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MHR University: Game Theory and Strategy

Hang on to your seats folks, hopefully what I'm about to discuss will have you looking at football in a completely different way.

Game theory is a mathematical method for predicting human behavior in strategic, multi-player situations. Game theory assumes that each player forms rational beliefs about what other players in the game will do and then chooses a response to those strategies that maximizes its own payoffs.


If you're an academic or a mathematician, I would suggest finishing that article--great stuff. It goes far beyond what I want to discuss here however. The way I think of game theory and strategy is to assess different scenarios and situations within a subset of circumstances and then trying to quantify the possible outcomes to those scenarios that you can then use to map out plans and actions that will put you in optimal positions to succeed.

Pure game theorists rely heavily on statistics and mathematics, and while football allows for that, I want to teach it to you here will help you develop your own way of thinking within a specific methodology and set of precepts. We'll use statistics in a more base manner just to make more informed decisions.

Defining the perimeters

Probably the first real blueprint or roadmap for game theory was created by the great Sun Tzu. Sun Tzu was a Chinese military general during the Zhou Dynasty who wrote a discourse based upon his knowledge of warfare that we know today as "The Art of War". Think of it as a book of proverbs to operate upon as a military strategist. If you're unfamiliar with Sun Tzu, here are some of the strategies from his writings:

"If you know the enemy and know yourself, you need not fear the result of a hundred battles. If you know yourself but not the enemy, for every victory gained you will also suffer a defeat. If you know neither the enemy nor yourself,
you will succumb in every battle"

"To know your Enemy, you must become your Enemy."

"Supreme excellence consists of breaking the enemy's resistance without fighting."

"All warfare is based on deception. Hence, when able to attack, we must seem unable; when using our forces, we must seem inactive; when we are near, we must make the enemy believe we are far away; when far away, we must make him believe we are near."

"Thus we may know that there are five essentials for victory:
1 He will win who knows when to fight and when not to fight.
2 He will win who knows how to handle both superior and inferior forces.
3 He will win whose army is animated by the same spirit throughout all its ranks.
4 He will win who, prepared himself, waits to take the enemy unprepared.
5 He will win who has military capacity and is not interfered with by the sovereign."

"Engage people with what they expect; it is what they are able to discern and confirms their projections. It settles them into predictable patterns of response, occupying their minds while you wait for the extraordinary moment — that which they cannot anticipate."

"When the enemy is relaxed, make them toil. When full, starve them. When settled, make them move."

"Treat your men as you would your own beloved sons. And they will follow you into the deepest valley."

"So in war, the way is to avoid what is strong, and strike at what is weak."

"One mark of a great soldier is that he fight on his own terms or fights not at all."

Now there is quite a bit here, but don't let that fool you. Everything above can be quantified as "information". The better and more complete information we have not only about ourselves but also about those around us will allow us to make more informed decisions. More informed decisions have a better likelihood of producing the desired result.

Football teams are managed at all levels. Want to know how Peyton and the coaches start to develop their gameplan everyweek? Starts with the quality control coaches. These poor shlubs are the lowest on the totem pole and get stuck with all the grunt work. These are the guys cutting up the film for the coordinators and players to use, they are the ones who painstakingly go through hours of tape to put statistical values on situational football. Let's start there.

What does an opponent like to do on 1st down? What personnel groupings do they run? What formations can we expect to see run and pass? When they pass what sort of route combinations do they use? When they run are they attacking a perceived weakness on defense or are they playing favorites with certain players/combos on their own line? Do they account for extra rushers? I literally can ask about 100 different questions about 1st down. And then you filter all that information through the circumstance of score, juncture in the game, and field position.

Once you consider all the permutations and possible scenarios, the sheer gravity of the seemingly infinite information is enough to make your head spin. I want to take this sea of information and thin it out to the most basic checklist so we can begin to learn how to use game theory:

1) Situation

2) Courses of Action
3) Likely Outcomes
4) Best Course of Action

Now let's pretend we're the head coach making decisions and go through through one basic football scenario to see if we can put this list into motion.


3rd and 4

Field Position:

opponents 38 yard-line


You: 17

Opponent: 20


4:42 4th Q, two timeouts


- (conservative) play for field goal

- (moderate) play for first down

- (aggressive) take a shot


- you convert 65% of the time on 3rd and 4 or less

- the opposing defense allows a conversion 55% of the time on 3rd and 4 or less

- you convert 75% of the time passing on 3rd and 4 or less

- the opposing defense allows a conversion 67% of the time through the air

- you convert 44% of the time rushing on 3rd and 4 or less

- the opposing defense allows a conversion 33% of the time on the ground

- your kicker is 45% from 50+, and 77% from 0-49.

- your RB fumbles the ball once every 100 touches

- your QB throws an INT once every 55 attempts

Base thoughts:

- If you don't get another yard, the FG will be from 55 yards, which you know is a coin-flip proposition at best with your kicker.

- You need 4 yards to convert but anything less than that does not significantly increase your chances of kicking a successful FG.

- The opposing defense will not give much on the ground

- You're more likely to succeed by passing, you're also more likely to extend the drive by passing.

1) Situation

3rd and 4, 4th Q down by three, more than 4 minutes left with 2-timeouts

2) Courses of Action

Run the ball, Pass the ball short, Pass the ball medium, Pass the ball deep

3) Likely Outcomes (in order from most likely to least likely)
Running the ball

No Gain, Minimal Gain, Negative Gain, Requisite Gain, Big Gain, Fumble, TD

Passing the Ball (Short)
Minimal Gain, Requisite Gain, Big Gain, No Gain, Negative Gain, TD, INT

Passing the Ball (Medium)

Requisite Gain, Big Gain, Minimal Gain, No Gain, Negative Gain TD, INT

Passing the Ball (Deep)

No Gain, Negative Gain, Big Gain, TD, INT

4) Best Course of Action

Short or Medium Pass


You're at a disadvantage running the ball because both your percentage of failure and your opponents percentage of stop are both significantly higher than when you pass the ball. Even if you manage to gain positive yardage, it isn't likely you will gain the first down, and you're only affecting field position by a couple of yards which doesn't give your kicker a better shot at tying the game.

Likewise, passing the ball deep makes it more likely you'll throw an incompletion, get sacked, or even throw a pick. Even if none of the big things on the list happens, you're still more likely to end up in the same predicament as when you run the ball.

If you pass the ball short, you take much of the risk of both a turnover and negative gain out of the equation, but you also run the risk of not converting either.

If you pass the ball medium, any completion is likely to convert and the higher risk outcomes are still far down the totem pole of likelihood.

Your correct course of action is to dial up some sort of medium range passing play


This was basic information, now let's assume your quarterback is Peyton Manning. Let's also assume he sees a one on one on the outside with Eric Decker or Demaryius Thomas. Peyton will take that shot downfield more often than not. Thinking here is that you still have 2 timeouts and plenty of time left. Risk/Reward might be too great here.

Now lets say one of those receivers has off man coverage on the outside. Perfect time to dial up a WR screen. Could be a big play. Will likely be a first down.

As you can see there is always more information to take into consideration which is why you'll also see players and coaches looking at stills and discussing things as the game progresses. God I love football!

Wrap Up

This is something I want to use as a feature article throughout the season. Each week I'll find a play to examine and go through this exact processes using real stats and info. You can use my method as a blueprint, you can develop your own--doesn't matter. The important thing to remember is that Game Theory and applying it to football and the team we love will have all of us "knowing our enemy and ourselves" on a much deeper level.

Feel free to use the comments to ask questions, debate scenarios, even propose some tweaks to my checklist...whatever you want MHR!