March Madness Statistics

I have been pondering a question posed by one of our fellow students today: What is the odds at picking a perfect march madness bracket? I'd like to try to answer that using our understanding of statistics. I'd also like to talk about the odds of picking the overall winner, which is obviously much easier. Lets do that first!

There are 64 teams in the bracket, so on first glance you would think that you have a 1 in 64 chance of picking the correct team. This is assuming all teams are just as likely to win. Historical data tells us otherwise! For instance, my alma mater Bucknell is an 11 seed which historically says they only have a 33% chance of beating 6 seed Butler. (Although in 2005 as a 14 seed they beat the odds winning over 3 seed Kansas). That being said, #1 seeds are basically 100% to win the first round, so picking a 1 seed to win it all is more like a 1 in 32 shot or a 3% chance. Now for the fun stuff, lets talk about a perfect bracket!

First of all, we need to know how many games there are:
32 in round 1; 16 in round 2; 8 in round 3; 4 in round 4; 2 in round 5; the championship
That is a total of 63 games, each with two possible outcomes. This means that we can choose one of two options 63 times. The total possible outcomes is therefore 2⁶³ or 9 x 10¹⁸! This means that to pick a perfect bracket randomly is IMPOSSIBLE! Lets assume everyone in the world ( 7 billion people ) each plays a bracket randomly every year. It would still take a BILLION years worth of tournaments to to get just one bracket that is perfect. But that is with random selection and most of us can pick better than that.

Historically speaking you can predict all the first round games with 75% accuracy. This means that for the first 32 games you have a 0.75³² or 1 in 9955 chance of picking correctly. However, you still have 31 more games to pick and each of these are basically a toss up. That means you have a 1 in 2³¹ (about 2 billion) chance of getting it right from here on. However, for the perfect bracket you need to pick the first 32 AND the second 31 games correctly. All in all you are still looking at a chance of 1 in 21 trillion to put together a perfect bracket. That means if everyone in the world played every year it would still take about 3,000 years for one person to get a perfect bracket. Good luck though!

How does a plane fly?

A lot of people think Bernoulli's Principle (moving fluids exert less pressure than static fluids) is true and that it is why planes fly. First, lets make sure it is true:

If we accept Bernoulli's Principle as true, it typically gets applied to flight like this:

But if that were the case, turning the wing upside down would cause planes to drop from the sky incredibly fast (even faster than in free fall). However, this doesn't happen. For instance, planes shouldn't be able to do this:

So what is the problem? Is Bernoulli's Principle true? Is it why planes fly? Does it have nothing to do with planes? Is there something else that also needs to be considered?

Pascal and Archimedes

Blaise Pascal (1623-1662) was a mathematician, physicist, philosopher, etc. He came up with, what we now call, Pascal's Principle: Pressure is transmitted undiminished in a fluid. Basically, this means that if you push on a fluid, that push is felt everywhere in the fluid. This can be demonstrated quite easily with The Blob.

Archimedes came around significantly earlier than Pascal (287 BCE - 212 BCE) but was a similarly accomplished mathematician, physicist, philosopher, etc. He came up with what we now call Archimedes Principle: The buoyant force on a body immersed in a fluid is equal to the weight of the fluid displaced. Here is a short Ted Ed video describing how Archimedes got started working on this principle. In FACT his method could be extremely useful for you in trying to measure volume for your A assignment.

Will It Float Results

Here are some examples of different techniques used for the Will It Float Competition. Below are the results. Post as a comment the properties of the materials that were MOST useful.

1-1: 170g     1-2: 100g     1-3: 250g     1-4: 240g

2-1: 300g     2-2: 220g     2-3: 300g     2-4: 200g

5-1: 200g     5-2: 150g     5-3: 110g     5-4: 70g

Here are some extra examples of the Ideal Gas Law in action:

Liquid Nitrogen is extremely cold. Watch what happens when it is poured on top of a balloon.

Here is a demonstration of a Fire Piston in action. A sealed compartment is shrunk incredibly small very quickly. Look at the effect at around 45 seconds into the video.

Lastly, check out this video of a glass beaker being heated up to extremely hot temperatures. Eventually it is exposed to a pool of cool water, you'll be shocked with what happens!