Building a Better Box Score

What is the most common line present in any analytics-based article/post/discussion of the game of football? My answer is some version of “Analytics in football are more difficult/impossible/can’t be done because of how interactive and interdependent the members of a football team are compared to other sports.” Sometimes that basic line is flavored differently, depending on the particular tone of the piece, but that line always seems to be there. It’s a seemingly necessary caveat of the genre. “Of course we can’t know everything about Quarterback X because so much of being a quarterback depends on [insert whatever point one want to make about interactivity on football teams].”

Why do we simply talk about that problem? Why do we constantly talk about the interdependence problem but never fix it? Can it actually be fixed and what would such a solution look like?

The Football Box score – A Model by Ralph Wiggum

To start, I’d like to spend some time developing the idea of why dealing with the interdependence problem is so difficult in football. After all, other industries deal with a similar problem. The entire job of management is interactive and interdependent by nature, we can still figure out who the good managers and the poor managers are. Why do we have such a difficult time in football? I argue it’s because of the modern football box sore, a ubiquitous, pervasive summary of the events on a football field that horribly misrepresents the realities of the game.

A good box score acts like a description of the events of a game, the same way that the model of the solar system you built in middle school acts as a basic description of how the solar system works, how it is set up, and how each component generally relates to the others. Your solar system model was also simplified. You didn’t put all of Jupiter’s 67 moons in your model. You probably didn’t put in the asteroid belt or the daily spin of each planet to an accurate degree (kudos to you if you did), and that’s okay. The purpose of any model is to get the major elements of the system correct while simplifying or eliminating the less important elements. And this is where the box score of a football game falls down dramatically. If a football box score were a model of the solar system, it would be a model created by Ralph Wiggum. This is true to some extent of the entire box score, but I’m going to focus mostly on the passing statistics element as it is the worst offender.

The passing yards box score for Florida State in their blowout loss to Oregon in the first round of the college football playoffs looks something like this.

Passing Yards

Jameis Winston, 29/45, 348 yards, 1 TD, 1 INT

Sean Maguire, 0/3, 0 yards, 0 TD, 0 INT

Receiving Yards

Travis Rudolph, 6 rec., 96 yards, 1 TD

Jesus Wilson, 5 rec., 72 yards, 0 TD

Karlos Williams, 5 rec., 59 yards, 0 TD

Rashad Greene, 6 rec., 69 yards, 0 TD

Dalvin Cook, 3 rec., 24 yards, 0 TD

Ermon Lane, 2 rec., 22 yards, 0 TD

Freddie Stevenson, 1 rec., 12 yards, 0 TD


There are lots of problems with how this data is presented, but let’s focus on two.

Problem 1 – Data Redundancy

The problem that upsets me the most about a football box score is needless redundancy. Every single yard gained by a forward pass is counted twice – once for the quarterback and once for the receiver. This is a problem, a big problem, because it means the data presented here do not reflect what actually happens in a football game. You don’t complete a forward pass and then immediately mark off the gained yardage again. However, in a football box score, because we call the events different things – completions vs. receptions and passing vs. receiving yards – suddenly it becomes okay to double count every single event in the passing game except attempts and interceptions. But they are the exact same event. Jameis Winston’s completion is Rashad Greene’s reception. One cannot happen without the other. Winston earns passing yards and Greene earns receiving yards on the exact same yards gained. We’re not modeling what actually happened in the game. We’re modeling a way to give credit in the most individualized way possible. However, as every single football analytics article will tell you, football is an interactive game. If the game is, in reality, interactive, why do we assign credit for the events in this individualized manner?

Problem #2 – Loss of Information

I think it’s rather ironic that a football box score has so much information redundancy, but it explicitly removes an important piece of information that would allow us to complete some very important analyses on team performance in football.

As an example of the loss of information, let’s look at a different example, this time from Oregon’s Week 1 win over the University of South Dakota. Early season games are useful for this example because it is very likely that the backup of the “high power” football program will spend a great deal of time in the game.

Passing Yards

Marcus Mariota, 14/20, 267 yards, 3 TDs, 0 INTs

Jeff Lockie, 11/12, 113 yards, 1 TD, 0 INTs

Receiving Yards

Byron Marshall, 8 rec., 138 yards, 2 TDs

Darren Carrington, 4 rec., 68 yards, 0 TDs

Dwayne Stanford, 1 rec., 62 yards, 1 TD

Pharaoh Brown, 2 rec., 32 yards, 1 TD

Johnny Mundt, 2 rec., 29 yards, 0 TDs

Keanon Lowe, 1 rec., 18 yards, 0 TDs

Royce Freeman, 1 rec., 11 yards, 0 TDs

Thomas Tyner, 3 rec., 8 yards, 0 TDs

Charles Nelson, 1 rec., 8 yards, 0 TDs

Devon Allen, 1 rec., 5 yards, 0 TDs

Johnathan Loyd, 1 rec., 1 yards, 0 TDs


Here we have two quarterbacks that completed a similar number of passes over the course of the game, but Marcus Mariota gained more than double the passing yards compared to Jeff Lockie. How was that accomplished? Which receivers gained all those yards for Marcus Mariota? Who caught those passes from Mariota to gain so many passing yards for him? Was it because Dwayne Stanford caught one long pass for a touchdown from Mariota? Or did Jeff Lockie complete that pass and only got 51 yards from the other 10 passes he completed? Who was the intended receiver on the six attempts that Mariota did not complete? How many times was any receiver an intended receiver, but did not complete the catch? Did Mariota target the same receiver over and over with no results? Or are his unsuccessful attempts scattered all over the place? We don’t know the answer to any of these questions from the box score description of this particular game. Answering these questions is of critical importance to a better understanding of the game of football.

Our first step to scientifically understanding football is to build a better box score. The question is, what would we want the box score to represent?

Begin with a Model

Before we can build a tool to aggregate data, we need to have a decent idea of what data we want and why we want it. We need to start with a theory of how a football offense works. This is our “model of the solar system” as it were. What things in a football offense are important and what things should we avoid for right now? Here is a figure of my current theory of a football offense.

Basic Model of a Football Passing Offense



This very basic theory says that a football offense begins with the offensive play caller. The play call made then filters down to whichever quarterback is currently in the game, and the ability of the quarterback then filters down to the receivers. Note that we could also include pass catching tight ends and running backs in this model.

Now, I’ve simplified the passing offense to a great extent in this model. Most notably, I’ve removed the impact of the offensive line here. That is by design, but not because I think that the offensive line is unimportant. Instead, I think the offensive line is like adding in the daily spin of the planets to your solar system model. Adding it in becomes incredibly complex and will probably take some specialized data that not is not publically available. For right now, we will keep the offensive line out of our model. Anything else that’s left out of this model we will consider as having such a limited effect that it won’t change our understanding to a large enough extent that we need to account for it.

A Better Box Score

Now that we have our model, we can adjust our box score so that it reflects the important elements inherent in our model. The most important element of the theory says that we must count passes as a single event and account for the coach that called the play, the quarterback that threw the pass, and the receiver that caught it. Such a thing isn’t terribly difficult to create. You can see an example of one below. In this example, I am allowing team to stand in as a proxy for the play caller.



Now all we need is a way to analyze data that fits our theoretical understanding and the data that our better box score is collecting.  Fortunately, such a way exists. Next week.

Are You My Mother?

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Published on: March 25, 2015

One of my daughter’s favorite books is Are You My Mother? by P.D. Eastman. In the book, a baby bird hatches while its mother is away finding food. The bird decides to leave the nest in search of its mother, all along not being sure exactly who his mother is or what she looks like. He has several ideas, attempting to connect with a kitten, a dog, a cow, and an airplane until he is finally returned to his nest by a hydraulic digger (it’s a very cute story) just before the mother returns to the nest with a worm.

For a while, I’ve felt like my writing on this blog has been akin to that bird and its quest. I feel like I’m trying to connect with different styles of writing, but those styles simply are not me. I’ve tried being irreverent, I’ve tried touting my knowledge without discussing methods, but the words ring hollow in my ears. Last week gave me the opportunity to actually sit and think for a few minutes (but only a few) about what I value and what I really want this blog to be.

I thought about the times I felt valued and like I made some small contribution to a discussion on the internet. The last time that happened was the night everyone was talking about #TheDress. Half the people in my department are vision researchers, so I’ve been subjected to a lot of vision presentations in my time. I had just finished teaching the section on luminance perception in my Intro class and I had something to say. I didn’t say much, but people seemed to find value in it and it felt very good.

I read Bill Connelly’s article about the important, unanswered questions in college football. It’s a good piece designed to spark a search for answers. The interesting thing for me is that the answers to two of the first five questions are sitting on my hard drive right now. Understanding how to answer them isn’t particularly complicated or inventive. It just takes finding the right tools. Tools I know a great deal about due to 10 years of studying interacting, interdependent groups and teams. Tools most other people don’t have because hardly anybody spends 10 years studying interacting teams unless one already has tenure (not me) or gets phenomenally lucky in employment (there I am).

I also thought about times when I didn’t feel right about my whole enterprise of data analysis of football, that being the Patriots deflated ball controversy. That was a weird time to be interested in data analysis of football because someone that isn’t particularly interested in reproducible, publicly available analysis attempted to answer a question. That question wasn’t answered particularly well, and the whole thing really spiraled out of control. However, it did get me thinking of the notion of credibility and how truly important credibility is to me. The guy that answered the question initially isn’t particularly credible, but then I had to confront the question of how much outward facing credibility I have given that we both hide how we arrive at the conclusions we do.

I thought about my academic area as a whole, and how much of a credibility hit it’s taken lately. I’m a social psychologist. You might not be aware of this, but for the last 3-4 years, social psychology has taken something of a walk off the credibility cliff in academic circles. Reports of outright falsification of data[link], poor data management, and “massaging” of results have become too numerous to mention them all. Frankly, it’s been very depressing to be a social psychologist these last few years. I’ve survived by teaching, but I haven’t been able to get excited about research the way I used to. I have a dissertation that was nominated for (but didn’t win) an international award just sitting, unpublished, because I can’t force myself to get it out the door. I’d never really connected my publication struggles to credibility before, but upon reflection I think that may be a major cause, if not the primary one.

So here is where we’re at.

  • Scientific credibility is important to me, both personally and for the field of social psychology and the sub-specialization of interacting groups that I work in
  • I need to do research to keep my day job
  • I am struggling to do research because I have issues with the credibility of certain elements of my field
  • In my own internet space, I am not acting in a way that brings about scientific credibility either to myself or to my chosen field

This is a contradiction I cannot have, and the solution is to change the approach. I’m going to continue publishing here in an attempt to rebuild my own sense of credibility. Hopefully, this will rebuild my taste for research in my day job with the ultimate goal of gaining some job security for once in my life. Starting next week, I’m opening up the kitchen [link] to show everyone how I’m building everything I’ve built here. I’ll be discussing science as it relates to interactive, interdependent teams in the context of professional football. Hopefully, you’ll be able to apply some of what I say to contexts beyond football. I’m going to be spending a lot of time covering techniques and methods used to study interacting teams as they are reasonably uncommon methods of data analysis. I’ll be talking in a very scientific, academic tone with how I approach these concepts as that’s what I am.

This has been my realization. I am not a scout or a journalist. I am not a gambler or a tout, or an information broker. I am a scientist.  Come back next week and we’ll learn something together.

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