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Offseason Stat Series: Unveiling the Expected Points Matrix 1.0

Another installment working towards a better college football team comparison tool.

Introducing Expected Points

Hello friends, and welcome to another installment of the Offseason Stat Series. Over the past few football-barren months, I’ve woven my way through the empirics of various aspects of the game of football, from punts to turnovers to field goals, and more. Last week, I began a naive approach towards constructing expected point values for each play in college football, for the purpose of using those values to determine how well or poorly a team performed over the course of a season.

As a matter of professional development, I’ve been re-working my way through Jim Albert’s masterful “Analyzing Baseball Data with R” book. If you’re the slightest interested in working with sports dat on your own, this book is a great resource. Giving ample credit to Albert and his coauthor Max Marchi, I want to yet again apply some baseball logic to football analysis with the expected points matrix.

Baseball is a game of discrete states; each batter comes to the plate, each pitch is thrown in a certain situation - it could be two outs with no runners on base, or no outs with one runner on base, etc. In fact, since there are 8 possible arrangements of the runners on base, and 3 possibilities for the number of outs, baseball is a game of 24 states. Those states are discrete in that a batter enters into one state, and after his at-bat, the game shifts into another state; there are no muddy transitions between states.

The idea of muddy transitions between states is what complicates a football expected point matrix. Whereas baseball’s expected matrix is a clean 8x3 matrix of expected runs in each state, football’s states are almost continuous: first and ten bleeds into second and five which bleeds into third and four which bleeds into first and ten and so on and so forth. Whereas in baseball we can cleanly calculate the average number of runs a team will score in an inning given they enter a certain state, the football expected points matrix will involve some choices.

In this article, I’ll parallel efforts to ascertain the average number of runs in a given state of a baseball game by considering plausible states for the game of football, calculating the average points scored after reaching each state, and for illustrative purposes, examining TCU’s performance compared to the matrix.

Considering States in College Football

The game of football often comes down to crucial fluctuations in game state - an interception in the red zone effectively steals a score, a special teams’ flub ruins a teams’ field position advantage. Those states, though, are fuzzily defined - insofar as anyone discusses them, they are related to arbitrary groupings of field position and abstract concepts of momentum or “game script”.

Bill C. has done some prior work considering game states, although his focuses on changes in team behavior given game clock and scoring margin. I’d like to parallel the expected runs matrix commonly used in baseball, and as such, I’m going to focus on alternate definitions of game states.

Defining game states

When considering states in college football, one is essentially trying to diagnose the most important factors distinguishing different situations. Now, the clock and the scoring margin will be strong determinants of strategy, and thus expected points - a team up 50 with three minutes left, even if they are at the opponent 20, will not score. There’s a case to make for the prudence of separating plays and situations by clock, but as the sample size of one season is small* and the data is adjusted for (extreme) garbage time, I contend that parsing by the clock is actually unhelpful.

Instead, again mimicking baseball, we should think about the on field situation a team enters. My thought is that the three determinants of expected points are: field position, down, and distance. Each play is a discrete situation, and by broadening the groupings of those plays, we can construct some pretty sensible “states” for football.

For field position, one might think that granularity is a blessing - we can attach a state to each yard line on the field. I feel this approach is insufficient based on two key arguments. First, substantial research has demonstrated that referees are biased towards hashmarks in placing a football. Second is the argument about removing grains from piles of sand: Are we really sure that first and ten at the 22 is really different than first and ten at the 23? No. Are we really sure that first and ten at the 22 is really different than first and ten at your opponent’s 35? Absolutely. In that case, I’m going to cluster broadly field position into four categories:

  1. Inside your own 20
  2. Between your 20 and the fifty
  3. Between the fifty and opponent’s 20
  4. Inside opponent’s 20

Are these categories arbitrary? Sure, and I’m happy to work to revise them if you think this categorization ruins the entire idea of the expected points matrix. I don’t think it does, and so for now, these are our “field position states”.

Down and distance are a more straightforward matter. Again, in the interest of not sacrificing any of an already small sample, I’m going with broad groupings. The downs, obviously, will stay first through fourth, but I am (again arbitrarily - see note above) segmenting distance into three situations: short, medium, and long.

In that case, we have our game states: 4 field position bundles * 4 downs * 3 distances gives us 48 States a team can possibly encounter over the course of a game.

Constructing the Matrix

I’ll spare you all the gory details here, and instead briefly summarize how I constructed this matrix. First, I adjusted the play by play data from my good friend for garbage time, and then labelled each down, distance, and field position combination with a unique identifier. For each unique drive, we have all the situations reached at any point across this drive. Here’s a TCU vs Baylor drive and the situations encountered, just to illustrate.

Fun reminder: TCU beat Baylor in Waco because of Ben Banogu, Jalen Reagor, and the Mule. This is TCU’s first drive, right after Charlie Butterfingers Brewer got the ball karate chopped out of his hand by Banogu. TCU reached 5 different situations and two different field positions over the course of this drive, for a total of 6 game states. They kicked a field goal here, so I attached 3 points to each situation on this drive. On drives where teams scored a touchdown, I attached 6 points. Where they got a safety, I attached -2, and so on.

Then, after I had attached the points scored on a drive to each situation, I averaged the number of points scored by a team after reaching each situation. I want to explain more, but it might be easier to just show you the matrix. (If the table is nasty, here’s the Google doc.)

Expected Points Matrix 1.0

Situation Inside Own 20 Own 20-50 Opponent 50-20 Inside Opp 20
Situation Inside Own 20 Own 20-50 Opponent 50-20 Inside Opp 20
First and Long 0.501 0.947 1.543 2.489
First and Medium 0.694 1.083 1.876 2.754
First and Short 3.484 0.953 1.842 4.271
Second and Long 0.361 0.693 1.413 2.558
Second and Medium 0.615 0.886 1.638 2.723
Second and Short 0.829 1.166 1.833 3.752
Third and Long 0.225 0.384 0.968 1.898
Third and Medium 0.305 0.531 1.285 2.379
Third and Short 0.486 0.811 0.16066 3.256
Fourth and Long 0.407 0.015873 1.343 2.414
Fourth and Medium 0.571 1.36 1.36 2.574
Fourth and Short 1.148 0.791 1.437 2.766

And there it is, an expected points matrix for each state! Granted, this is version 1.0 and subject to plenty of revision before I start calculating values for teams and all, but this is a great initial tool and a pretty huge step in my analysis plan for this upcoming season (if I say so myself).

The Matrix in Practice:
Comparing the Frogs’ Reality and Expectations

So, then, what does this matrix do for us? Well, what we can do then, is calculate the averages for TCU specifically, and see how they performed in each state, relative to the “expectation”.

TCU Game State Performance, Offense 2018

Here is TCU’s actual points per drive, conditional on situation, plotted against the expectation. The red line is equality - where actual and expected points equal each other. This picture alone does a lot for us in terms of diagnosing quality - here’s Clemson’s graph, for comparison.

Clemson Game State Performance, Offense 2018

Whereas TCU’s offense achieves fewer points than expected from any given state, Clemson is substantially above on almost every drive. You can also see the impact of turnovers - Clemson lost only 17 all season, and as a result, most of their points per drive are zero at worst, whereas TCU lost 26. These graphs embed a lot of information, much of which Bill C. captures in his excellent Advanced Stats pages. But, these graphs confirm that quantifying plays by expectation does provide information for valuing team performance!

For fun, here’s TCU’s defense.

TCU Game State Performance, Defense 2018

As we’d expect, TCU’s defense held teams at or below expected points for most situations, except the red zone! I’m using an exclamation point there, because this analysis is in line with our prior belief about TCU’s defense, and even reflects some heterogeneity in performance.


I’m very excited about these Game State Performance graphs - they provide a simple reference for absolute team quality, relative to average. They also represent a plethora of possibility: I can divide these by conference, for rush and pass, and more. These comparisons will be especially useful for previewing teams this fall, and will also in the same vein serve for some serious diagnostic granularity in recaps. Most importantly, they confirm the direction of the xWSR statistic I’m constructing.

Let me know what you think about the Expected Points Matrix 1.0, and how these graphs play in terms of comprehension! I’ll be back next week with some more stats and wonkery. College football will be here sooner than you think, friends!