Football Math

David Cowles

Nov 30, 2022

“At last, an opportunity to watch football in peace! … Just beer, pretzels and picking out the next Tom Brady.”

Who doesn’t love college football? There are dozens of games, good games, on national television every week. Often, you have no allegiance to either team playing and, mercifully, for once, neither team is depending on your armchair cheering to tilt the outcome of the game in its favor.


At last, an opportunity to watch football in peace! No responsibilities. Just beer, pretzels and picking out the next Tom Brady.


Incredible feats of strength and speed, paradigms of grit and determination, and coaching stratagems worthy of a chess master. What’s not to love!


And then there’s the game itself, the ebb and flow, the score. Early score differentials (‘spreads’) are sometimes amplified as the game progresses, but just as often they are dampened, and in some cases, they are actually reversed.


Football is a 21st century cultural phenom. In this age of social fragmentation, it’s just about the only thing we still have in common. Everyone speaks football. If baseball is our national pastime, football has become our national language and every Saturday/Sunday we celebrate our secular liturgy in the vernacular. 


A football game is all about the unfolding of patterns (every ‘play’ is really a pattern), and after watching over a dozen games this season, it occurred to me: while there are numerous patterns inside each game, do the games themselves form any patterns?


For example, can the scores of multiple games between various opponents tell us anything? Or are they just random? Do scores evolve arithmetically over the course of a game? Or is there something else, something non-linear, at work?


To test this, I looked at score differentials at the end of the first half and compared them with score differentials at the end of the same games. Easy-peasy? Well, no! In fact, solving the problem requires us to invent (or deploy) a whole new math: football math.


A football game is an example of a discontinuous process. We deal with whole numbers only (no fractions). Plus, unlike most other sports (soccer, baseball, e.g.), those numbers do not increase iteratively. What do I mean by that?


Say a team scores 5 times in the course of a game (5 runs, 5 goals, etc.). In most sports, that would result in a score of “5” for that team. Not in football.


First, in ‘football math’ there are only 3 digits: 2, 3, and X where the value of X can be 6, 7, or 8. Crazy!

But if you are a regular reader of Thoughts While Shaving (TWS) and Aletheia Today Magazine (ATM), you’ll realize that it’s not so crazy after all. You already know about civilizations that ‘play the game of life’ with no numbers whatsoever, or with a very limited inventory of numbers (e.g., 1, 2, X where X refers to any collection of 3 or more items).


Compared to these societies, ‘football math’ is pretty powerful. Granted, we only have 3 digits (2, 3, X), but one of those digits (X) can represent any one of three different values (6, 7, or 8). So, in essence we have 5 digits (2, 3, 6, 7, 8). Plus, we can ‘add’ those digits together to generate even higher, ‘secondary’ numbers. 


So far so good, but please, don’t get too comfortable! It turns out that the score of a football game is an example of Zeno’s Paradox. Zeno-math applies in universes, like football games, where quantity is not infinitely divisible.


In our search for patterns, we need to look at the event from 3 perspectives: pre-game, game, and post-game. Pre-game began at Big Bang. (If you’re tailgating, you might want to take an Uber…and invest in a port-o-potty. 15 billion years equates to a lot of Budweiser.)


Pre-game, the so-called ‘score’ is always 0 – 0. A whistle blows: the kick-off, a play that could result in X points (6, 7 or 8) for one team; but otherwise, it’s still part of pre-game.


Remember, for the purposes of this exercise, we are not concerned with a 60 yard rope, a one-handed snag, a blocked punt, or a pick-six. We are only tracking score and so far, we have no score. We say that the score is 0 to 0 at the start of the game, but that is just a useful convention. The fact is that we have no score at all until we have a score (credit Y. Berra for that inspiration).


Sidebar: Suppose the game ends in a 0 to 0 tie: then for our purposes, there was no game. The game never started. We’re only tracking variations in score and in this scenario, there was nothing to track. There was no variation because there was no score.


For us, the game begins when one team ‘puts points on the board’. Only then, can we talk about winning or losing.


What we normally call ‘the final score’ is part of the post-game. The ‘final score’ is not settled until the play clock reads 00:00, in other words, until the game is over and post-game has begun.


The final play is still part of the game, but the final score is part of the post-game. The ending of the game is simultaneously the beginning of post-game.


So, Blue scores and the game has begun; Blue leads, right? Wrong! Blue does not lead; the game is still ‘statistically tied’. How come?


After Blue scores, the scoreboard reads 2 – 0 or 3 – 0 or 6 – 0 or 7 – 0 or 8 – 0. 


But either team can score 8 points on any given play, even if it is the last play of the game. So, a lead of 8 points or fewer is actually no lead at all because it can be erased at any second so long as the ball is still in play (i.e., the game clock reads something other than 00:00).


British philosopher, Alfred North Whitehead, ‘the process philosopher’, describes every event in the real world the same way we just described a football game. What we call pre-game, he calls ‘the actual world’; what we call post-game, he calls ‘objective immortality’.


Every event arises out of an actual world and dissolves into an objective world. Every football game begins from pre-game (0 – 0) and ends at post-game (the final score).


Games consist of a finite number of discrete plays. The exact number varies, but the median game has approximately 120 plays. Each play is potentially worth 8 points to either team.


Assume there is an 8 point differential heading into what will be the final play of the game. The final score will reflect a differential somewhere between 14 points and 0. (A Touchdown scored on the last play of a game can only be worth 6 points to the winning team.)


In the language of political polling, we would say that the provisional score at any point in the game has a margin of error of up to 8 points. Therefore, when the ball is still in play and Blue leads Red by 8 points, the game is statistically tied.


Ground rules in place (and hopefully agreed), we can now get back to our search for patterns; I examined the box scores of all 13 FBS games played during week #7 of the season, in which at least one of the teams playing is ranked in the Top 25 (quality control).


Of those 13 games, 5 ended with a differential of 8 points or fewer (one score), 6 ended with a differential of 16 points or fewer (two scores) and 2 games ended with a differential of more than 16 points (three scores or more).


Now let’s look at the same games at the end of the first half.


Hypothesis: On average, the differential in points at the end of the first half should be half of what it will be at the end of the game. If so, 11 games (out of 13) should have been ‘statistically tied’ (point differential of 8 or less) at the half.


Observation: The total number of points scored was roughly the same in both halves, as expected; but only 9 games were statistically tied at the half (vs. the 11 anticipated).


This means that there is a centripetal force at work in a football game that offsets, at least in part, that ubiquitous centrifugal force we know as ‘time’ (or duration). In English, scores tighten, not absolutely but relative to time played.


Can learn something from this analysis that we can apply beyond the universe of football?

A football game is an example of a single event with conflicting objectives.  Like any system in a state of quantum coherence, it often manages inherent conflict by delaying its ‘winner reveal party’ until the very last play of the game.


While ‘there can only be one winner’, the game itself is shaped by both sides of the conflict. Objectively speaking, it doesn’t matter which team wins; it’s a zero-sum game. Subjectively speaking, of course, it makes all the difference in the world; it’s an all or nothing proposition!


Conclusion: Process is self-modifying. Things diverge less than expected, based on Newtonian arithmetic. Interaction favors convergence. Things do not fall apart as rapidly as expected. Interactivity inserts another variable into the cosmic equation. Even in the face of inexorable entropy, perhaps there is hope!


 

David Cowles is the founder and editor-in-chief of Aletheia Today Magazine. He lives with his family in Massachusetts where he studies and writes about philosophy, science, theology, and scripture. He can be reached at david@aletheiatoday.com.

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