The NFL Combine in Two Dimensions
By: Andrew Doss
Tags: Principal Component, Data Visualization, Unsupervised Learning, NFL, Data Science

Cool, but…

We recently published an analysis of pandemic unemployment and drinking where we used a data analysis technique called Principal Component Analysis (PCA) to visualize several variables in one plot. We received feedback from readers who were interested in learning more about PCA but have previously found it hard to interpret and difficult to apply with real datasets.

PCA is known for being cool to look at, but not always useful due to a lack of interpretability. We’ll walk through applying PCA to NFL combine data, explaining how to use it, the factors we considered, and how we build an intuition for useful analysis. We will also provide links to the data and Python implementations from the article so you can immediately apply PCA in your own work.

A particular perspective

There are multiple applications of principal components including feature engineering, compressing data with minimal information loss, and visualizing high dimensional data. Here, we focus on the third application and analyze principal components as a means of better understanding structure, particularly how variables tend to change when others change, in a dataset.

PCA can be studied from different perspectives including linear algebra, mathematical statistics, and computational methods. Here, we focus on the less formal perspective of exploratory data analysis. This application and perspective puts us in the setting of unsupervised learning for exploratory data analysis, with the general objective of summarizing a dataset in a way that reveals new insights.

Bivariate beginnings

We’ll start by applying PCA to a small, bivariate subset of a dataset from the 2021 NFL Scouting Combine and work our way up to the eight variables shown in our introduction.

The NFL Combine is an annual event where elite college athletes complete a series of tests in preparation for the draft. The measurements taken at the combine yield a dataset describing the variability of physical attributes and performance within this group. We’ll start building our intuition for PCA using just two variables, height and weight.

PCA assumes that variance is what is interesting about a dataset. When variables in our dataset are correlated, some of their variance is redundant. We can summarize this covariance with a smaller number of new variables, called principal components. Principal components are weighted averages of the original variables that possess particular properties.

In the plot below, it appears that athlete height and weight are correlated — when height increases, so does weight. If you had to choose one, and only one, variable to summarize the variability in these players, what would it be?

You could pick one of the existing variables (height or weight). However, the correlation between height and weight indicates that we can construct a more general variable related to both. Let’s call this more general variable player “size”, and define it as an average of height and weight. You might not know how to compute that average, but if you had these athletes in a lineup, you would likely still have some intuition for sorting them by “size.”

In essence, PCA enables us to measure players by the single variable “size.” Specifically, PCA finds the optimal weighted average of height and weight for summarizing the variability of both height and weight with a single value. That single dimension is the first principal component of this dataset.

Note: from here on, we will display all variables in standardized form, a nuance that we explain further in the appendix for practitioners.