• When launching the lesson, it’s helpful to play up the fact that the “Astrological Law of Sports” is not only surprising, but it’s also astonishingly widespread across varying sports and across the globe. This helps invest students in the context of the lesson and the Discussion Question.
• The AP Exam isn’t incredibly picky about rounding. However, as a good rule of thumb, you can tell students that three significant figures is usually sufficient for proportions (e.g. 0.273 or 27.3%).
• It’s unlikely that the AP Exam will ask students to draw graphs. Instead, students will mostly be asked to interpret pre-printed graphs. Having students draw their own bar chart and pie chart once or twice is helpful for learning the concepts behind each visualization. However, drawing graphs takes up a lot of class time, so it’s best to focus student practice on interpretation.
• When showing the graphs comparing the birthdays of the Italian population with the birthdays of Italian soccer players, ask students what these graphs might look like if the y-axes used raw counts, instead of percentages. Of course, because the sample sizes are very different (there are far more Italians than there are Italian professional soccer players), the graphs would no longer be comparable. This is why percentages are called relative frequencies – they allow us to relate the information across sample sizes.

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.

• At first, some students may draw a blank on the discussion question, especially those with little experience in youth sports. Expanding on the hint in the following ways may be helpful:
• “If everyone born in 2015 is in the same group, would players born in January 2015 be the oldest or youngest in the cohort?”
• “Which players might tend to display the most athleticism in a youth group: the oldest players or the youngest players? Why?”
• “Which players might tend to get the most attention and coaching: the more athletic ones or the less athletic ones? Why?”
• The phenomenon described in the Discussion Question is known in academic literature as the “relative age effect.” Numerous journal articles have been written on the relative age effect, in contexts that include education, the workplace,and psychology. Although the exact causal mechanism discussed here (older kids getting better opportunities due to initial age advantage) cannot be fully proven without an experiment, the prevalence of the relative age effect across many sports and other contexts provides substantial evidence for this explanation.

• This lesson utilizes the 12 zodiac signs of Western astrology as a playful hook to draw students into the lesson. Of course, there are a multitude of other astrological traditions that can be referenced. Ultimately, as students discover, the trends have more to do with how youth leagues group athletes, rather than anything astrological.
• The phenomenon described in the Discussion Question is known in academic literature as the “relative age effect.” Numerous journal articles have been written on the relative age effect, in contexts that include education, the workplace,and psychology. Although the exact causal mechanism discussed here (older kids getting better opportunities due to initial age advantage) cannot be fully proven without an experiment, the prevalence of the relative age effect across many sports and other contexts provides substantial evidence for this explanation.
• The relative age effect was most popularized by Malcolm Gladwell in his book Outliers (2008). The example Gladwell discussed focused on hockey. The lesson focuses on Italian soccer due to the strength of the relative age effect in this context and the readily available data from this journal article. However, the relative age effect has also been observed for Handball, Rugby, Track & Field, Skiing, Hockey, Tennis, and the Olympics.

• Generally, bar charts are preferred to pie charts among most statisticians. The human eye is much more perceptive of the relative size of bar heights than the relative size of sector areas. See this demonstration as an example. In addition, pie charts become very difficult to read when a variable has more than five or six categories, whereas bar charts are still fairly readable with a high number of categories.
• There are multiple ways to make visualizations of categorical data misleading. These include using pictures in place of bars for bar graphs, creating pie charts that don’t add to 100%, or using odd axis scales. Check out our Classic AP Stats 1.1 Lesson (created before the 2026 course revision) or High School Statistics Lesson 1.1 for examples. Note that misleading graphs are not covered in the current AP Statistics Course and Exam Description.