This is the sixth in a series of baseball-themed lessons we’re calling FanGraphs Prep. In light of so many parents suddenly having their school-aged kids learning from home, we hope is that these units offer a thoughtfully designed, baseball-themed supplement to the school work your student might already be doing. The first, second, third, fourth, and fifth units can be found here, here, here, here, and here.

Overview: A one-week unit centered around understanding the concept of regression to the mean. This can be a difficult concept to grasp but it’s important for any aspiring statistician to understand.

Learning Objectives:

• Explain the difference between “true talent” and a statistic.
• Use algebra to calculate probabilities.
• Estimate future performance using a projection.
• Identify and apply Regression to the Mean.

Target Grade-Level: 9-10

Daily Activities:
Day 1
Strat-O-Matic is a two-player card-based baseball game. You start by making lineups and then play out a series of batter-pitcher matchups like the one below between Mike Trout and Clayton Kershaw.

Each matchup involves rolling three six-sided dice. The first one tells you which column to use and the next two determine the outcome, although sometimes we will need to roll an additional 20-sided die. For instance, if the first die roll is a 1, we’ll direct our eyes to the left-most column on Trout’s card. If the next two dice add up to 7, Trout has worked a walk. Read the rest of this entry »

This is the third in a series of baseball-themed lessons we’re calling FanGraphs Prep. In light of so many parents suddenly having their school-aged kids learning from home, we hope is that these units offer a thoughtfully designed, baseball-themed supplement to the school work your student might already be doing. The first and second units can be found here and here.

Overview: A two-week unit centered around building and testing your own projection system.

From the simplest forecasts to the most complex projection systems, one of the most challenging questions to try to answer with statistics is predicting player performance from one year to the next. We do this by using their past stats to create an estimate for their future performance. Accounting for other factors like age and injury adds complexity, though not necessarily accuracy. In this unit, you’ll create a simple projection system and then test its accuracy.

Learning Objectives:

• Identify and apply a weighted mean.
• Gather and organize data from various sources.
• Construct a weighted projection using historical data.
• Explain why a projection system produces errors.
• Identify and apply Mean Absolute Error.
• Identity and apply Root Mean Square Error.
• Evaluate which projection error to use for a given problem.
• Review a projection system and adjust to fit data.

Target Grade-Level: 9-10

Read the rest of this entry »