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Luck and Randomness in Sports

This page is authored by Andrew Cahoon, Colby-Sawyer College.
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This material is replicated on a number of sites as part of the SERC Pedagogic Service Project


In this assignment students will investigate an outcome in sports that involves some degree of randomness and assess the role that luck has played for the particular outcomes of teams or individuals. It has been designed for beginning statistics students familiar with the basics of probability and probability distributions. Students will first choose an outcome that is of interest and submit a synopsis describing: their chosen topic, what data they will collect, and their plans to analyze the data. After receiving feedback on their synopses, students will focus on collecting and analyzing their data. As part of their analysis, students will determine a likely range of values for the particular outcome of interest to them. They will need to decide on their own standards for what is deemed "lucky" and "probable". Then they will apply those standards to the outcomes for specific teams or individuals. The assignment will culminate with a report of both their process and findings.

Learning Goals

Understanding the role of randomness in real world events
Interpreting probability distributions
Collecting and analyzing real data
Learning how to support written arguments with numerical information

Context for Use

This project is aimed for students who are in or have taken college level statistics including a presentation of probability distributions. It is a longer assignment, possibly a term project, that involves some data collection and analysis and culminates with a written paper. Students would benefit from making one or more drafts before the final submission.

Description and Teaching Materials

The only tools needed are a program to do statistical analysis (MS Excel or another spreadsheet program would suffice) and a source for data. For students interested in professional sports, websites such as or will most likely contain the necessary data. However students may choose to investigate college, high school, or club sports whose statistical information may be cataloged in a variety of different places.

Teaching Notes and Tips

The synopsis can be an extremely benficial tool for students. Typically, it is difficult for beginning statistics students to see the relation between a variable and an associated probability distribution. Therefore, it is useful to have them think through the analysis in their project at the very beginning. By addressing these difficulties in the synopsis, students will have an easier time conceptualizing their work and will lead to quicker progress once data has been collected.


The final paper will be graded on:

How well the student has introduced and motivated the topic

The originality and appropriateness of the topic

The quality of the data collection

The effectiveness (and correct-ness) of the methods of displaying the data

How well the data is summarized in writing, including use of numerical summaries

The accuracy of the analysis from a quantitative/technical standpoint

The appropriateness of conclusions

The overall quality of writing (The paper should be written as a logical story. Is it compelling? Easy to follow? Are numerical results explained effectively in words?)

References and Resources

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