• Not all students will be familiar with the home run derby. Asking students who play baseball or who are fans of the sport to explain the derby – and how it might incentivize players to adopt uppercut swings – helps motivate why the “curse” might be real. This will help the whole class get invested in the exploration.
• The probability calculations in this lesson utilize two contexts that can be simulated in the classroom: marbles in a jar and flipping coins. Consider using a real container of marbles (or other items) or real coins in class to simulate the probabilities we calculate in the lesson. This tactile experience can help some students obtain a firmer grasp of the concepts.
• When setting up the fake “home run derby” in class for the Discussion Question, you can ask the three selected students to participate in an exercise using items commonly found in a classroom. For instance, they could try to hit balls of crumpled paper with a ruler in front of the class. They could even choose their own pitcher among their classmates (just like hitters choose their own pitchers in the derby). Then, after participating, students can click the applet again on your computer (projected on the board, for the whole class to see), thereby simulating their second half of the season. The fake derby can be fun for the whole class to watch. Plus, it sets up the ultimate point of the Discussion Question: their worse performance in the second half of the season (their second run of the applet) isn’t truly connected to their participation in the in-class derby. Rather, it’s a natural result of the law of large numbers.
• Learning about the law of large numbers can sometimes bring up the common probability myth of being “due for one.” For example, when flipping a fair coin, if a student gets a long string of heads, they may believe that the next flip is more likely to be a tails (since they’re “due for” a tails). However, if the coin is truly fair, prior results won’t influence the probability of future outcomes. Emphasizing this point when discussing the law of large numbers will help students avoid believing the “due for one” myth and will better position them to learn about the idea of independence in future lessons.

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.

• When setting up the fake “home run derby” in class for the Discussion Question, you can ask the three selected students to participate in an exercise using items commonly found in a classroom. For instance, they could try to hit balls of crumpled paper with a ruler in front of the class. They could even choose their own pitcher among their classmates (just like hitters choose their own pitchers in the derby). Then, after participating, students can click the applet again on your computer (projected on the board, for the whole class to see), thereby simulating their second half of the season. The fake derby can be fun for the whole class to watch. Plus, it sets up the ultimate point of the Discussion Question: their worse performance in the second half of the season (their second run of the applet) isn’t truly connected to their participation in the in-class derby. Rather, it’s a natural result of the law of large numbers.
• It can be helpful to point out that all-star players, like Aaron Judge, aren’t just “getting lucky” all the time. Great players will have generally better stats (e.g. higher batting averages) compared to other players. The key aspect to point out is that they may also experience some luck that helps them overperform, on top of their already high baseline levels. The seasons in which all-star players experience some luck are often the seasons where they may get selected for the derby. After the derby, their performance returns to their own baseline level. That baseline level is still quite good. But not as good as the first half of their season.

• A deeper discussion of the home run derby “curse” and the law of large numbers can be found here: Jaiclin, M. & McCollum J. “Home Run Derby Curse: Fact or Fiction?” Baseball Research Journal, (2010).
• A counter example to the curse can be surfaced by seeing the Cal Raleigh 2025 story.

• The definition of probability provided in this lesson (the relative frequency of an outcome after many trials) is the frequentist definition of probability. However, for events that don’t happen many times or that can’t be simulated, this definition may be limited.
• The other common definition of probability is the Bayesian interpretation. In the Bayesian view, events that have never happened before or that can’t be simulated still have probabilities – and we can estimate those probabilities based on our own level of knowledge or expectation that the event will happen.
• Traditionally, the frequentist interpretation has been the preeminent view in the field, and it’s the view taken by AP Statistics and the AP Exam. However, the Bayesian view has gained some popularity in recent years, especially as computers have made Bayesian calculations easier to perform. A lot can be said about the difference between these schools of thought. Our favorite commentary is this cartoon by xkcd.