name: date: hour: march madness probability project...march madness probability project it’s that...

Name: _________________________________________________ Date: ____________________Hour:_____________

MARCH MADNESS PROBABILITY PROJECT

It’s that special month of the year – MARCH!! It’s full of St. Patrick’s

Day, National Pig Day, Pi Day, Dr. Seuss’ Birthday, but most of all

MARCH MADNESS! For college basketball, this is the time that the

best 68 teams get a chance to contend for the national title through a

huge one-elimination tournament.

Throughout this project we will be following the games played in

the trounament, the teams involved, and the math and

statistics/probability that are also prevalent. There will be a prize

for the person(s) that score the most points.

MY TOTAL POINTS AT THE END OF THE TOURNAMNET: _______________________

(Fill out at the end of the Tournament)

DUE MONDAY, APRIL 9th

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The assignments and point values for this project are listed below, rubrics for

each are attached to each individual assignment.

You will turn in the ENTIRE PACKET at once on Monday, April 9th. You will have time in class to work on a majority of the project.

ASSIGNMENT #1 (pg. 3): COMPLETE Past Performance Based on Seed Worksheet (10

points)

ASSIGNMENT #2: WATCH the Selection Show on Sunday, March 11, 2018. You can see

it on TBS at 6:00PM or stream it live on NCAA.com. This is where the teams for the NCAA

March Madness tournament are anounced and seeded. In the upcoming class time, you will

be filling out our own brackets and choosing the teams you think will advance in each game

until the final round. You will be able to keep track of the teams that advance and the ones

you correctly chose each day.

ASSIGNMENT #3: COMPLETE NCAA Tournament Bracket (15 points)

ASSIGNMENT #4 (pg. 5-6): COMPLETE What’s the Theoretical Probability Worksheet

(15 points)

ASSIGNMENT #5 (pg. 7-8): COMPLETE March Mathness Worksheet (15 points)

ASSIGNMENT #6 (pg. 10-11): COMPLETE NCAA March Madness Bracket Check-In

Part 1 (After Round 1 and Round 2) (20 points)

ASSIGNMENT #7 (pg. 12-13): COMPLETE NCAA March Madness Bracket Check-In

Part 2 (After Sweet 16 and Elite 8) (20 points)

ASSIGNMENT #8 (pg. 14-15): COMPLETE 2017 Tournament Free Throw Analysis

Worksheet (15 points)

TOTAL: March Madness Project = 110 SUMMATIVE POINTS

(DUE MON. APRIL 9th)

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PAST PERFORMANCE BY SEED SINCE 1985 Find the experimental probability of each seed winning the tournament and appearing in

the Final 4 based on the information in the chart from the previous years of the

tournament.

Tournament Wins by Seed SEED CHAMPIONSHIP

WINS PROBABILITY (Fraction)

PROBABILITY (Decimal)

PROBABILITY (Percent)

1 20 2 5 3 4 4 1 5 0 6 1 7 1 8 1 9 0 10 0 11 0 12 0 13 0 14 0 15 0 16 0

Final Four Appearances by Seed

SEED Final Four Appearances

PROBABILITY (Fraction)

PROBABILITY (Decimal)

PROBABILITY (Percent)

1 54 2 28 3 15 4 13 5 6 6 3 7 3 8 5 9 1 10 1 11 3 12 0 13 0 14 0 15 0 16 0

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RUBRIC – Past Performance by Seed Worksheet

10 Points 8 points 6 points 4 points 2 points 0 points All work is shown and all answers are correct.

All work is shown and only 1 or 2 minor errors in probability calculations.

All work is shown and more than 2 minor errors in probability calculations.

All work is shown and 2 - 3 major errors in probability calculations

No work is shown and/or more than 3 major errors in probability calculations.

No questions are answered or worksheet Is not turned in.

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If all 64 teams were put into a hat,

WHAT’S THE THEORETICAL PROBABILITY… 1. Of choosing Michigan or Michigan State?

2. Of choosing a 5 seed?

3. Of choosing a team that will eventually make it to the Sweet 16?

4. Of choosing a team that is at least a 4 seed?

5. Of choosing a 1 or a 16 seed?

6. Of drawing an even seeded team, replacing that team, and then drawing another

even seeded team?

7. Of drawing an even seeded team, and another even seeded team without replacing

the first?

8. Of drawing a team from the Big Ten, then from the ACC, then from the Big East

without replacement? (See the conference maps in the front of the room if you are

unsure of which teams are in these conferences)

9. Of drawing 3 teams from the Big Ten without replacement? (Use the conference

maps as a reference)

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10. Of choosing a team from Ohio?

11. Of choosing a team that starts with the letter M or plays in the West

Region?

12. Of drawing Michigan State and then drawing Michigan (without

replacement)?

13. Make your own probability questions about the tournament that use

“AND” and “OR” that are mutually exclusive or not. Then show the

calculations and answer to your problem.

AND:

OR:

RUBRIC – What’s the Probability 15 Points 12 points 9 points 6 points 3 points 0 points All work is shown and all answers are correct. Probability questions for #13 are well thought out and solved correctly.

All work is shown and all but 1 answers are correct. Probability questions for #13 are well thought out and solved correctly.

All work is shown and all but 2 answers are correct. Probability questions for #13 are attempted , but not solved correctly.

All work is shown and more than 2 answers are incorrect. Probability questions for #13 are either not attempted or are not done correctly.

No work is shown and more than 2 answers are incorrect. Probability questions for #13 are not attempted.

No questions are answered or worksheet is not turned in.

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MARCH MATHNESS!

YOU WILL NEED: Your filled out Tournament Bracket AND the Past Performance by Seed

Table (pg. 3). Use these to answer the following questions.

1. Using the Past Performance by Seed tables, which seed

is the MOST LIKELY to win the tournament? Second

most? Third most? Explain your answers.

2. Using your bracket and the Past Performance by Seed tables,

what is the probability of your chosen champion making it to

the Final Four?

3. Using your bracket and the Past Performance by Seed tables, what is the probability

of your team winning the tournament?

4. Are your probabilities from questions 2 and 3 different

than if we chose the Final Four and the Champion by

drawing teams’ names from a hat? Why are they different?

FACT: No #16 seed

has ever won a

tournament game.

FACT: Only once in

the past 17 years

have all four #2

seeds reached the

Sweet 16 (3rd round)

FACT: In the tournament’s history, only eight #15 seeds have won their opening round game. Only one has ever won in their second round.

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5. Using your bracket and the Past Performance by Seed

tables, what is the probability that you have correctly picked

the two teams playing in the Championship(First team makes

it to the Championship Game AND the second team makes it to

the Championship Game)?

5. Using your bracket and the Past Performance by Seed

tables, what is the probability that you have correctly

picked all four Final 4 teams (Team 1 makes it to Final 4

AND Team 2 makes it to Final 4 AND Team 3 makes it to

Final 4 AND Team 4 makes it to Final 4)?

6. FACT: The 2011 tournament set a record for high seeded teams advancing to the

Final Four. The Final Four was comprised of the following seeds: 3, 4, 11, and 8.

Using your bracket and the Past Performance by Seed tables, what is the probability

that what happened in 2011 will happen again and a #3 AND #4 AND #11 AND #8

seed will all make it to the Final Four?

RUBRIC – March Mathness Worksheet







FACT: The first

and only time

that all four #1

seeds advanced

to the Final Four

was 2008

FACT: There have

been three

tournaments where

no #1 seeds have

reached the Final

Four: 1980, 2006,

and 2011

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Tournament Probabilities – Historical Data This table has the probability of each seed winning their game each round of the tournament. The

probabilities from box to box are all independent of each other. For example, the probability that a

#1 seed wins their Elite 8 Game is .603, is just based on the amount of #1 seeds that have played an

Elite 8 game and how many of them won; NOT based on the probabilities of winning all previous

games. YOU WILL NEED THIS TABLE FOR THE FOLLOWING 2 ASSIGNMENTS.

Therefore, if you wanted to calculate the probability of a #4 seed winning their Round 1

AND Round 2 games, you will have to use what you have learned about “AND” Probability

to calculate that.

SEED

Probability of winning

Round 1 Game


Round 2 Game

Probability of winning Sweet 16

Game


Elite 8 Game


Final 4 Game


Championship Game

#1 1.00

.880 .830 .603 .545 .625

#2 .960

.667 .719 .478 .500 .364

#3

.850 .612 .481 .520 .615 .375

#4

.790 .544 .326 .643 .222 .500

#5

.660 .545 .139 .800 .500 .000

#6

.690 .507 .343 .250 .667 .500

#7

.610 .295 .333 .000 .000 .000

#8

.460 .196 .667 .500 .333 1.000

#9

.540 .056 .333 .000 .000 .000

#10

.390 .462 .389 .000 .000 .000

#11

.310 .355 .364 .500 .000 .000

#12

.340 .500 .059 .000 .000 .000

#13

.210 .190 .000 .000 .000 .000

#14

.150 .133 .000 .000 .000 .000

#15

.040 .000 .000 .000 .000 .000

#16

.000 .000 .000 .000 .000 .000

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NCAA MARCH MADNESS BRACKET CHECK-IN Part 1

After First AND Second Rounds: Do you still have a chance?? Use YOUR bracket and the Tournament Probabilities – Historical Data Sheet (pg 11)

to answer the following questions.

If your champion has been eliminated, then you may choose another remaining team for

the purposes of this worksheet: My Champion for this Worksheet is:___________________________

If your runner up has been eliminated, you will need to choose a new runner up as well.

Use your FIRST Round data only to answer the following questions. Assume Round 2

has not yet happened.

1. How many games were played in the FIRST Round? ______________

2. What is the experimental probability that an upset occurred (a higher seed beating a

lower seed)?

3. What is the experimental probability that a team won their first round game given they

were a #16 seed?

4. What is the experimental probability that a #8 seed won their first round game?

5. What is the experimental probability that a team won their first round game given they were a #2 seed?

Use your SECOND Round data to answer the following questions. Assume BOTH

rounds have occurred.

6. How many games were played in the second round? _____________


lower seed)?

8. What is the experimental probability that a #1 seed won their second round game?

9. What is the experimental probability that a team won their second round game given

they were a #2 seed?

10. What is the experimental probability that a #8 seed won both their first AND second

round games?

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Theoretical Probability – Use the “Tournament Probabilities – Historical Data Sheet”

(Pg 11) and your bracket to answer the following questions.

11. What is the probability that your chosen champion will win their Sweet 16 game?

12. What is the probability that your chosen champion will move on to the Final Four? (Win

their Sweet 16 AND Elite 8 games)

13. What is the probability that your chosen runner up (Loser of Championship Game) will

make it to the Final Four?

14. What is the probability that your chosen champion will make it to the Championship Game?

15. What is the probability that your remaining Final Four teams (any that are not

eliminated yet) will ALL make it to the Final Four (Team 1 wins Sweet 16 AND Elite 8 AND Team 2 wins Sweet 16 AND Elite 8 AND…etc.)?

16. What is the probability that your chosen champion will WIN the Tournament (Win all upcoming games)?

Based on our chosen scoring system, what is your current score after Rounds 1 and

2? _____________________________

RUBRIC – NCAA March Madness Bracket Check-In Part 1







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NCAA MARCH MADNESS BRACKET CHECK-IN Part 2

After Sweet 16 AND Elite 8: Do you still have a chance?? Use YOUR bracket and the Tournament Probabilities – Historical Data Sheet (pg 11)

to answer the following questions.

If your champion has been eliminated, then you may choose another remaining team for

the purposes of this worksheet: My Champion for this Worksheet is:___________________________

If your runner up has been eliminated, you will need to choose a new runner up as well.

Use your Sweet 16 Round data only to answer the following questions. Assume the

Elite 8 round has not yet happened.

1. How many games were played in the Sweet 16 Round? ______________


lower seed)?

3. What is the experimental probability that a team won their Sweet 16 round game given

they were a #1 seed?

4. What is the experimental probability that a #8 seed won their Sweet 16 round game?

5. What is the experimental probability that a #2 seed won their First AND Second AND Sweet 16 round games?

Use your Elite 8 Round data to answer the following questions. Assume ALL previous

rounds have occurred.

6. How many games were played in the Elite 8 Round? ______________


lower seed)?

8. What is the experimental probability that a #1 seed won their Elite 8 round game?

9. What is the experimental probability that one of your chosen Final Four teams won

their Elite 8 game?

10. What is the experimental probability that a #1 seed won their First AND Second AND

Sweet 16 AND Elite 8 Round games?

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Theoretical Probability – Use the “Tournament Probabilities – Historical Data Sheet”

(Pg 11) and your bracket to answer the following questions.

11. What is the probability that your chosen champion will win their Final 4 game?

12. What is the probability that your chosen runner up will make it to the Championship

Game (Win their Final 4 game?)

13. What is the probability that your chosen champion will win the NCAA Tournament (win

ALL upcoming games)?

14. What is the probability that your chosen runner up will win the NCAA Tournament

(One final upset!)?

15. What is the probability that both your Final 2 teams make it to the Championship game (Team 1 wins Final 4 AND Team 2 wins Final 4)?

Based on our chosen scoring system, what is your current score after the Sweet 16

and Elite 8 Rounds? _____________________________

RUBRIC – NCAA March Madness Bracket Check-In Part 2 20 Points 16 points 12 points 8 points 4 points 0 points All work is shown and all answers are correct.






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2017 TOURNAMENT CHALLENGE FREE THROW ANALYSIS

Choose ONE of the Elite 8 game Box Scores.

The game I chose was: _________________________________ vs. ________________________________

Look at the column labeled FTM-A and use it to answer the following questions. The first

number is the number of free throws made and the second number is the number of free

throws attempted. A Free Throw in Basketball is a when a player is fouled and gets a

chance to shoot 1 or 2 baskets without interference from the free throw line. One free

throw is worth 1 point.

1. Would the outcome of the game have changed if all the attempted free throws had

been made for both teams? Explain.

2. What percentage of free throws would need to be made by the loosing team to

change the outcome of the game? Is it even possible for the outcome to change just

based on free throws?

3. What if only one player from either team made all his free throws? Could that

change the outcome? If so, which player?

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4. Choose the player from the winning team that attempted the most free throws.

What was that player’s experimental probability of making a free throw?

5. Using the same player from question 4, if that player was to get fouled in the next

game and had to shoot two free throws; what is the probability that he would make

BOTH (1st AND 2nd)?

6. Choose the player from the loosing team that attempted the most free throws. What

was that player’s experimental probability of making a free thrown?

7. Using the same player from question 6, if that player was to get fouled in the next

game and had to shoot two free throws; what is the probability that he would make

the first one AND miss the second one?

RUBRIC – 2018 Tournament Challenge Free Throw Analysis







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March Madness Probability Project Final Score Sheet

Student Name: ___________________________________________________________ Hour: ________________

ASSIGNMENT #1: Past Performance Based on Seed Worksheet ___________/10

ASSIGNMENT #3: NCAA Tournament Bracket _______________/15

ASSIGNMENT #4: What’s the Probability Worksheet ___________/15

ASSIGNMENT #5: March Mathness Worksheet ______________/15

ASSIGNMENT #6: NCAA March Madness Bracket Check-In Part 1 ____________/20

ASSIGNMENT #7: NCAA March Madness Bracket Check-In Part 2 ____________/20

ASSIGNMENT #8: 2017 Tournament Free Throw Analysis Worksheet ______________/15

TOTAL: ______________________/110

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