Wednesday, August 12, 2020

Bracketology

We congratulate both the women’s and men’s basketball teams from the University of Maryland, College Park, on being selected to the NCAA basketball tournament this spring. The men, hoping to get to Indianapolis for a championship game on April 6, will face Valparaiso in the Second Round on March 20. The women, who are seeded on top of the West bracket and hope to get to Tampa for a championship game on April 7, will face New Mexico State on March 21.

We also take this opportunity to express our support for college athletes, who receive no financial compensation for playing, despite the millions of dollars their coaches are paid and the tens of millions of dollars they bring in for many of the top sport-centered universities.

In case any teachers among our readers were trying to make a geometry problem out of basketball, we provide the following dimensions for reference, as supplied by the NCAA:

Distances on an NCAA basketball court

• Court length: 94 feet (about 2.87 m)
• Court width: 50 feet (about 1.52 m)
• Length of each coaching box: 28 feet (about 853.4 cm)
• Backboard width: 6 feet (about 183 cm)
• Baseline to backboard: 4 feet (about 122 cm)
• Width of lane: 12 feet (about 366 cm)
• Baseline to free throw line: 19 feet (about 579 cm)

• Hoop: 9 inches (about 22.9 cm)
• Center circle: 6 feet (about 183 cm)
• Center of hoop to 3-point line: 19 feet 9 inches (about 602 cm)
• Semicircle at top of key: 6 feet (about 183 cm)

The circumference of a basketball must be between 29½ and 30¼ inches. How many grip dots are on an average regulation basketball if there are 122 grip dots per square inch? Then, determine the minimum and maximum volumes of a regulation basketball. See Common Core eighth-grade geometry standard 8.G.C.9 for more information.

The formulas below apply to spheres:

$V = \frac{4}{3} \pi r^3$
$r = \sqrt[\leftroot{-2}\uproot{2}3]{\frac{V}{\frac{4}{3} \pi}}$

For high school, do some statistical analysis

It is interesting to note that very few top seeds have ever lost a game in the Round of 64. In fact, very few have ever lost a game in the Round of 32.

Writes Ian Powers in the New York Daily News:

When you start your bracket, just place the Nos. 1 and 2 seeds in the second round. In fact, place your 1-seeds in the third round. Since 1985, 1-seeds are 120-0 and 2-seeds are 113-7 in the first round. 1-seeds are 104-16 in second-round games.

He goes on to provide statistical advice for choosing the winners of games in the tournament. (He only works with the men’s tournament.)

However, he ultimately advises those who fill out brackets to put the math in a secondary role: “One thing I want to stress is that numbers alone do not beat the eye test. That is where a team like Kentucky separates itself this season.”

Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more information, see the About page.

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