Do you make this mistake with your March Madness pool?

You want to win your March Madness pool

 

You know that numbers can help. For example, the higher ranked team in The Power Rank has won 71.4% (650-261) of tournament games over the last 14 years.

 

Then winning your pool is simple.  Fill out your bracket with the higher ranked team in each game.

 

Most years, your bracket will look boring, and you might stab yourself in the eye from having to repeatedly cheer for Kansas and Duke.  But analytics will carry you to a glorious win, right?

 

No.  Analytics can’t help if you enter the wrong pool.  To explain, consider this analogy.

 

Drunks throwing darts at a dartboard

 

You and a friend walk into a bar and find the employees of a start-up company there.  They have just secured their Series A funding from a venture capital firm and feel good about their future.  In anticipation of becoming millionaires, they start throwing back flutes of Champagne.

 

After a few too many drinks, the workers from the company congregate near a dartboard.  Against better judgment, they decide to play a game.

 

Each person gets one throw at a dartboard.  Hit the bullseye and earn a free drink.

 

You laugh at the spectacle, thinking that not a single person will hit the bullseye.  It doesn’t matter that the bar has installed a magnetic field that directs all errant darts back toward the dartboard.  Great for safety, but the bar still won’t be serving up any drinks.

 

Your friend bets you that someone will hit the bullseye.  Should you take the bet?

 

It depends on the number of people lined up to throw a dart.  Let’s assume that a dart from a drunk person has an equal chance of landing anywhere on the dartboard thanks to the magnetic field.  The odds that any one drunk hits the bullseye is small, about 0.5%.

 

However, to win your bet, you need every drunk person to miss.  There is a 99.5% probability that the first drunk misses, but you must multiply 0.995 by 0.995 to get the likelihood that both the first and second drunk miss.  If the company has 20 drunks that step up to fling a dart, there’s a 90.5% chance that all of them miss.  This implies a 9.5% chance that at least one drunk hits the bullseye.

 

For an increasing number of drunks, the probability that at least one hits the bullseye increases rapidly.  At 100, there’s a 39.4% chance for someone to hit the bullseye, and this probability increases to 86.5% for 400 people.

 

How win probability decreases with pool size

 

The same principle of luck applies to your March Madness pool.

 

To show this, I’ve performed simulations of past tourneys.  These Monte Carlo calculations, which are used to study topics such as polymer fluids and the stock market, capture two types of randomness in your pool.

 

Randomness in basketball games.  The simulation uses my numbers at The Power Rank to assign a win probability for each game. Randomness in pools.  The simulation uses data from ESPN to estimate the types brackets that others will submit to your pool

 

Based on these two factors, I can calculate your win probability for filling out a bracket with higher ranked teams by my numbers.  The visual shows representative results from 2010, a year in which your bracket would have Kansas over Duke in the title game.  Other years look the same.

 

poolsize_winprob

 

By picking all favorites, you have a 38% chance to win a 10 person pool.  You’ll win about every other year, which is pretty good.  If winning is your only goal, enter a small pool.

 

For a 30 person pool, your chance of winning the pool drops to 16%.  With your choice of Kansas as champion, there are enough others in your pool with this choice that someone else will win based on luck in picking earlier games.

 

For a 100 person pool, your probability to win a pool drops to 5%.  A 400 person pool?  I’m not even going to do the calculation.  Don’t enter a pool that big.  Even with the best analytics, you’d be better off lighting your entry fee on fire.

 

Ed Feng is the founder of The Power Rank.  He has much more bracket advice in his book How to Win Your NCAA Tournament Pool.

 

The #1 Tip for Winning Your NCAA Tournament Pool

 

The #1 Tip for Winning Your NCAA Tournament Pool

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