As a follow-up to my last post, which attempted to use poker to as a proxy for football, and explain why aggression is important to each, I'm going to give what I hope is a thought-provoking (and somewhat novel) theory on how a team with lesser defensive talent can neutralize some of the advantages a team with a superior offense enjoys.  It may run a bit long, but bear with me, because it should be an interesting discussion.  As I did last time, I'm going to start with poker, weave a little game theory into my argument, and conclude by tying it in to football.

Suppose for a minute that you entered the World Series of Poker Main Event and somehow, through a combination of intuition and luck, have made it to the final two.  You are heads up (yay!) and have only one person left to knock out.  If you do, money, fame, fortune and a bevy of hot blondes are yours for the taking -- you'll be so rich that you could cover your bed with money and roll around on it while you cavort with a variety of lovely women.  Sounds great, right? 

There's only one more obstacle to overcome before you can release your inner baller, and his name is Patrik Antonius.  Antonius is one of the most feared players on the planet.  He plays in, and wins, the biggest games in the world.  He's not afraid of anything, isn't intimidated by the money, and is basically a stone-cold killer as far as poker is concerned.  You playing against him is like trying to go one-on-one against Yao Ming.  You know that over time, his edge is so great that your chips will practically jump into his stack on their own.  Your only hope appears to be luck, right?  Is there any other hope you have of defeating your foe and becoming the poker celebrity that you've always wanted to be?

Let's be clear: in the long run, you have no edge, and no hope of winning - any more than you have against Yao Ming.  However, tournaments - particularly the heads-up portion at the end - are all about the short term.  All you have to do is win one big pot against your opponent and you either win the tournament or cripple your opponent to the point that he'll be eliminated in short order.

All hold-em starting hands are ranked in order of their strength.  This is most important in a heads-up situation because it's more rare that a person makes a big hand (i.e. a straight or flush) and, therefore, a high card (like an unpaired ace or king) or pair is most likely to win the hand.  In a nutshell, the strongest hand in a heads-up situation is a pair of aces, and the weakest hand is an unsuited 32.  

The biggest advantage your opponent will have over you is that he will quickly be able to put you on a range of hands.  So if you raise with only strong starting hands like aces, kings and ace-king, he'll be firing bets at any pot you don't raise knowing you'll probably fold.  Furthermore, if you start putting money into the pot with one of your premium hands and he hangs around, he's probably got something that beats you.  Eww.

So, what's this magic strategy that you can use against superior opposition? In order to keep your opponent guessing, you'll need to mix up your play.  In practice this means occasionally raising with your weaker hands so that your opponent has a harder time figuring out what your hand range is.  If, for example, you raise with aces, kings, queens and ace-king but also raise with 32 and 42, you've played almost twice as many hands and your opponent will have a harder time putting you on a specific hand.

There's an even better way to mix up your range, and it's so effective you could actually tell your opponent what your strategy is and it wouldn't matter.  It's simple: randomization.  You randomize the cards you play against him.  Let me explain why (and how) that works.  Then I'll relate it to football.

In the above example, you've widened your range by adding two hands to it.  An observant opponent will sniff that out pretty quickly.  A better strategy is to find some kind of randomizing element to determine when you play your weaker hands.  Based on the size of the money in the pot and the size of the bet you intend to make, game theory, in the form of the Nash equilibrium, can tell you how often you need to mix in your bluffs in order to make yourself un-readable by your opponents (I won't go into detail in this post, but if you're interested, you can check out the math here).

The idea is that you bluff enough that your opponent can't tell whether you are playing a strong hand or a weak one.  The way you choose when to bluff is by randomly selecting a hand you would normally fold in the first betting round and raise with it.  You determine how often you do that by using the aforementioned Nash equilibrium, but you don't really have to be that exact.  For simplicity's sake, you could probably raise with about twenty percent of the hands you'd ordinarily fold and that would be tricky enough. 

You've now created an unexploitable strategy that, in the short term, increases your chances of winning.  In the long term, your opponent will pick you apart in the later betting rounds, but like I said earlier, tournament heads up sessions are rarely long, so you've given yourself as good a chance as possible.  And since you're playing random cards, your opponent will not know if you're betting because you have a good hand or a bad one, even if you tell him what you're doing.

So, how do you pick a random hand? There are any number of ways, but the easiest way is to look at your watch.  If you're bluffing twenty percent of the time, you just look down at your watch, and if the second hand is anywhere between one and twelve seconds (twelve being twenty percent of 60), you bet.  It's that simple.

It's important to note that you only need to do this in games where you don't have an edge.  It's an, uhm, defensive strategy that seeks to make your intentions harder to read.  If you're already better than everyone you're playing against, then you don't need to go to such lengths to make yourself harder to read.

Well, that's awesome, but how does it relate to football?  I'm glad you asked.  This kind of strategy works best against when you're playing against someone who is good at divining what you're going to do.  So you would want to use it against a team with a quarterback that is able to notice larger patterns in your defensive play, sniff out your tendencies and anticipate what you're going to do, and make split-second decisions based on what he sees.  Sounds a lot like Peyton Manning.

In practice, it would work something like this: the Texans line up in a base defensive formation, depending on down, distance and game situation.  They can run any number of different sets at the offense from this formation - they can blitz one or more players, they can drop back into coverage, they can read-and-react, whatever.  Let's say that in any given formation, there are ten possible sets.  Some of the time, the defensive coordinator is going to call a play based on what he thinks the opposing quarterback's tendencies are: which receiver he's been favoring, if a running back has been running the screen particularly well, etc.  Basically the standard cat-and-mouse game between offense and defense. 

However, because the qb in this situation is Peyton Manning, he is able to sniff out what the defense is likely doing and make the right adjustment most of the time, because he's also aware of the defense's tendencies, etc.  Here's where our poker-game theory example comes into play.  A certain percentage of the time, our defensive coordinator is going to send in a random play.  He won't change the defensive formation, but he's going to use whatever random number generator he wants to and use that to determine which play he's going to call. 

He won't do it all the time, because there is a lot of value in adjusting your defense to what the offense is doing well or poorly.  If he's really mathematically inclined, he can use the Nash equilibrium to determine how frequently he'll do it in each particular situation.  But even if he does it, say, twenty percent of the time, he can have a real impact on Peyton's game management.  Again, you would not want to do this against a qb like Vince Young who has a limited ability to read the field, but it could be effective against a Tom Brady or Peyton Manning.

It may sound like I've just spent a ton of time and space discussing something radical and far-fetched, and I would be surprised if any coach ever did this, but I think a lot of modern coaching theory supports this idea, even if it isn't so academic.

For example, here's a quote from a great article in The Atlantic. The author spent a day with Andy Reid watching footage of the 1958 NFL Championship game and wrote about Reid's analysis.  From the article:

"If I’m calling the plays" on offense, [Reid] went on, "I get paid to get into a rhythm with the guy calling the defense" on the other side. When a coach achieves the right "rhythm," he can sense what his opponent is thinking—and for Reid, grasping the "rhythm" of the classic game was fairly easy. "I can see what the offense is doing," he said. "You can almost call it offensively and defensively."

The strategy I've laid out is simply a scientific way of determining how not to get into that rhythm that Reid talks about.  Another example of the importance of unpredictability is the idea of scripting a team's first fifteen or twenty plays on offense.  The reason this is done is so that a defense can't anticipate what the offense will do.  My theory is just a way to extend that unpredictability into the rest of the game.

This has turned into a long post, and it's not quite as sexy as talking about the draft or our free agent needs.  But I hope those of you who have stuck with me this far have something new to think about when you put on your Andre Johnson pajamas and dream of Steve Slaton running over Albert Haynesworth.