Probability Performance Task #1 Due: December 16th/17th

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The Hot Hand Effect: The hot hand effect is psychological effect whereby a string of success or failures affects the probability that you will continue to succeed or fail. This is most commonly associated with basketball where a player having made a series of shots is deemed to be ‘hot’ and perceived probability of him/her making the next shot is increased. Much research has been done to prove/disprove the statistical existence of the ‘hot hand’. Attached is an article on the hot hand.

Your Task: Over the next three weeks you and a team of three total students from your class will work to gather and analyze raw data and create a representative computer model in an attempt to either prove or disprove the existence of the ‘hot hand’ in free throw shooting for our Junior Basketball team.

Data Collection: Your team will be assigned a basket and a shooter for Friday December 3rd at Lunch Hour. At least two members from your group MUST be present during the data collection process. You will collect data on the shooters results as a string of H-hits and M-misses for the entire 35 minutes. You should collect the results from at least 200 shots. At the end of the time conduct a brief interview of the shooter filling out the ‘shooter information sheet’.

Analysis of the Raw Data: You will use the empirical (experimental) data to find the following probabilities: , ,, ,. You will also analyze the streaks of success in the raw data. As discussed in the attached paper (Koehler and Conley 2003) streaks would be extended and there would be less total streaks of successive hits/misses. Count and tally the streaks and create a bar graph with ‘Number of Streaks” on the vertical axis and ‘Streak Length’ on the horizontal axis. Comment on the amount of raw data collected and whether or not it is enough data to draw reasonable conclusions for all the different associated probabilities.

Creating a Computer Model: In Microsoft Excel you will create a computer model of your free throw shooter; this would be to create a ‘theoretical’ expectation for probabilities and streaks. You will do this by using your empirical value of as a success rate for hitting a free throw and use the same amount of random throws in your computer model as your shooter was able to shoot during the allotted experiment time. This process is very similar to the assignment we did for flipping heads/tails in excel except you will use the value instead of the 50/50 chance of the coin flip. You will analyze the computer results for evidence of streaking for multiple trials and create a bar graph with the same axis titles as you did for the raw data. You may need to perform this several times to find an ‘average’ set of expected streak lengths.

Marking: This project will be worth 5% of your overall mark on your final report card. The attached rubric will be used to evaluate your submissions.

Deliverables:

Today: Create a group of three students that you can work with and who are reliable.

Work Periods: Over the next 3-4 weeks you will be given several class periods to work on your analysis and report.

Submission: On December 16/17 you will submit your written report of your findings and have a 3-5 minute exit interview with your teacher to discuss your findings and understanding of the project. You will also submit a copy of your Excel File to the student shared folder, sub file Saylor-MDM4U-Day1/2 with your names in the title of the file.

The Report: Your report should be computer typed and have the following headings

1.  Your team – a brief discussion of the research/analysis team members and the shooter, a breakdown of the responsibilities of each member and any problems that you encountered in collecting data, analyzing the data or writing the report.

2.  Introduction: Introduce the concept of ‘hot hand’.

3.  Methodology: Discuss the process you are going to use to collect data, analyze data, model and report.

4.  Expected Results: What do you think you will find? Do you have any preconceived notions about what you will find?

5.  Shooters Results: A discussion on the shooters results. The shooters overall probabilities as well as the dependant probabilities and their implication with regards to evidence of the ‘hot hand’. State how each was calculated and the number of occurrences that were used to calculate the probabilities. Include your bar graph showing the streaks of the shooter. Attach your raw collected data in an appendix at the back of your report.

6.  Computer Model: A discussion of the computer generated results. Include the bar graph of the modeled streaks. How does the computer generated graph compare to that of the shooters raw data, does this support the existence of ‘hot hand’.

7.  Accuracy: State any limitations on the accuracy of your results. How might this alter the results? Were there enough trials/occurrences to accurately state the empirical dependant probabilities?

8.  Conclusion: State your overall findings.

9.  Applications: How might your findings affect your view of sports and human psychology in general?

10.  Appendix: Raw Data, Full page sized versions of Empirical and Modeled Streaks Graphs, Any necessary summary charts of the modeled data.

Marking: The following rubric will be used to evaluate your submissions:

Heading / Level 1 / Level 2 / Level 3 / Level 4
Data Collection
KU / Group does not collect data on proper day. / Group collects data on proper day, but not all group members are present and their deportment is inappropriate. / Group members collect data on proper day, their deportment is acceptable and two group members are present. / Data is collected on appropriate day, deportment is excellent and all group members are present. / /4
Raw Data Analysis
AP / Analysis is largely incomplete or largely incorrect. / Analysis is mostly complete but with some errors. / Analysis fully completed with very few errors. / Analysis is complete with no errors. / /12
Computer Model
TH / Computer model is completely incorrect or non-existent. / Computer model was mostly correct. Some required aspects are missing. The data is not clearly formatted. / Computer model has all aspects of the analysis. The data is not displayed clearly and neatly. / Computer model is clearly laid out, all data is formatted and no part of the analysis is missing. / /12
Report
CM / Report is missing several sections, lacks flow and logical progression of thought. / Report covers all major topics but is messy and is hard to follow. Report shows little understanding of the project and the results. / Report is not missing any sections, is easy to read and understand. Shows a good understanding by the group of the project and results. / Report covers all sections, flows logically and leaves the reader with a complete understanding of the findings of the group. / /12
Exit Interview
CM / Group members not present. Group shows minimal understanding of the project process and results. / Group members are present but not all members demonstrate an acceptable understanding of the project process and results. / All group members are present and show a good understanding of the process and results. / All group members are present and all show a full understanding of the project and the results. / /4
Total Grade / /44

Raw Data Collection Sheet:

Group Members: ______, ______, ______

Date: ______

Shooters Name: ______

Shooters Results:

For best results:

Remind shooter to not rush and to take the process seriously. It would be good to get as many trials as possible, but not at the expense of the shooter rushing. One group member should be in charge of rebounding the ball and passing it back to the shooter to help speed the process. All data should be taken from a single shooter. If the shooter needs to take a two minute break, that is ok. If the shooter has shot a sufficient number of free throws (100-200) you may cease the experiment.

Shooters Thoughts:

Has the shooter ever experienced being ‘hot’?

Did the shooter feel they were getting tired during this process? ______