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# Simple vs. Complex Offenses, Part 2

Moving from visualizing offensive complexity to quantifying it.

In the previous post, I took a look at the diversity of formations for a given team’s offense. In this post, we’ll take a look at distilling that diversity into a single number representing the overall complexity of the offense, so we can do more quantitative analysis and compare offensive complexity to actual offensive output.

Offensive complexity, as defined in the previous post, is how similar or dissimilar the formations of the called plays are to one another. Complex offenses will have a very broad range of play formations; simple offenses will have very few formations. It’s easy enough to see different styles from the range of formations like we did previously.

Quantifying how complex the play calling is, however, requires some interpretation of how similar one formation is to another. A goal-line setup with zero receivers and 3 backs is probably as dissimilar as possible to an empty backfield from the shotgun, but what about everything in between? How close is a 2-back, 3WR shotgun snap to a 1-back, 3WR pistol snap? How similar is a 2-back, 2WR snap to a 1-back, 3WR snap if they’re both from under center?

To answer this question, I borrowed from previous work I did in grouping and classifying tennis players. I originally grouped tennis players using the Euclidean distance between distinct attributes each player has to see how similar or dissimilar their playing styles are. That approach can be adapted to football formations as well, using the distinguishing attributes of each formation (number of backs, number of receivers, quarterback location).

I started with a simple approach, where each of these three features are weighted equally in deciding how similar or dissimilar formations are. The rough formula for similarity between formations that I used is as follows: (1/3)*((difference in # of backs/3) + (difference in # of WRs / 5) + (difference in QB position)). For QB position, I converted distance from center to the following numerical values: under center is 0, pistol and wildcat to 0.5, and shotgun to 1.

Using the above formula, here are the complexity scores for each of the charted teams. Higher numbers indicate more complex offenses.

It’s tough to look at these numbers alone and get an intuitive sense for why a given offense might rate as complex or simple. Staring at the formula until it clicks isn’t exactly helpful either. Instead, I think it’s easier to look at complexity scores along with visualizations of the data from which the scores are derived to get an empirical sense of why certain teams score as high as they do. So here’s the above bar graph thrown into the visualization from the previous post:

In the final analysis post, we’ll try and actually answer the question of which is better: simple or complex offenses.