Sampling Distributions: Shai Gilgeous-Alexander 2024-25 Points

Sampling Distributions

Simulation

Central Limit Theorem

Explore the concept of sampling distributions using Shai Gilgeous-Alexander’s regular season scoring data to simulate playoff scenarios.

Authors

Affiliation

Cooper Olney

St. Lawrence University

Ivan Ramler

St. Lawrence University

Robin Lock

St. Lawrence University

Published

July 1, 2025

Module

Please note that these material have not yet completed the required pedagogical and industry peer-reviews to become a published module on the SCORE Network. However, instructors are still welcome to use these materials if they are so inclined.

Introduction

The 2024-25 NBA season was a historic one for the Oklahoma City Thunder, who captured their first ever NBA Championship. The NBA Playoffs consist of four rounds, First Round, Second Round, Conference Finals, and NBA Finals, with each round played as a best of seven series. In the 2025, playoffs, the Thunder played a total of 23 games: 4 in the First Round, 7 in the Second Round, 5 in the Conference Finals, and 7 in the NBA Finals.

At the heart of this title run was Shai Gilgeous-Alexander (SGA), or SGA for short. SGA led the league in scoring, was named NBA MVP and capped off the season by earning the Finals MVP. His scoring consistency and ability to take over games made him one of the most dominant offensive forces in the league. This dataset, which contains SGA’s point totals from every regular season game, offers a snapshot of one of the most impressive individual season in recent NBA history.

SGA Highlight Reel

For those not familiar with Shai Gilgeous-Alexander, feel free to check out his highlight reel from the 2024-25 season!

In addition to its basketball significance, this dataset allows us to explore how statistical tools (such as StatKey) can be used to simulate real-world scenarios. By treating SGA’s regular season point totals as the population, we can model specific playoff situations by drawing random samples of different sizes. These simulations help us understand how much variation we might expect in his performances and how likely different playoff outcomes are are based on his regular season scoring.

Activity Length

This could serve as an in class activity and should take roughly a half an hour to complete.

Learning Objectives

By the end of this activity, you will be able to:

Describe the shape, center and spread of a statistical distribution.
Use simulation tools (such as StatKey) to create sampling distributions of the sample mean.
Comparing sampling distributions from different sample sizes.

Methods

Technology Requirement:

This activity uses Statkey (or a similar tool) for generating sampling distributions

Students should have prior knowledge in:

Understanding and interpreting distributions (shape, center, spread)
Distinguishing between a population and a sample
Knowledge of Normal Distributions is helpful.

Data

The sga_points_2025.csv dataset contains 77 rows and 1 column. Each row represents a game that Shai Gilgeous-Alexander played in during the 2024-25 NBA regular season. Note this dataset includes the NBA Cup Championship, but stats from that game are not officially counted in NBA season totals.

Download Data: sga_points_2025.csv

Variable Descriptions

Variable	Description
points	Total number of points Shai Gilgeous-Alexander scored in that game.

Data Sources

Saiem Gilani (2023). hoopR: Access Men’s Basketball Play by Play Data. R package version 2.1.0, https://CRAN.R-project.org/package=hoopR

Materials

Class Handout - MS Word version using StatKey

Class handout - with solutions

Conclusion

Through this module, you’ve used NBA data to explore how sample size affects the behavior of sampling distributions. By treating Shai Gilgeous-Alexander’s regular season point totals as a population, you’ve simulated different playoff scenarios and investigated how consistent or unusual his actual performances were. These simulations provide a hands-on way to see how sample means vary, and how distribution shape changes with sample size. This foundation sets the stage for a deeper understanding of the Central Limit Theorem and Normal Approximation methods.