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/ 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 9 th
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 9 th. 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 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 9 th ) 2
PAST PERFORMANCE BY SEED SINCE 1985 Find the experimental 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 PROBABILITY WINS (Fraction) 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 PROBABILITY (Decimal) PROBABILITY (Percent) Final Four Appearances by Seed SEED 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 Final Four Appearances PROBABILITY (Fraction) PROBABILITY (Decimal) PROBABILITY (Percent) 3
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. shown and only 1 or 2 minor errors in shown and more than 2 minor errors in shown and 2-3 major errors in calculations No work is shown and/or more than 3 major errors in No questions are answered or worksheet Is not turned in. 4
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) 5
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 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 15 Points 12 points 9 points 6 points 3 points 0 points shown and all answers are correct. questions for #13 are well thought out and solved correctly. shown and all but 1 answers are correct. questions for #13 are well thought out and solved correctly. shown and all but 2 answers are correct. questions for #13 are attempted, but not solved correctly. shown and more than 2 answers are incorrect. questions for #13 are either not attempted or are not done correctly. No work is shown and more than 2 answers are incorrect. questions for #13 are not attempted. No questions are answered or worksheet is not turned in. 6
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. FACT: No #16 seed has ever won a tournament game. 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. 2. Using your bracket and the Past Performance by Seed tables, what is the of your chosen champion making it to the Final Four? 3. Using your bracket and the Past Performance by Seed tables, what is the 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: Only once in the past 17 years have all four #2 seeds reached the Sweet 16 (3 rd round) 7
FACT: The first and only time that all four #1 seeds advanced to the Final Four was 2008 5. Using your bracket and the Past Performance by Seed tables, what is the 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 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)? FACT: There have been three tournaments where no #1 seeds have reached the Final Four: 1980, 2006, and 2011 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 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 15 Points 12 points 9 points 6 points 3 points 0 points shown and all answers are correct. shown and only 1 or 2 minor errors in shown and more than 2 minor errors in shown and 2-3 major errors in calculations No work is shown and/or more than 3 major errors in No questions are answered or worksheet Is not turned in. 8
Tournament Probabilities Historical Data This table has the 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 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 of a #4 seed winning their Round 1 AND Round 2 games, you will have to use what you have learned about AND to calculate that. of winning Round 1 Game of winning Round 2 Game of winning Sweet 16 Game of winning Elite 8 Game of winning Final 4 Game of winning Championship Game SEED #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 9
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 that an upset occurred (a higher seed beating a lower seed)? 3. What is the experimental that a team won their first round game given they were a #16 seed? 4. What is the experimental that a #8 seed won their first round game? 5. What is the experimental 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? 7. What is the experimental that an upset occurred (a higher seed beating a lower seed)? 8. What is the experimental that a #1 seed won their second round game? 9. What is the experimental that a team won their second round game given they were a #2 seed? 10. What is the experimental that a #8 seed won both their first AND second round games? 10
Theoretical Use the Tournament Probabilities Historical Data Sheet (Pg 11) and your bracket to answer the following questions. 11. What is the that your chosen champion will win their Sweet 16 game? 12. What is the that your chosen champion will move on to the Final Four? (Win their Sweet 16 AND Elite 8 games) 13. What is the that your chosen runner up (Loser of Championship Game) will make it to the Final Four? 14. What is the that your chosen champion will make it to the Championship Game? 15. What is the 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 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 20 Points 16 points 12 points 8 points 4 points 0 points All work is shown and all answers are correct. shown and only 1 or 2 minor errors in shown and more than 2 minor errors in shown and 2-3 major errors in calculations No work is shown and/or more than 3 major errors in No questions are answered or worksheet Is not turned in. 11
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? 2. What is the experimental that an upset occurred (a higher seed beating a lower seed)? 3. What is the experimental that a team won their Sweet 16 round game given they were a #1 seed? 4. What is the experimental that a #8 seed won their Sweet 16 round game? 5. What is the experimental 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? 7. What is the experimental that an upset occurred (a higher seed beating a lower seed)? 8. What is the experimental that a #1 seed won their Elite 8 round game? 9. What is the experimental that one of your chosen Final Four teams won their Elite 8 game? 10. What is the experimental that a #1 seed won their First AND Second AND Sweet 16 AND Elite 8 Round games? 12
Theoretical Use the Tournament Probabilities Historical Data Sheet (Pg 11) and your bracket to answer the following questions. 11. What is the that your chosen champion will win their Final 4 game? 12. What is the that your chosen runner up will make it to the Championship Game (Win their Final 4 game?) 13. What is the that your chosen champion will win the NCAA Tournament (win ALL upcoming games)? 14. What is the that your chosen runner up will win the NCAA Tournament (One final upset!)? 15. What is the 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 shown and all answers are correct. shown and only 1 or 2 minor errors in shown and more than 2 minor errors in shown and 2-3 major errors in calculations No work is shown and/or more than 3 major errors in No questions are answered or worksheet Is not turned in. 13
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? 14
4. Choose the player from the winning team that attempted the most free throws. What was that player s experimental 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 that he would make BOTH (1 st AND 2 nd )? 6. Choose the player from the loosing team that attempted the most free throws. What was that player s experimental 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 that he would make the first one AND miss the second one? RUBRIC 2018 Tournament Challenge Free Throw Analysis 15 Points 12 points 9 points 6 points 3 points 0 points shown and all answers are correct. shown and only 1 or 2 minor errors in shown and more than 2 minor errors in shown and 2-3 major errors in calculations No work is shown and/or more than 3 major errors in No questions are answered or worksheet Is not turned in. 15
March Madness 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 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 16