ANSWER KEY
Shooting Hoops
1. (1-pointer) What percentage of 1-pointers were made by our class? How about 2-pointers? 3pointers? (Answer: divide the number made by the number attempted in each category)
2. (2-pointer) What percentage of overall shots were made by the class? (Answer: divide the number
made by the number attempted)
3. (3-pointer) What strategy appears to be the best? For example, should a student shoot all 1-pointers,
or all 2-pointers, or all 3-pointers?
Answer: Most students should make about 90% of the 1-pointers, about 60% of the 2-pointers, and
about 25% of the 3-pointers. Individual classes will vary. However, if they shoot five 1-pointers, they
would expect to make 0.90 x 5 = 4.5 shots x 1 point each = 4.5 points. If they shoot five 2-pointers, they
would expect to make 0.60 x 5 = 3 shots x 2 points each = 6 points. If they shoot five 3-pointers, they
would expect to make 0.25 x 5=1.25 shots x 3 points each = 3.75 points. So, the average student would
score the highest taking all 2-point shots.
Bracket word problems
A. (1-pointer) If there are 64 teams, how many games are played in the entire tournament? (Answer:
63, since each team but one loses)
(2-pointer) If they played a double-elimination tournament, how many games would be played?
(Answer: 126 or 127, since 63 teams lose twice and the winner may lose once)
(3-pointer) If they played a round-robin tournament (each team played every other team), how many
games would be played? (Answer: 2016= 64x632)
B. (1-pointer) How many games must a team win in order to win the championship? (Answer: 6)
(2-pointer) How many games would a team have to win if there were 256 teams in the tournament?
(Answer: 8)
(3-pointer) If your team is ranked 10th in the coaches poll and 12th in the media poll, how many games
would you expect your team to win? (Answer: 2, since you would be seeded 3 rd in your region and likely
lose to the 2nd seed in the third round)
“The RPI (Rating Percentage Index) is a measure of strength of schedule and how a team does against
that schedule. It is used by the NCAA as one of their factors in deciding which teams to invite to the
NCAA tournament and where to seed them. The basic formula is 25% team winning percentage (WP),
50% opponents' average winning percentage (OWP), and 25% opponents' opponents' average winning
percentage (OOWP).” www.collegerpi.com
RPI = .25 (WP) + .50 (OWP) + .25 (OOWP)
A team's winning percentage (WP) is calculated by first adjusting the win total and loss total:
Win Total = 1.4 (road wins) + (neutral wins) + 0.6 (home wins)
Loss Total = 0.6 (road losses) + (neutral losses) + 1.4 (home loss)
C. (1-pointer) How many of the 64 teams lose their last game? (Answer: 63)
(2-pointer) How many teams are eliminated after 3 rounds of the tournament? (Answer: 56, with 8 left)
(3-pointer) What percentage of the 64 teams are left after 4 rounds? (Answer: 6.25%, which is 4 of the
64)
D. (1-pointer) If every team has the same probability of winning the championship, what is the
probability your team will win? (Answer: 1/64)
(2-pointer) If the Big Ten gets 7 teams into the tournament, what is the probability that a Big Ten team
will win? (Answer: 7/64)
(3-pointer) If the probability your team will win each game is 1/2, what is the probability your team will
win the championship? (Answer: (1/2)6= 1/64)