Using Basic Statistics to fill out an NCAA Bracket Peter Legner Math Resource Center Specialist, College of Southern Nevada I am happy to share all slides and information shared in this presentation

Odds of Advancing Past 1stPast 2ndPast 3rdFinalFinalChampion RoundRoundRound42 1 Seed100%90%65%35%25%17.5% 2 Seed92.5%65%47.5%20%7.5%0% 3 Seed87.5%57.5%30%7.5%5%5% 4 Seed77.5%47.5%17.5%15%2.5%0% 5 Seed55%27.5%10%7.5%2.5%0% 6 Seed57.5%25%5%0%0%0% 7 Seed62.5%17.5%7.5%2.5%2.5%2.5% 8 Seed55%5%5%5%5%0% 9 Seed45%5%2.5%2.5%0%0% 10 Seed37.5%15%2.5%0%0%0% 11 Seed42.5%17.5%7.5%5%0%0% 12 Seed45%17.5%0%0%0%0% 13 Seed22.5%7.5%0%0%0%0% 14 Seed12.5%0%0%0%0%0% 15 Seed7.5%2.5%0%0%0%0% 16 Seed0%0%0%0%0%0%

Odds of Advancing Past 1 st Round

Odds of Advancing Past 2nd Round

Odds of Advancing Past 3rd Round

Odds of Advancing FINAL 4

Odds of Advancing FINAL 2

Odds of Advancing TO CHAMPION

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) = = +.25

Expected Value Regional Bracket:

T he 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 + z + 5 = yx – y + z = -5 x = z + 5x + 0y - z = 5

Colley and Massey Method For 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 63 CSN 72, Michigan 71 CSN 54, Louisville 52 UNLV 105, Duke 41 UNLV 93, Michigan 17 UNLV 76, Louisville 80 Duke 43, Michigan 40 Michigan 65, Louisville 59 Duke 78, Louisville 65 CSN is about to play UNLV What should we expect to happen??? 2015 Basketball Scores:

Colley Method only looks at wins vs losses CSN has a rating of.743 UNLV has a rating of.543 CSN 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 -7.7 UNLV has a rating of 35.9 UNLV should win by a margin of 44 points

Do the formulas actually work??? Colley Ratings: Massey Ratings: I Scatter Plot Diagram Compares 2 Variables Predicted Score vs Actual Score

r =.99

r =.40

r =.43

LRMC  Also called Bayesian  Uses Markov probability

r =.39

r=.44

r =.47

2013 Results: Colley: 50 Massey: 66 Sagarin: 71 Seeds: 68 Vegas: 71

2014 Results: Colley:64 Massey:59 Sagarin:57 Seeds:60 Vegas:62

Combined Results: Colley:114 Massey:125 Sagarin:128 Seeds:128 Vegas: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, “Generation Jobless: Students Pick Easier Majors Despite Less Pay,” by Joe Light, Wall Street Journal, November 9, “Tufts finds the right formula for math students,” by Julia Miller, Tufts Daily-Campus Newspaper, October 9, “Why Science Majors Change Their Minds”, by Stephen Drew, New York Times, November 4, “Solving America’s Math Problem,” by Jacob Vigdor, Education Next, Winter, “College Math on the Rebound,” by Mark Clayton, Christian Science Monitor, August 13, 2002.