Using Basic Statistics to fill out an NCAA Bracket

Peter Legner

peter.legner@csn.eduMath Resource Center Specialist, College of Southern Nevada I am happy to share all slides and information shared in this presentation

Odds of Advancing

Past 1st Past 2nd Past 3rd Final Final Champion Round Round Round 4 2

 1 Seed 100% 90% 65% 35% 25% 17.5%2 Seed 92.5% 65% 47.5% 20% 7.5% 0%3 Seed 87.5% 57.5% 30% 7.5% 5% 5%4 Seed 77.5% 47.5% 17.5% 15% 2.5% 0%5 Seed 55% 27.5% 10% 7.5% 2.5% 0%6 Seed 57.5% 25% 5% 0% 0% 0%7 Seed 62.5% 17.5% 7.5% 2.5% 2.5% 2.5%8 Seed 55% 5% 5% 5% 5% 0%9 Seed 45% 5% 2.5% 2.5% 0% 0%10 Seed 37.5% 15% 2.5% 0% 0% 0%11 Seed 42.5% 17.5% 7.5% 5% 0% 0%12 Seed 45% 17.5% 0% 0% 0% 0%13 Seed 22.5% 7.5% 0% 0% 0% 0%14 Seed 12.5% 0% 0% 0% 0% 0%15 Seed 7.5% 2.5% 0% 0% 0% 0%16 Seed 0% 0% 0% 0% 0% 0%

Odds of AdvancingPast 1st Round

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Odds of AdvancingPast 2nd Round

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Odds of AdvancingPast 3rd Round

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Odds of AdvancingFINAL 4

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Odds of AdvancingFINAL 2

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Odds of Advancing TO

CHAMPION

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Expected Value:

Sum of (percent chance of winning/losing times pay off for each possibility)  Example:

You pay me $1 to watch me flip a coin twice. If it comes up heads both times, I give you back $5.

Expected Value: EV = (3/4 times -$1.00 plus ¼ times +$4.00) = -.75 + 1.00 = +.25

Expected Value Regional Bracket:

The CSN basketball team scores 65 points in one game. The number of two point shots they make is 5 more than the number of 1 and 3 point shots they make. They make 5 more 1 point shots than they make 3 point shots. How many shots of each type did they make?

x + 2y + 3z = 65 x + 2y + 3z = 65x + z + 5 = y x – y + z = -5 x = z + 5 x + 0y - z = 5

Colley and Massey MethodFor a more detailed explanation

Mathematics and Sports, Edited by Joseph Gallian

Chapter 5, “Bracketology”By Tim Chartier, Erick Kreutzer, Amy Langville, and Kathyrn Pedings

Colley Method

Each game a team played is evaluated on whether they won or lost and on the strength of the team they played

A win over a ‘bad’ team does not count as much as a win over a ‘good’ team

A loss to a really good team is not that bad

CSN 65, Duke 63CSN 72, Michigan 71CSN 54, Louisville 52 UNLV 105, Duke 41

UNLV 93, Michigan 17UNLV 76, Louisville 80

Duke 43, Michigan 40Michigan 65, Louisville 59

Duke 78, Louisville 65

CSN is about to play UNLVWhat should we expect to happen???

2015 Basketball Scores:

Colley Method only looks at wins vs losses

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5 0 1 1 1 2.5

0 5 1 1 1 1.5

1 1 6 1 1 0

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CSN has a rating of .743UNLV has a rating of .543CSN should win

Massey Method Each game a team played is evaluated on the point

spread of victory or defeat and on the strength of the team played

A close win over a ‘bad’ team is not favorable A close loss to a ‘good’ team is favorable

Massey Method looks at margin of victory

CSN has a rating of -7.7UNLV has a rating of 35.9UNLV should win by a margin of 44 points

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3 0 1 1 1 5

0 3 1 1 1 136

1 1 4 1 1 74

1 1 1 4 1 50

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Do the formulas actually work???

Colley Ratings: http://www.colleyrankings.com/hcurrank.html

Massey Ratings: http://www.masseyratings.com/rate.php?

lg=cb&sub=NCAA I

Scatter Plot Diagram Compares 2 Variables Predicted Score vs Actual Score

r = .99

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Nearly Perfect Scatter Plot

r = .40

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Colley Scatter Plot

r = .43

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Massey Scatter Plot

LRMC

Also called Bayesian

Uses Markov probability

http://www2.isye.gatech.edu/~jsokol/lrmc/

r = .39

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LRMC Scatter Plot

r=.44

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Vegas Scatter Plot

r = .47

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Sagarin Scatter Plot

2013 Results:

Colley: 50 Massey: 66 Sagarin: 71 Seeds: 68 Vegas: 71

2014 Results:

Colley: 64Massey: 59Sagarin: 57Seeds: 60Vegas: 62

Combined Results:

Colley: 114Massey: 125Sagarin: 128Seeds: 128Vegas: 133

Articles on Engaging Students in Math Classes:“Why More Americans Don’t Major in the Math and Science,” by James Joyner, Outsidethebeltway.com, November 9, 2011.

“Generation Jobless: Students Pick Easier Majors Despite Less Pay,” by Joe Light, Wall Street Journal, November 9, 2011.

“Tufts finds the right formula for math students,” by Julia Miller, Tufts Daily-Campus Newspaper, October 9, 2007.

“Why Science Majors Change Their Minds”, by Stephen Drew, New York Times, November 4, 2011.

“Solving America’s Math Problem,” by Jacob Vigdor, Education Next, Winter, 2013.

“College Math on the Rebound,” by Mark Clayton, Christian Science Monitor, August 13, 2002.