Homework Policy

Each homework submission may be a maximum of one page, front and back. To clarify, this means that two pages is the maximum length allowed for a homework submission. It should be typeset on a computer. You will have to upload your submission on Gradescope. You can enroll for the course with the following entry code: MDKDZG.

Homework 1

Due Wednesday, April 17

Grading Rubric

Past exemplary work:

For the team sport of your choosing, invent a method for evaluating individual performance in terms of how it leads to team success. Imagine that you have been hired as a statistical analyst and the general manager has tasked you with creating ratings for individual players. How can the team determine which players to acquire?

Your assignment is to write a report describing in detail how to compute your proposed player ratings. Your method should lead to a statistic which estimates the value added by each player to whom it applies, in terms of team winning or scoring, relative to a league-average player. Note that your task is not to actually compute this statistic but rather to describe how to do so in enough detail that another statistical analyst could read your proposal and implement it herself. You may choose to focus on just one aspect of the sport. For example, the only aspect of baseball that wOBA evaluates is batting. Your report should address the following questions:

What data are needed to compute these player evaluations? Are these data available publicly? Privately? If these data do not currently exist, what labor or technology would be required to gather the data?

What are the limitations of the proposed method? In what ways might it fail to accurately isolate individual performance from team performance? What aspects of performance does it miss?

What is the most similar statistic in the public domain for evaluating individual performance? How is the proposed statistic different from what is publicly available?

If you are struggling to find inspiration, here is an idea that you may use as the basis of your report:

Invent a method for rating NFL quarterbacks in terms of point scoring. For each quarterback, this rating should estimate how many fewer (or more) points his team would score per game if he were replaced by a league-average quarterback.

Feel free to choose a sport that you feel passionate about, and to provide us with specific instances in which your method would be effective and/or deficient. We want to learn things from you!

Homework 2

Due Friday, April 26

Grading Rubric

Past exemplary work:

Pick a statistic (e.g. pass completion percentage in soccer) and find a dataset which reports this statistic for a set of athletes. Perform regression to the mean to estimate the true talent level in this statistic for all of the athletes in the dataset. A necessary component of this assignment is estimating the population standard deviation in underlying true talent for this statistic, in the set of athletes you have chosen to consider. If the statistic you have chosen is not a binomial percentage, then you will also have to estimate the sampling variance of the statistic. It can be interesting (but not mandatory) to also try and apply on the same statistic the Empirical Bayes method studied in class, where you first estimate the distribution of your statistic across all players, and then find individual estimates for each of them. In particular, you can compare how this Bayes estimator compares with the James-Stein estimator (regression to the mean).

Report your estimate of population standard deviation in underlying true talent for the statistic, and present a plot of estimated true talent versus observed statistic, with each athlete being one datapoint. In that plot, include the diagonal line y = x for reference. Pick one athlete and give that athlete's statistic and estimated true talent. Explain the interpretation of your estimated true talent for that athlete. In summary, your report should include:

An explanation of the statistic and dataset you chose (and where you found it)

An estimate of the population standard deviation in underlying true talent for this statistic

A plot of estimated true talent versus observed statistic

The interpretation of the results for one athlete of your choice

Your code in a separate document (see below)

As with all homework reports, imagine that your audience is a front office executive and write prose that smoothly addresses all of the components of the prompt.

When you submit your homework, include the code as an appendix to your main write-up.. We expect your code to fit on one page, front and back. If it does not, this suggests that you're making this harder on yourself than it needs to be. Consult the course staff for help.

If you are struggling for inspiration, you may use the dataset below as the basis of your report. For all players in the 2015-16 English Premier League, it includes total number of attempted passes and total number of successful passes. Estimate the true talent successful pass percentage for all players in the dataset. You are of course free to choose any statistic reflecting any personal interest or preference, or even one which could later lead to a more through analysis in a potential final project.

EPLpassing15-16.csv

Homework 3

Due Wednesday, May 8

Grading Rubric

Past exemplary work:

Find a dataset of game scores for the league or competition of your choice. Hold out the last (chronologically) 20% of the data as a test set. On the first 80% of the data, fit (1) the regularized normal Bradley-Terry model and (2) the regularized binomial Bradley-Terry model to rank the teams or players in the league or competition. Use each model to predict the winners of the matchups in the last 20% of the data, which you had previously held out. Present a figure which visualizes some aspect of your results, and include your code as an appendix to your homework submission.

The meat of this assignment is your presentation and interpretation of your results. Include several paragraphs (roughly half to three-quarters of a page) discussing your results. Questions that you could address in this discussion include: Which teams or players did each model identify as the best (and worst)? Does that agree with the popular consensus of who the best and worst teams are? What data are missing from these models that could lead to better rankings or matchup predictions? How does your model compare with how accurately Las Vegas sportsbooks are able to pick winners in this league or competition? Think up your own questions, too.

At minimum, your report should include:

Results (rankings) from fitting the Bradley-Terry models to the first 80% of the data

Results of using each model to predict winners in the last 20% of the data (Which model did better?)

A figure of your choice visualizing some aspect of your results

A (several-paragraph) discussion of your results (as a whole) on this dataset (see above)

Your code as an appendix

As always, prepare your report for a front office executive (or coach) in the league you are analyzing. Imagine that your audience is interested in understanding who are the best teams in the league, with more sophisticated analysis than counting wins and losses. The task here is not just to find "the answer" but to communicate all of your findings effectively.

If your code does not fit on one page, front and back, seek help. If you are struggling for inspiration, use the college basketball data from R Tutorial 2.

Homework 4

Due Wednesday, May 15

Grading Rubric

Past exemplary work:

Find a dataset of event results (as opposed to game results for the previous assignment) for the sport of your choosing. The data should include the identity of at least one player for each event. Examples of datasets you could use are:

Soccer : Shots

Offensive adversary: the shooter

Defensive adversary: the goalie

Other variables: the location of the shot, e.g.

Outcome variable: indicator of whether goal is scored

: Shots Offensive adversary: the shooter Defensive adversary: the goalie Other variables: the location of the shot, e.g. Outcome variable: indicator of whether goal is scored Football : Running plays

Offensive adversary: the running back

Defensive adversary: the defensive team

Other variables: the distance to go for first down, e.g.

Outcome variable: number of yards gained by rusher

: Running plays Offensive adversary: the running back Defensive adversary: the defensive team Other variables: the distance to go for first down, e.g. Outcome variable: number of yards gained by rusher Basketball : Missed shots

Offensive adversaries: the offensive players on the floor

Defensive adversaries: the defensive players on the floor

Other variables: indicator of whether shot was a three-pointer, e.g.

Outcome variable: indicator of whether defense got the rebound

: Missed shots Offensive adversaries: the offensive players on the floor Defensive adversaries: the defensive players on the floor Other variables: indicator of whether shot was a three-pointer, e.g. Outcome variable: indicator of whether defense got the rebound Baseball : At bats

Offensive adversary: the batter

Defensive adversary: the pitcher

Other variables: the stadium, e.g.

Outcome to model: wOBA value of the at bat result

: At bats Offensive adversary: the batter Defensive adversary: the pitcher Other variables: the stadium, e.g. Outcome to model: wOBA value of the at bat result Golf: Holes

Offensive adversary: the golfer

Defensive adversary: the hole

Outcome variable: number of strokes

For your chosen dataset, describe the offensive and defensive adversaries, what other variables you have chosen to include in the model, and what outcome variable you are modelling. Use the data to fit a Rasch model. Report the top five and bottom five offensive and defensive adversaries from your model fit. Comment on the estimated regression coefficients for the "other" variables. Do the values match your intuition for what they should be? What other variables have you not included in the model that might be worth including? Include some vizualization of your results. Try to address all of the points in this paragraph through a smooth discussion of your results.

The objective here is not to just "answer all of the questions" but rather to present the results you obtain from fitting the Rasch model in smooth prose. Imagine that a front office executive has asked you to evaluate the offensive and defensive adversaries in your model and that he is going to use your report to make decisions about what players to acquire.

Include your code as an appendix to your submission. If your code does not fit on one page, front and back, seek help. If you are struggling for inspiration, use the MLB play-by-play data from R Tutorial 3. You could, for example, model the probability that a plate appearance results in a strikeout. Alternatively, you could model the probability that a plate appearance results in a home run. A more comprehensive task would be to model the wOBA weight of the plate appearance outcome. The choice is yours!