This is the second of a series of posts on decision-making and football.
We saw last week that the action on the field depends on the procedural decision-making system. To remind you, procedural decision-making depends on recognizing categories and releasing well-practiced actions based on those categories.
That categorization process is perceptual. Just as an adult human recognizes a tree, not blobs of brown and green, a football expert recognizes the categories within the game. But unlike the tree, in football, there is another team trying to make those categories hard to recognize. This leads to an arms race between perception and deception.
Let’s start with a simple example of perceptual recognition. The two teams line up. Once lined up, the linemen cannot move until the ball is hiked. So they are waiting for the right moment to start. The quarterback would like to give his team an advantage of moving first, so he provides information about when they are going to hike the ball (the count). At the same time, the quarterback doesn’t want the defense to know when the play is actually going to start, so he obscures the count and tries not to provide any information about when the hike will occur.
During the play itself, we also have a whole set of categories that one team is trying to recognize and the other team is trying to hide.
Imagine a linebacker trying to figure out if the handoff is real or fake. The defense wants to categorize the play into a running or a pass play. (Real categories are going to be much more complex, but this will explain the basic computations.) If it's a running play, the linebacker will want to move forward to cover the line; if it's a pass play, he wants to move back to cover the potential receiver. The quarterback tries to make fake handoffs look as much like real handoffs as possible, to make it hard to categorize. (Remember, this categorization and act process is happening quickly. The linebacker is not actually saying these words to himself. But he's learned to recognize cues that help him categorize real and fake handoffs, such as the way the quarterback moves after giving the ball to the running back.)
Similarly, the offense is always trying to ask Is it a blitz or not? If the offense can “recognize the blitz” and where it’s coming from, then they can bring in the extra men to respond to it. A defense might line up seven players with the potential to try to sack the quarterback, but, as the play starts, two might drop back to cover what the offense thought was open territory.
This arms race is all about information and builds on a mathematics of information theory. Information theory is about identifying relationships between cues and categories. It asks whether cues are more likely to occur in one category or another. If a team always passes on first down, then the defense has information about that. Even if a team passes 60 percent of the time on first down, then the defense has information about that. The fact that it is “first down” tells the defense that a pass play is more likely than a run play. Of course, if the offense knows that the defense knows that they usually pass on first down, and if they think the defense has gotten complacent, then maybe it’s time to run on first down.  That’s what makes the game interesting.
The arms race is happening at all levels, at the individual level of a runner trying to juke past a defender, at the pair level of whether a quarterback can throw to an potentially open receiver or not, at the tactical team level of trying to determine or hide whether the handoff is real or not, and at the strategic level of whether the play is a pass or a run.
Next week, we’ll take on the difference between strategic decisions made by coaches in the booth and on the sideline from tactical decisions made by players on the field.
 The best description of information theory is actually Neal Stephenson’s book Cryptonomicon, which is about World War II and using broken codes to win the war without letting the Axis know that the Allies had broken their codes. Similarly football teams are trying to balance maximizing the probability of success (when to run, when to pass, when to blitz) against not letting the other team know what they are going to do.