• When playing the initial clip of Brad Pitt (“There are rich teams and there are poor teams. Then there’s 50 feet of crap. And then there’s us.”), pause to have students consider how player talent may vary between the rich teams and the poor teams – and whether that’s “fair” in their eyes. This helps motivate the analysis of the distribution of team payrolls throughout the lesson.
• In a future lesson, students will learn how to find and calculate exact measures of the center (the mean and median). For now, you can let them know that a rough visual estimate of the “middle” or “central” value is sufficient.
• The exact minimum and maximum values are not visible in a histogram. So, in the guided notes, students describe the spread for a histogram as the distance between the lowest bin of values and highest bin of values. Advise students that for dotplots and stem-and-leaf plots – where the exact minimum and maximum data values are visible – they should report the spread as the distance between the minimum and maximum.

First, download this lesson's Handout Key and read through its Discussion Question section. Then, check out our model discussion norms and the additional background notes below.

• For part (b) of the Discussion Question, another point that the “yes” side might raise: if a team is consistently not competitive, their fan base will get tired of seeing the losses and will tune out. For the fandom of the sport to thrive, you’d want as many teams as possible to be competitive. Making team payrolls more equal helps this outcome.
• To help students visualize the distribution before and after the luxury tax, you can use these extra slides: ppt, pdf.

• To help students make connections between payrolls and team quality throughout the lesson, ask them early in the lesson: “Which teams would you expect to get the best players? Why?”
• The field of statistical analysis for baseball is called sabermetrics, named for the Society of American Baseball Research (SABR). The movie Moneyball helped popularize sabermetrics, and it has grown into a deep field of research and study. The second movie clip in the lesson gives motivation for sabermetrics, displays some real sabermetric formulas, and mentions Bill James – a famous early pioneer of sports statistics. Of course, students do not need to know anything about sabermetrics to fully participate in the lesson. But it’s a great first look for students interested in exploring the field of sports statistics as a career.

• For practicing data scientists, one of the first steps of any analysis process (after retrieving and cleaning data) is visualizing data. Because models can be heavily influenced by undetected outliers, faulty data, or unusual features, going straight into calculations or model building before “getting to know the data” by visualizing and exploring it can lead to missteps. This step of visualizing and exploring data is sometimes called Exploratory Data Analysis or EDA.
• Stem-and-leaf plots were especially useful in the pre-computer era. However, they aren’t used in the field much anymore. For small data sets, dotplots are most common. For larger data sets, histograms and boxplots (covered in a later lesson) are most common.