Probability. It's really the heart and soul of most statistical analyses. Anytime you get a p-value, you're dealing with a probability. The probability is telling you how likely it was (or will be) for an event to occur. It has numerous applications across a wide variety of areas. But today I want to focus on the probability of a specific event.

I’ll be using the Sagarin ratings to determine the probability each team has of advancing in the NCAA tournament using a binary logistic model created with Minitab Statistical Software. You can find the details of how the probabilities are being calculated here.

Before we start, I’d also like to mention one other set of basketball ratings, called the Pomeroy Ratings. Both the Sagarin ratings and the Pomeroy ratings have shown to be pretty accurate in predicting college basketball games. But Ken Pomeroy always breaks down the tournament using his system. So instead of duplicating his numbers, I like to use the Sagarin ratings. But I’ll be sure to mention places where the two systems disagree, and you can select the one you want to go with!

Alright, enough with the small talk. Let’s get to the statistics!

# South

The following table has the probabilities each team in the South Region has of advancing in each round (up to the Final Four).

 Team 2nd Round Sweet 16 Elite 8 Final 4 (1) Kansas 99% 82% 65% 44% (2) Villanova 96% 66% 41% 21% (3) Miami FL 92% 50% 23% 9% (5) Maryland 83% 51% 15% 7% (6) Arizona 61% 32% 15% 6% (7) Iowa 83% 31% 14% 5% (4) California 75% 37% 10% 4% (9) Connecticut 63% 13% 7% 2% (11) Wichita St/Vanderbilt 39% 17% 6% 2% (8) Colorado 37% 5% 2% 0.5% (13) Hawaii 25% 7% 1% 0.2% (12) South Dakota St 17% 5% 0.5% 0.1% (10) Temple 17% 2% 0.4% < 0.1% (14) Buffalo 8% 1% 0.1% < 0.1% (15) UNC Asheville 4% 1% <0.1% < 0.1% (16) Austin Peay 1% <0.1% < 0.1% < 0.1%

Kansas is by far the favorite to come out of the South. Their probability is over twice that of the next most likely team. Kansas is also the highest rated team in both the Sagarin Ratings and the Pomeroy Ratings. However, even with all the considered, their probability of them going to the Final Four is still less than 50%. That means it's more likely that a team other than Kansas wins the South.

The next most likely team after Kansas is Villanova. But the selection committee did the Wildcats no favors. They'll likely face a very dangerous Iowa team in the 2nd round, and if they'll almost certainly face a good team if they get to the Sweet Sixteen. That's because the bottom half of the South bracket features six teams ranked in the Sagarin top 25 (Villanova, Miami, Arizona, Iowa, Vanderbilt, and Wichita State). It's absolutely stacked. Villanova is definitely the best team our of the six, but you really shouldn't be surprised if any one of those teams advance to the regional finals.

Things have the potential to get even more crazy if you look at the Pomeroy Ratings, which have Wichita State has the the 12th ranked team (ahead of Miami and Arizona)! They are 25h in the Sagarin ratings, but keep in mind for 3 of their early season losses, Wichita St was without their best player. The statistics don't know that, so Wichita St may even be better than their numbers indicate!

In the top half of the bracket, the 13 seed actually has a better chance of beating the 4 seed than the 12 seed has of beating the 5. In fact, the Sagarin ratings have California ranked 27th, which means they are a very overrated 4 seed (a theme you'll see coming for every Pac-12 team in the tournament). If you feel like picking an upset (especially if your bracket offers upset points) Hawaii over California isn't a bad choice at all. And the Pomeroy Ratings like Hawaii even more, giving them a 31.2% chance of winning as opposed to the 25% chance they have here. And even if you don't pick Hawaii in the first round, don't have California going too far. We see that the 5, 6, and 7 seeds all have better chances of making it to the Final Four than California.

If you like picking upsets in your bracket, but still want to pick a good Final Four team, a good strategy here might be putting Kansas in the Final Four and going chaos in the rest of the region. Iowa over Villanova, Hawaii over Cal, either Arizona or Vanderbilt/Wichita State over Miami. Whatever you like!

# West

 Team 2nd Round Sweet 16 Elite 8 Final 4 (2) Oklahoma 93% 71% 45% 27% (1) Oregon 98% 68% 40% 21% (3) Texas A&M 91% 62% 32% 17% (4) Duke 85% 51% 27% 14% (5) Baylor 71% 36% 17% 8% (6) Texas 72% 29% 12% 5% (9) Cincinnati 56% 20% 8.6% 3% (10) VCU 57% 17% 6% 2% (8) Saint Joseph's 44% 12% 5% 1% (7) Oregon St 43% 10% 3% 0.8% (12) Yale 29% 9% 3% 0.7% (11) Northern Iowa 28% 7% 2% 0.3% (13) UNC Wilmington 15% 4% 1% 0.1% (15) CSU Bakersfield 7% 2% 0.2% <0.1% (14) Green Bay 9% 2% 0.2% <0.1% (16) Holy Cross/Southern 2% 0.1% <0.1% <0.1%

The west is by far the weakest region in the tournament. Oklahoma is the only team ranked in the Sagarin top 10 (they're ranked 7th). Oregon is 15th, Duke is 16th, and Texas A&M is 17th. That means this region is wide open, and you would be fine taking any one of those 4 teams to advance. One caveat about Duke: the Pomeroy ratings have them all the way down at 22, and they have UNC Wilmington 15 spots higher than Sagarin does. According to Pomeroy, Wilmington has a 28% chance of upsetting Duke in the first round. And when you consider that Duke is usually picked often in most office pools (because everybody knows their name) it could be wise to avoid advancing Duke too far in your bracket.

While we're on the subject of upsets, the 10 seed in this region is actually favored over the 7 seed. So go ahead and pick VCU, especially if your pool gives bonus points for upsets. And Yale is another team to watch out for. The 29% chance they have here isn't bad for a 12 seed, but Pomeroy likes them even more, giving them a 39% chance of beating Baylor. An Ivy league team has won a game in the tournament 2 out of the last 3 years (and only lost by 2 points the year they didn't win a game). Yale has a great chance to make that streak 3 of the last 4 years.

And lastly, if you're going to pick a 1 seed to lose before the Sweet Sixteen, this is the region to do it. Cincinnati would have about a 33% chance of upsetting the Ducks if they played them. That's best chance you're going to have in any potential 1 vs 8/9 game. The only problem is, Cincinnati could absolutely lose their first game against Saint Joseph's. So it all comes down to how big of a risk you want to take!

# East

 Team 2nd Round Sweet 16 Elite 8 Final 4 (1) North Carolina 98% 83% 53% 36% (3) West Virginia 84% 65% 45% 22% (4) Kentucky 89% 50% 22% 13% (2) Xavier 92% 60% 29% 11% (5) Indiana 90% 47% 20% 11% (6) Notre Dame 54% 19% 6% 2% (10) Pittsburgh 50% 19% 6% 2% (7) Wisconsin 50% 19% 6% 2% (11) Michigan/Tulsa 47% 13% 5% 1% (8) USC 50% 9% 2% 0.7% (9) Providence 50% 9% 2% 0.7% (14) SF Austin 16% 7% 2% 0.3% (13) Stony Brook 11% 2% 0.2% < 0.1% (12) Chattanooga 10% 1% 0.1% < 0.1% (15) Weber St 8% 1% 0.1% < 0.1% (16) Florida Gulf Coast 2% 0.3% < 0.1% < 0.1%

Talk about top heavy! The top 5 seeds in this region are all ranked inside the Sagarin top 14. And the lowest ranked of those 5 teams is actually Xavier, coming in at 14. Xavier is a good team, but they're the worst 2 seed in the tournament. In fact, the winner of Pittsburgh/Wisconsin will have a good shot of knocking off Xavier before the Sweet Sixteen.

This all works out very well for West Virginia, who is ranked #6 in the Sagarin ratings despite being a 3 seed. Not only are they matched up with the weakest 2 seed in the tournament, they also have the weakest 6 seed in Notre Dame. However, where West Virginia got very unlucky is their first round game. Stephen F. Austin is a very good 14 seed. In fact, their Sagarin ranking of #57 is higher than every other 13 seed, three of the four 12 seeds, and even two of the 11 seeds! (Tulsa and Northern Iowa). And if that's not enough for you, the Pomeroy Ratings have them at #33 and give them a 30% chance of beating West Virginia. West Virginia can absolutely make a run to the final four, but they could lose their opening game too! Good luck deciding what to do with them in your bracket!

I mentioned earlier that Notre Dame is the worst 6 seed in the tournament. If Michigan wins the play in game, that 6/11 match up is basically a coin flip (the probabilities above for the 11 seed use Michigan's numbers). And if you want to find a Cinderella in this region, listen to this. According the Pomeroy ratings, Stephen F. Austin would actually be favored against Notre Dame, Michigan, or Tulsa! And even though Sagarin wouldn't favor SF Austin over Michigan or Notre Dame (although they would over Tulsa) they would have them as only 3 point underdogs! It's just a shame that SF Austin got such a hard 1st round opponent. But even despite that, they have a realistic chance of having that glass slipper fit.

In the top half of the region, things look pretty bleak for Cinderella. North Carolina should make the Sweet Sixteen and Kentucky and Indiana should both win their opening round games. But then things get tricky. Kentucky is ranked #8 in Sagarin and Indiana is #11. That's one heck of a 2nd round game! And the winner could absolutely beat North Carolina in the next round.

# Midwest

 Team 2nd Round Sweet 16 Elite 8 Final 4 (2) Michigan St 96% 81% 61% 37% (1) Virginia 99% 79% 52% 30% (5) Purdue 85% 58% 27% 14% (3) Utah 83% 43% 14% 5% (4) Iowa St 84% 35% 12% 5% (11) Gonzaga 54% 30% 11% 4% (6) Seton Hall 46% 23% 7% 2% (9) Butler 59% 14% 6% 2% (10) Syracuse 52% 10% 3% 0.8% (7) Dayton 48% 9% 3% 0.6% (8) Texas Tech 41% 7% 2% 0.5% (12) Arkansas LR 15% 5% 0.7% 0.1% (14) Fresno St 17% 3% 0.4% < 0.1% (13) Iona 17% 2% 0.3% < 0.1% (15) Mid Tenn St 4% 0.9% 0.1% < 0.1% (16) Hampton 1% 0.1% < 0.1% < 0.1%

A lot was said about Michigan St not getting a 1 seed, but they may be better off where they are. Utah is the weakest 3 seed in the tournament, and that's who  Michigan St is paired with. In fact, the highest ranked team Michigan St would have to play before the regional finals is the 11 seed! Gonzaga is ranked #22 in the Sagarin Ratings, and is actually favored over Seton Hall in the opening round. And if they win, the Sagrain Ratings would favor them over Utah too! If your pool gives you bonus points for upsets, you should absolutely have Gonzaga in your Sweet Sixteen. And if you don't get upset points, having any of Seton Hall/Gonzaga/Utah in the Sweet Sixteen is fine. But considering literally any of them could get there, the safe play would then have Michigan St beating whoever you picked.

I've mentioned several times now how the Pomeroy rankings have some of the lower seeds ranked higher than Sagarin does (Wichita St, Hawaii, SF Austin). The same is true here for Arkansas Little Rock and Iona. In fact, across the board all of the "mid-major" schools appear to be ranked higher in Pomeroy. And not just a few spots, in almost all cases the difference in the rankings is 15-20 spots. So while Sagarin gives both Iowa St and Purdue about an 85% chance of winning their opening game, their probabilities of winning are 75% and 71% in Pomeroy. I've been comparing these two rankings for a couple years now, and this is the first time something like this has happened. I'm not sure what to make of it other than Pomeroy will be predicting more first round upsets than Sagarin. So it'll be interesting after the tournament to go back and see which one was more accurate (although it's not like a handful of games are going to give us a definitive answer either way).

Anyway, if you're looking for a dark horse Final Four in this tournament, Purdue could be your answer. They are #9 in Sagarin and #10 in Pomeroy, which is very high for a 5 seed. According to Sagarin, they'd be about a 3 point favorite over Iowa St in the 2nd round, and only a 2 point underdog to Virginia in the Sweet Sixteen. And they beat Michigan St earlier in the season too. You could do worse than Purdue in the Final Four. Of course, they could also lose in the first round to Arkansas Little Rock, especially if the Pomeroy ratings are more accurate! But, that's the chance you taking going with a 5 seed.

If you want to play it safe, the way to go is Virginia vs. Michigan State in the regional finals. That game would be a coin flip, so feel free to take either team. Michigan State has actually knocked Virginia out of the NCAA tournament the last two years. Could the third time be the charm for Virginia, or will the Spartans continue to haunt them?

# Final Four

 Team Final Four Semifinal Champion (1) Kansas 44% 30% 18% (2) Michigan St 37% 22% 13% (1) North Carolina 36% 20% 12% (1) Virginia 30% 16% 9% (2) Villanova 21% 13% 7% (2) Oklahoma 27% 13% 6% (3) West Virginia 22% 11% 6% (1) Oregon 21% 8% 3% (5) Purdue 14% 6% 3% (4) Kentucky 13% 6% 3%

The top 5 ranked teams in the Sagarin ratings are Kansas, Michigan State, North Carolina, Virginia, and Villanova. So it's no surprise that those teams have the top 5 probabilities of winning the entire tournament. But it's really wide open. Kansas is the best team, and only has a 18% chance of winning the title. That's a far cry from the 41% chance Kentucky had as the top team last year. So when you pick your champion, try and think about who other people entering your pool will choose. You want to try and pick a champion that few other people will pick (but still has a realistic shot). Do you live in Michigan? Then you should probably avoid Michigan State. Live in ACC country? Then maybe don't go with North Carolina or Virginia. And in general, you should avoid the high seeds that are overrated (Oregon, Xavier, Utah). But other than that, the choice is yours. Good luck and let the madness begin!