no bracket pool lets you submit 25 entries, so that doesn’t mean much.

How can our model be improved for next year? There are plenty of ideas I’d like to implement into the model for future tournaments, such as accounting for injuries, a superstar ¹ factor, tournament experience, etc.

While the model was unable to live up to the crazy standards set by its performance in 2019, it wasn’t too far off from how other models performed. Maybe it’ll have more success next year.

The post March Madness 2021: Assessing Our Statistical Model’s Performance appeared first on The Spax.

Two years ago, I created a model to predict the 2019 March Madness tournament. It performed pretty well, most notably picking Auburn to advance to the Final Four and correctly predicting that Virginia would win the National Championship. On the whole, the model’s forecasted bracket finished in the 99th percentile of ESPN’s Tournament Challenge.

Back then, I used a massive Excel spreadsheet to train a linear regression model that violated many fundamental rules of statistics. While the result may have been solid, the actual creation of the model was awful and it almost certainly would’ve performed poorly in the long run. Come on.

Of course, I was a beginner at the time, so it’s hard to blame myself too much. Since then, I’ve learned a lot about data science, and this time around I started from scratch and created the model in Python. I conducted exhaustive feature selection and hyperparameter tuning in order to optimize its predictive ability, which was not the case in 2019.

While the model is different, the idea at its core remains the same. I want to holistically assess a team’s chance of winning each game based on a variety of different variables, including their recent performance leading up to the tournament, their performances against opponents representative of a tournament field, playstyle, etc.

Anyway, let’s get into the predictions.

First Four

Wichita State beating Drake is the closest thing to a safe bet here, but even that’s not exactly a sure thing. Oddly enough, the projected losers in all four of these games are actually the odds-on favorites to win. Not by much, of course.

West Region

Top Team: Gonzaga is entering the tournament as the clear favorites — Vegas gives them implied odds of around 32% to win the tournament, with Illinois at a distant second at just 16%. There’s a very real chance that they will finish their season undefeated. And the model doesn’t really think they’re facing any stout competition in their region. Anything short of a Final Four berth would be a surprise.

Potential Disappointment: Neither the No. 2 Iowa Hawkeyes or the No. 3 Kansas Jayhawks are given a super optimistic shot at making it to the Sweet Sixteen. Both of them have their hands full with No. 6 USC and No. 7 Oregon respectively in the second round.

Sleeper Pick: Along the same lines, USC and Oregon both have relatively solid odds to make it to the Elite Eight. If USC were to upset Kansas and move on to play Iowa in the Sweet Sixteen, they’re projected to have a 48% win probability in that game. And if Oregon moves on to play Kansas in the Sweet Sixteen, the model actually slightly favors them to advance with a 53% win probability. Both teams would still be massive underdogs against Gonzaga in the Elite Eight, but still. Knocking off the No. 2 and No. 3 teams in the region would be a superb rub.

Most Probable First-Round Upsets: No. 11 Wichita State over No. 6 USC (40.58 percent chance)

East Region

Top Team: Michigan isn’t considered a juggernaut to the degree of Gonzaga, but they’re certainly still the favorites to come out of the East. None of Michigan’s projected opponents have a win probability of 33% or higher against them.

Potential Disappointment: Alabama’s 57% chance of defeating No. 7 Connecticut in the second round is not as high as you’d expect for a 2v7 matchup. It would be a massive disappointment if Alabama was knocked off that early, although it would be great for the Huskies, who would have a projected 55.28% chance of beating Texas in the Sweet Sixteen.

Sleeper Pick:  The team in this region that has the best shot at knocking off Michigan if they played is actually the No. 4 Florida State Seminoles. In this hypothetical matchup (which the model does not think will occur), the Seminoles would have a projected 43 percent chance of coming out on top, in which case they would advance to the Elite Eight to most likely play Texas or Alabama. The model projects that Florida State would have a 46% chance of winning both of those matchups — not an awful shot at a Final Four berth. Oddly enough, the No. 7 Huskies are actually projected to have a better chance (56%) at beating Florida State in an Elite Eight matchup. That would be an even more exciting run.

Most Probable First-Round Upsets: No. 12 Georgetown over No. 5 Colorado (35.09 percent chance)

South Region

Top Team: Baylor’s projected path is quite similar to Michigan’s in the East. Neither team is expected to dominate like Gonzaga, but they’re also not expected to have a particularly tough time. Unlike Michigan though, there’s no hypothetical interregionional matchup that poses a serious threat for an upset. Baylor maintains their high win probability against teams like Purdue, Arkansas, Texas Tech, etc.

Potential Disappointment: The model really doesn’t seem to love Arkansas. For whatever reason, the 15 seed Colgate Raiders are forecasted to have a 37.5 percent chance of defeating No. 3 Arkansas in the first round. Wow. And while Arkansas is still projected to advance to the second round, their run is expected to stop then with a loss to Texas Tech. A second round exit (and potential first round loss!) for a three seed would be a huge disappointment.

Sleeper Pick: The No. 6 Texas Tech Red Raiders are the obvious pick here. The model gives them the edge over No. 3 Arkansas and projects that they have a solid 43% chance at knocking off No. 2 Ohio State. Their chances at advancing to the Elite Eight aren’t bad at all. The bigger sleeper, though, is in the first round. Texas Tech actually only has a 53% chance of advancing to the second round, as the No. 11 Utah State Aggies are projected to have a favorable 47% win probability. That’s almost a coin flip. If they were to win, the Aggies would have a solid 45% chance of topping Arkansas in the second round to advance to the Sweet Sixteen. Not bad.

Most Probable First-Round Upsets:  No. 11 Utah State over No. 3 Texas Tech (47.27 percent chance), No. 14 Colgate over No. 3 Arkansas (37.50 percent chance)¹

Midwest Region

Top Team: The No. 2 Houston Cougars are the only two seed favored by the model to win their region and it’s not even that close. While Vegas gives the No. 1 Illinois Fighting Illini the second best odds to win the tournament, our model doesn’t even think their chances of beating Houston in the Elite Eight is above 35%. Houston would also be expected to crush teams like No. 7 Clemson, No. 5 Tennessee, No. 4 Oklahoma State, and No. 3 West Virginia if those matchups occurred.

Potential Disappointment: The No. 3 West Virginia Mountaineers are projected to lose in the second round to the No. 6 San Diego State Aztecs, and it’s not exactly a close call. The Mountaineers are only given a 32.6 percent shot at advancing to the Sweet Sixteen, and if they do, don’t expect them to go any further. Houston would have a 76% edge in such a matchup if it were to occur.

Sleeper Pick: The San Diego State Aztecs are clearly projected to make an impressive Sweet Sixteen run, although the model’s confident that they won’t go any further than that. Liberty and Syracuse are given decent chances to pull off first round exits, but they would both have bad to advance to the Sweet Sixteen after that. Tennessee would have a slightly better chance (64%) at beating Illinois than Oklahoma State, but not by much. All in all, don’t expect any massive surprises. The model likes the chances of a one seed versus two seed matchup in the Elite Eight.

Most Probable First-Round Upsets: No. 13 Liberty over No. 4 Oklahoma State (36.52 percent chance), No. 11 Syracuse over No. 6 San Diego State (39.35 percent chance), No. 10 Rutgers over No. 7 Clemson (51.94 percent chance)

Final Four

Michigan isn’t expected to have a great shot at defeating Gonzaga in the Final Four, and while the Baylor-Houston matchup is a tighter call, Houston still has a decisive 63% win probability. In the projected National Championship, Gonzaga has their toughest matchup of the tournament against the two seed Cougars, but they’re predicted to come out on top nonetheless. And with that, the Gonzaga Bulldogs are the projected 2021 champions of the college basketball world.

Afterword

It’s funny that this model is much improved since the 2019 version, yet it will almost certainly perform worse. Predicting the tournament is a very delicate thing — New Mexico State was two missed free throws away from making the Auburn Final Four prediction look very stupid. There are a few features of the model that were probably quite obvious to you already. For instance, it’s shy. The one seeds certainly have a greater than 90% chance of winning in the first round, but the model refuses to be so optimistic. There are also plenty of variables that are unaccounted for, such as injuries, the whole pandemic thing impacting the tournament, and other tournament results.²

In any case, I’m hopeful that I’ll be able to continue improving the model throughout the years just like I did this time around. Maybe it won’t finish in the 99th percentile of ESPN brackets, though.

If you’d like to see the model’s projections for matchups not listed above, you can search for them in table below which consists of 2,278 rows, one for every possible matchup. Just type the name of the two teams separated by a space. For instance, if you want to search for the Gonzaga-Baylor matchup, type “Gonzaga Baylor” into the search bar.

The post Forecasting the 2021 NCAA Division I Men’s Basketball Tournament appeared first on The Spax.

After a long, grueling journey, the Virginia Cavaliers emerged victorious in the 2019 NCAA men’s basketball tournament. It wasn’t a huge surprise — the Cavaliers had the second-best odds to be the ones cutting down the nets in Minneapolis. However, the events that led to this moment included plenty of shockers. For example, the Auburn Tigers reached the Final Four for the first time in team history after upsetting the North Carolina Tar Heels and the Kentucky Wildcats. Who could have predicted that? Well … we did.

Our statistical model excelled in its inaugural appearance. On ESPN’s Tournament Challenge, it finished in the 99th percentile of all brackets. That’s shockingly good for a purely statistical approach. A few weeks ago, we observed how the model stacked up against other objective techniques of bracketology after the first round. Now, we can take a look at the final results.

Other than a slip-up in the Round of 32, our model rose above the rest of the competition. Because of the enormous number of points rewarded to brackets which correctly predict the National Championship winner, I calculated the points accumulated before the national championship game as well as the real total. In the last column, you can see that other than our own model, every model performed at around the same level going into the final game. The final result just increased the gap.

While a final score of 1360 is undoubtedly amazing, there were obviously a few predictions which the model missed on. The most notable of which is likely the Texas Tech Red Raiders’ run to the National Championship. Our algorithm gave Michigan a 52.28% chance at beating the Red Raiders in the Sweet 16. In reality, Texas Tech came out on top by 19 points. Also, while our model gave the 12-seed Oregon Ducks a decent 42.03% chance at pulling off a first-round upset over the Wisconsin Badgers, it didn’t anticipate the Ducks advancing all the way to the Sweet Sixteen.

There are a few improvements which could be made to this model. It is currently made up of 30 weighted inputs, but that number could easily be increased. Also, the algorithm is essentially an example of machine learning — theoretically, it should improve every year as the dataset grows. In other words, the model should learn from its mistakes and adjust its formula to account for them. Of course, the problem with this idea is the amount of randomness and luck inherently ingrained into the tournament. Auburn could have easily lost to New Mexico State (seriously, though), in which case our entire model would have looked very stupid.

I also believe that this model could be used even more effectively if combined with actual human knowledge of college basketball. If Duke had won the tournament, one of my brackets (which were based on this model) would have finished with 1500 points. Considering I have nearly no actual knowledge of college basketball, that’s quite impressive. Maybe a college basketball fanatic could have pushed the limit even further.

It’ll be interesting to see how well the model performs in future years. Maintaining any consistency in a tournament called March Madness would be very impressive but not quite realistic. All we can say with certainty is that this algorithm was the most accurate of its kind in this year’s tournament. That’s pretty cool.

The post March Madness 2019: Grading Our Statistical Model’s Final Performance appeared first on The Spax.

With the NBA regular season coming to a close and the NBA playoffs right around the corner, the 14 teams that won’t make the playoffs will be finishing their draft evaluations in preparation for the draft on June 20th. There are many prospects coming out of college that look rock solid and NBA ready. However, Cam Reddish has emerged as the most hit-or-miss prospect in the draft by far, thus leaving many potential suitors at a quandary.

Reddish has been an enigma since he first entered the college scene. He has shown flashes throughout the season that he can be a major deep threat while also providing great and reliable defense on the other end of the floor. He has exemplified this in his performance on January 12th against Florida State in which he scored 23 points (with Zion Williamson injured for the majority of the game) and hit the game-winning three-pointer to give Duke a 14-1 record.

Expectations were high for Cam Reddish coming out of high school as a 5-star recruit and ranked third in the nation by ESPN. This past season, he averaged a disappointing 13.5 PPG on a dismal 35.6 FG%. However, there were several games in which he scored 20-plus points on a decent FG%. With teammates like R.J. Barrett and Zion Williamson, who were also top three in the nation coming out of high school and projected top-5 picks in the upcoming NBA Draft, it’s hard to stand out. But I believe that Reddish proved enough in college to be a lottery pick in the draft.

Reddish’s 6’8’’ frame makes him the prototypical build for a 3-and-D wing player. He’s a very streaky shooter and can catch fire in an instant, but there were games this past season in which he was ice cold. In fact, there were several stretches during the season in which he had a sub-50 FG%. These stretches are to blame for his poor total FG% for the season.

Even though his season statistics show that he isn’t NBA ready, I do believe that Reddish has the potential to be a great NBA player. In a system with two other ball-dominant players like R.J. Barrett and Zion Williamson, it’s difficult to showcase one’s basketball prowess. Under the right circumstances, I think that Cam Reddish can shine and prove that he belongs in the NBA.

The post The Cam Reddish Conundrum appeared first on The Spax.

Last week I posted a model which predicted the outcome of all 67 games of the 2019 NCAA Division I Men’s Basketball Tournament. With the first round in the books, now’s a good time to see how our algorithm fared against the most well-known predictive models out there.

The two most popular models used during March Madness were created by FiveThirtyEight and SportsLine. While FiveThirtyEight’s content is freely available for public use, SportsLine charges $9.99/month for their statistical models — one should expect the highest-quality analysis from them. I checked how accurate these models were through the first thirty-two games of the tournament. I also included the accuracy of two other methods to see if utilizing these models had any value over other common methods.

Method	Round of 64 Accuracy
The Spax's Model	22/32 (68.8%)
FiveThirtyEight's Model	21/32 (65.6%)
SportsLine's Model	21/32 (65.6%)
Picking the Vegas Favorite	21/32 (65.6%)
Picking the Higher Seed	20/32 (62.5%)

While our model was the most accurate, there’s not a significant margin between it and the other methods. So, what’s the point of using it? Well, the tight gap between our model and the other methods is partially due to the fact that the model rarely favors a double-digit seeded team; it just gives them relatively a relatively high chance of pulling off an upset. If a person used The Spax’s model but picked the lower-seeded whenever they are given a win probability of at least 45.0%, they would have accurately predicted the outcome of 27 of the 32 first-round games. That’s pretty good for a purely statistical model.

The five games that this method missed on are listed below.

Predicted Winner	Actual Winner	Actual Winner's Win Probability
(8) VCU	(9) UCF	37.30%
(7) Louisville	(10) Minnesota	30.44%
(5) Marquette	(12) Murray State	39.88%
(5) Wisconsin	(12) Oregon	42.03%
(4) Kansas State	(13) UC Irvine	36.96%

There are a few factors which made these upsets less surprising, but these factors are not accounted for in the model. It’s not easy to quantify the sheer ability of a superstar like Ja Morant to take over a game. Predicting Murray State to beat Marquette wasn’t an unpopular opinion because of Morant’s excellence. Also, the model doesn’t factor injuries into the equation. Dean Wade’s injury made Kansas State a threat to be upset by UC Irvine; lo and behold, the Wildcats lost. The Oregon Ducks were not an unpopular upset pick either — the five-seed Wisconsin Badgers were just two-point favorites. Oddsmakers also listed UCF as slight favorites, contrary to our analysis. The model failed to anticipate the likelihood of these games ending with the lower-seeded team on top.

Theoretically, though, our model should improve every year because the computer is given more data to use to predict future results. The model’s accuracy through the first round has been fairly promising considering that this tournament is its first time being used.

The post March Madness 2019: Grading Our Model’s First Round Predictions appeared first on The Spax.