A Little Bit of March Madness Math

I wrote this piece with my 16 year old son, Jack.  Prior to putting our thoughts on “paper”, he kept repeating, “Mom, when are you gonna be ready to collaborate?”  Not something I often hear from my teenager.  His words were music to my ears and I wanted to procrastinate just to hear those words a few more times.

What’s his urgency?  He’s a teenager, so we know it’s not the opportunity to work with his mom.  His real motivation stems from his love of college basketball. It’s March and the NCAA Men’s Basketball Tournament begins in a few days.

March Madness has taken over the house. The pre-tournament championships are on TV, discussions and debates of the bubble teams fill the air and both father and son are glued to various electronic devices in an attempt to retrieve the most recent updates.  The tournament starts on Tuesday March 17th with the play in games.  And if we are to collaborate, then our deadline to post is the morning of March 19th – before the round of 64 begins.

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The post’s inception:

About a month ago, I tossed out the idea of working together on a blog post. It went down like this…

Me: Maybe we could work together on a March madness post …  if you’re interest.

Jack: What would it be about?

Me: The probability of winning.

Taking a pic w/ mom is so painful 🙂

Jack:  (Just looks at me)

Me:  Theoretically each team has a 1/64 chance of winning.

Jack:  WHAT!?!? NO! NO! NO! Mom, a 16th seed has NEVER beaten a #1 seed since the field was expanded to 64 teams in 1985.

Me:  Smiling and thinking, ” I got him”

That interaction solidified the collaboration.

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Using the Fundamental Counting Principle, I’ll explain the theoretical aspect of the bracket breakdown – viewing it as if all teams had equal ability. Then Jack gets to have fun debunking that viewpoint with his extensive knowledge of college basketball.

Discussion of the Outcomes

Once the field of 64 teams has been decided on, a team must win 6 games in order to claim the title.

Game 1               G2                 G3                 G4                 G5                      G6                           Round               Round             Sweet               Elite               Final                   Final                          of 64                   of 32                 16                      8                     4               Championship

Fundamental Counting Principal

For each game (aka event), there are 2 possible outcomes:                                                                       a.  Outcome 1:  The team wins                                                                                                              b.  Outcome 2:  The team loses

Game 1          G2             G3             G4             G5             G6     =   Total Outcomes                   2        •         2        •        2        •        2       •         2       •       2                           64

Only 1 team out of the 64 will have the following outcome:                                                                                                                                                                                            Game 1          G2             G3             G4             G5             G6     =       Ending Outcome        Win              Win            Win            Win            Win             Win                 NCAA Champs

Their opponent has the following outcome, which again only 1 team out of 64 could possibly get:                                                                                                                                               Game 1          G2             G3             G4             G5             G6     =       Ending Outcome        Win              Win            Win            Win            Win            Lose                 Runner ups

As I thought more about the outcomes, I knew I had to factor in the single elimination aspect of the tournament.  Once a team loses, they’re out.  They can’t play anymore games. So in reality, there are less than 64 actual outcomes.  They are:

Ending         # of Teams w/ Game 1       G2          G3          G4          G5         G6     =        Result           this Outcome  lose               n/a          n/a          n/a          n/a           n/a                   out                            32

win               lose          n/a          n/a          n/a           n/a                   out                            16

win               win          lose          n/a          n/a           n/a                   out                            8

win               win          win          lose          n/a           n/a                   out                            4

win               win          win          win          lose           n/a                out but                        2                                                                                                                        regional champs

win               win          win          win          win           lose              out but                          1                                                                                                                         regional champs

win           win          win           win             win            win       NCAA Champions            1                                                                                                                                                            64 Teams

Because of the single elimination aspect, there are actually only 7 possible outcomes that collectively occur 64 times – which is why a team, not taking into account ability, has a 1/64 chance of winning the NCAA Men’s Basketball Tournament.

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Now for Jack’s part:

The facts listed below clearly show that not every team has an equal chance of winning the NCAA tournament. All facts are based on the tournaments that occurred since the field expanded to 64 teams in 1985

1.  The 16th seed has never beaten the number 1 seed.  Based on this fact, there is one team per region that has a 100% chance of moving onto the round of 32.

2. The chance that a 15 seed beats a 2 seed is also         very low.                                                                                      a.  A 15 seed has beaten a 2 seed only 7 times.                b.  And only 1 of those 7 times has a 15 seed                        advanced to the sweet sixteen.                                           (Florida Gulf Coast, 2013)

3.  A No. 1 seed has won the tournament  19 times.       That’s a rate of 63 percent which is quite high.

4. The lowest seed to win it all was 8th seeded Villanova in 1985.

5.  As I said above, an 8 seed is the lowest seed to win it all. It’s also the lowest seed to advance to the final game. On two other occasions, Kentucky in 2014 and Butler in 2011, went to the final but lost.

6.  At least one No. 1 seed has been to the Final Four in all but 2 of the Final Fours.

7. The lowest seed to advance to the Final 4 was an 11 seed and that’s happened 3 times.           a. The first time was in 1986 with LSU.                                                                                               b. The second time was with George Mason in 2006 and                                                               c. The last time was with VCU in 2011.

8. In the first round of the NCAA tournament, the higher seed has won Its games more times than it has lost. Even with that, there are still plenty of upsets in this round. As of today, 3/20/15, two 14 seeds have beaten 3 seeds.

Insights to the 2015 tournament:

1. For the second consecutive year, a team has entered the NCAA tournament unbeaten. Last year it was Wichita State. This year it’s Kentucky.

2.  Kentucky actually beat Wichita State in the Round of 32 last year to end Wichita’s perfect  season.

3. No team has finished the entire season unbeaten since Indiana in the 1975-1976 season.

4.  During that season, Indiana went 32-0, 8                   fewer games than Kentucky would have to play                                                                             in order to  go unbeaten. UK is already 34-0 and would play six games in the NCAA Tournament if they want to go to the final.