As I’m sure you’ve heard by now, Kentucky is really good at basketball. They're the only team in the country without a loss, and they have a realistic shot at becoming to first team to win the championship with an undefeated record since the 1976 Indiana Hoosiers. Under any ranking system you want to use, Kentucky is clearly the #1 team in college basketball.

Well, almost any ranking system.

All right, I have to confess that those rankings are from February 23. But still, Kansas had to lose six games before Kentucky finally moved ahead of them in the RPI. (Just a friendly reminder to ignore the RPI when filling out your brackets in March.)

Back to the question at hand: Kentucky is really good, but just how much better are they than top-ranked teams from previous years? To answer this question, I’ll use Minitab Statistical Software to dig into the Pythagorean rating from kenpom.com. Basically, this rating estimates what a team’s winning percentage "should" be based on the number of points they scored and allowed. Currently Kentucky’s Pythagorean rating is 0.9794. Last year, the #1 ranked team in the Pomeroy Ratings (Louisville) had a Pythagorean rating of 0.952. So even though both teams were ranked #1, we see that Kentucky is better due to the higher rating.

## Comparing Kentucky to Previous #1 Teams

So how does Kentucky stack up to previous teams? I took the top ranked team in the Pomeroy Ratings for every year since 2002 (since that’s as far back as the ratings go). I also took the ratings before the NCAA tournament, to best represent the point in the season that Kentucky is currently at.

The individual value plot above makes it plain how much higher Kentucky’s rating is than #1 teams in previous years. In fact, from 2002-2014, the #1 ranked team in the Pomeroy Ratings had an average rating of 0.9614 with a standard deviation of 0.0084. That makes Kentucky’s rating more than 2 standard deviations higher than the average #1 team. Impressive.

## How Will it Affect their Odds of Winning the Tournament?

The great thing about the Pythagorean ratings is that you can use them to calculate the probability one team has of beating another. So let’s see how different ratings change the probability of Kentucky going on a hypothetical run through the NCAA tournament. I noted where Kentucky is in the latest Joe Lunardi mock bracket, and obtained the Pythagorean ratings of the 6 teams they would have to face (assuming the higher seed advanced in each round). Then I calculated the probability of beating each team with a rating equal to the average #1 team, the previous high rating (Illinois in 2005), and the rating Kentucky currently has.

 Opponent Average #1 Team Illinois 2005 2015 Kentucky Sacramento St 97% 98% 98% Ohio St 76% 81% 86% Notre Dame 78% 83% 87% Wisconsin 58% 65% 73% Gonzaga 57% 64% 71% Virginia 47% 54% 63% Win the Championship 9% 15% 24%

Kentucky’s chances of winning the championship are 15 percentage points higher than the average #1 team, and 9 percentage points higher than the team that previously had the highest Pythagorean rating. But you’ll notice that their overall chance of winning is still only 1 out of 4...pretty low for what could be the greatest team ever. Of course, part of this is because I simply advanced the highest seed in each game, and that ended up being a brutal path. After Sacramento State, the remaining 5 teams are all in the Pomeroy Top 20 with 3 of them being in the top 6! And Virginia is so good they would actually be favored against the average #1 team!

But we know that upsets happen in the tournament. So what would their probability look like with a slightly easier path? Let’s take the teams #1 seed Florida would have had to beat to win the 2014 tournament. The ratings for our 6 opponents come from the final 2014 Pomeroy Ratings.

 Opponent Average #1 Team Illinois 2005 2015 Kentucky Albany 97% 97% 98% Pitt 76% 82% 86% UCLA 75% 80% 85% Dayton 86% 89% 92% Connecticut 71% 77% 83% Kentucky 73% 79% 84% Win the Championship 25% 35% 46%

Against an easier tournament run, Kentucky’s chances of winning are 21 percentage points greater than the average #1 team. That's huge! Kentucky will most likely be the biggest favorite ever in this year's NCAA tournament. But even against weaker competition (only 1 of these 6 teams finished in the Pomeroy Top 10, and they that team was only #8) Kentucky still has slightly less than a 50% chance of winning the championship. And that’s with their probability of winning each individual at 83% or higher!

This just shows how hard it is to win 6 straight games in a single elimination tournament. And Kentucky’s path might look a little closer to the first table. Because……..well……..

## Kentucky Has Company

Remember how Virginia would actually be favored against the average #1 team? That’s because despite being ranked #2 behind Kentucky, they are a very strong team. Not only is their Pythagorean rating higher than every other #2 ranked team from 2002-2014, it’s higher than 7 of the 13 #1-ranked teams!

I decided to look at every team in the top 10. I collected the ratings of the top 10 teams in the Pomeroy ratings (right before the NCAA tournament) from 2002-2014. For each ranking (1 through 10) I calculated the average rating, the third quartile, and the highest rating. For example, from 2002-2014 the average rating for the #2 ranked team was 0.9522, the third quartile was 0.9568, and the highest was 0.9589.

I then took the ratings of the current teams ranked in the Pomeroy top 10, and subtracted the values of teams from previous years. Virginia is currently the #2 ranked team with a rating of 0.9661. Since their rating is the highest of any #2 ranked team to come before them, their difference will be positive for the mean, third quartile, and the highest. Here are the results for the entire Pomeroy top 10, displayed in an Individual Value Plot created in Minitab Statistical Software:

Every team currently in the Pomeroy top 10 has a rating higher than the average for their ranking. Oklahoma (#9) is the only team with a rating less than third quartile for every other 9th ranked team. And, shockingly, 8 of the 10 teams in the top 10 have the highest rating of any similarly ranked team to come before them. The top-ranked teams are stacked. If you’re hoping this is the year that a 16 seed beats a 1 seed, don’t hold your breath.

Kentucky will still be an overwhelming favorite, but the data indicate that even against weaker teams their chances of winning would still be lower than 50%...and Kentucky’s top contenders this year are anything but weak. So don't think this is going going to be a cakewalk for the Wildcats.

After all, they don't call it March Madness for nothing.