There are just 3 games left in the 2012 NCAA basketball tournament. This means we have 64 games that we can do some data analysis on! So before the games get underway this weekend, I'm going to use Minitab to break down the some of the craziest things that happened in this year's tournament.

How do I define crazy? Well, since I'm a stat nerd, I'm going to use probability! The lower the probability, the crazier the event. All of these probabilities are based on predictions by the regression model I developed over the last few weeks.

**NOTE:** The regression model calculates probabilities based on where the two teams are ranked in the LRMC rankings. However, the LRMC rankings stopped updating after Selection Sunday. So all probabilities are based on where the teams were ranked *before *the tournament started.

# 6: All of the #1 seeds reached the Sweet 16 (21%).

Wait, doesn’t this happen every year? Um, no. Remember Butler last year? Or how about Northern Iowa two years ago? The fact is that 8 games have to be won for all the 1 seeds to reach the sweet sixteen. Now, we know that 1 seeds are 112-0 in the first round (more on that later), but that second round game is no gimmie.

This year each 1 seed had a 85% chance or better of beating their 16 seed, and a 69% chance or better of beating their respective 8/9 seed. But when you multiply all those probabilities together, the odds of the 1 seeds going 8-0 was only 21%. And the really surprising part is the closest a 1 seed came to losing was Syracuse to UNC-Asheville.

# 5. Ohio won 2 Games (20%).

Ladies and Gentlemen, playing the role of Cinderella tonight will be none other than the *Ohio Bobcats!* Yes, this was surprising, but not as surprising as you might think, which is why it’s only #5. The model said Ohio had a 39% chance of beating Michigan, and a 51% chance of beating South Florida. That comes out to odds of 1 in 5. So the odds were against the Bobcats, but they definitely had a reasonable chance.

Things would have been *really *crazy if they'd beat North Carolina. The model only gave them a 15% chance of upsetting the Tar Heels. But D. J. Cooper's half-court shot was just off to the right and Ohio fell in overtime, which meant the clock struck midnight for Cinderella.

# 4. All of the #3 seeds won in the first round (11%).

Okay, this is where I take my beating for talking up Belmont so much. The model gave the Bruins a 57% chance of beating Georgetown, which brings this probability down a bit. But even so, they weren't the only 14 seed with a shot at an upset.

Marquette, Baylor, and Florida St had chances of 61%, 62%, and 70% of winning their first round games. So even when you remove Belmont, the odds of all 3 of those teams winning is still only 26%. South Dakota State and St. Bonaventure came close, but no 14 seed pulled an upset. Still, things didn't work out well for the victors, as two of the 3 seeds lost their next game. And the only 3 seed to reach the Elite Eight (Baylor) got there by playing three double-digit seeds. Their reward was playing a Kentucky team that is pretty good at basketball.

# 3. Two #15 seeds won a game (6%).

We can't just multiply the odds of Lehigh and Norfolk St winning and call it a day because there were 2 *other *15 seeds that could have won. In all, there were 6 different ways that two 15 seeds could have won a game. The table below breaks down the combinations and the probability of each. Then we add the probabilities together to get the overall probability!

Teams | Probability | Approximate Odds |
---|---|---|

Lehigh and Detroit | 1.75% | 1 in 57 |

Lehigh and Loyola MD | 1.5% | 1 in 67 |

Lehigh and Norfolk St | 1.5% | 1 in 67 |

Detroit and Loyola MD | 0.42% | 1 in 238 |

Detroit and Norfolk St | 0.42% | 1 in 238 |

Loyola MD and Norfolk St | 0.36% | 1 in 278 |

Any two teams | 6% | 1 in 17 |

I'm sure most years a 15 seed doesn't have as good of a shot at winning as Lehigh did this year. So expecting two 15 seeds to win a game once every 17 years is probably a bit low. In other words, enjoy the fact that it happened this year, because it will probably be a long time before you see it again!

# 2. Louisville made it to the Final Four (3%).

Of the 64 games in the tournament, the regression model predicted that in 24 of them the favorite would win between 50% and 59% of the time. This is why the tournament is so hard to predict. Imagine flipping a coin 24 times and trying to call each one correctly. I know a team with a 51%-59% chance of winning has a somewhat better chance than a coin flip, but really, these games could still go either way. Unless, of course, you're Louisville.

The model said 3 of the Cardinals' 4 games would be coin flips. And Louisville won them all. They were favored against Davidson (winning 56% of the time) and underdogs to New Mexico and Florida (winning 42% and 49% of the time). The odds were stacked against them when they played Michigan St, as the model gave Louisville a slim 27% chance of winning. If you multiply the probability that Rick Pitino's team had of winning all 4 of their games, you get a probability of 3%. Now this isn't as crazy as Butler or VCU's run last year, but they are by far the biggest long shots of the 2012 tournament.

# 1. A #16 seed didn't beat a #1 seed (let's just say its low).

The craziest thing that happened in the 2012 tournament is that a 16 seed *didn't* beat a 1 seed. Let me explain, it'll blow your mind. There were four games that involved a 16 seed and a 1 seed. Here are the probabilities that the 16 seeds had of winning:

- Western Kentucky - 2%
- LIU Brooklyn - 6%
- Vermont - 10%
- UNC Asheville - 15%

The odds that all 4 of these teams would lose to their respective 1 seeds was 70%. What is so crazy about that? Well, I'm going to cheat a little and re-word my first sentence in this section: It's not crazy that a 16 seed didn't beat a 1 seed *in the 2012 tournament*. No, what's crazy is that after the 2012 tournament, a 16 seed has still *never *beaten a 1 seed!

The tournament expanded to 64 teams in 1985, and since then there have been 112 games between a 1 seed and 16 seed. So what are the odds of the 1 seeds going 112-0? Well, this year wasn't typical, as 16 seeds usually aren't as good as Vermont and UNC-Asheville. So let's say that, on average, a 16 seed has a 5% chance of beating a 1 seed. So the probability that 1 seeds would go 112-0 is

0.95^112 = 0.0032 = 0.32% = **1 in 313**

What?!?! Are you kidding me?!?! This can't be right! One seeds must have had a better than 95% chance of winning. Let's look at some other values.

Probability of 1 Seed Winning | Probability of going 112-0 | Approximate Odds |
---|---|---|

96% | 1% | 1 in 97 |

97% | 3.3% | 1 in 30 |

98% | 10% | 1 in 10 |

99% | 32% | 1 in 3 |

So even if we assume that *every single #1 seed, ever* had a 99% chance of winning (which I think is ridiculous), the odds *still *say a 16 seed would win at least one game 68% of the time. Seriously, how has this not happened yet?!?!?! Sooner or later it must happen. But until then, the lack of a 16 seed beating a 1 seed will continue to be the craziest thing in the NCAA tournament.

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