Using Basic Statistics to fill out an NCAA Bracket Peter Legner [email protected] Math Resource...
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Transcript of Using Basic Statistics to fill out an NCAA Bracket Peter Legner [email protected] Math Resource...
Using Basic Statistics to fill out an NCAA Bracket
Peter Legner
[email protected] 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
Seed1
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Odds of AdvancingPast 2nd Round
Seed1
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Odds of AdvancingPast 3rd Round
Seed1
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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
Seed1
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602468
101214161820
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
1
2
3
4
5
5 0 1 1 1 2.5
0 5 1 1 1 1.5
1 1 6 1 1 0
1 1 1 6 1 1
1 1 1 1 6 0
r
r
r
r
r
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
1
2
3
4
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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
1 1 1 1 1 0
r
r
r
r
r
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
-30 -20 -10 0 10 20 30
-30
-20
-10
0
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30
Nearly Perfect Scatter Plot
r = .40
-15 -10 -5 0 5 10 15
-30
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0
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Colley Scatter Plot
r = .43
-10 -5 0 5 10 15 20
-30
-20
-10
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Massey Scatter Plot
LRMC
Also called Bayesian
Uses Markov probability
http://www2.isye.gatech.edu/~jsokol/lrmc/
r = .39
-5 0 5 10 15 20
-30
-20
-10
0
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LRMC Scatter Plot
r=.44
0 2 4 6 8 10 12 14 16
-30
-20
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0
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Vegas Scatter Plot
r = .47
-4 -2 0 2 4 6 8 10 12 14 16
-30
-20
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0
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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.