Game Theory

For your Christmas present this year, allow me to introduce you to a little Game Theory. Let's start with Minimax Theory. Impress your friends! Freak out your relatives! Here's a summary of that theory:

"For every two-person, zero-sum game with finite strategies, there exists a value V and a mixed strategy for each player, such that (a) Given player 2's strategy, the best payoff possible for player 1 is V, and (b) Given player 1's strategy, the best payoff possible for player 2 is −V."

Let me take a crack at it for you, without the algebra... Two opponents in a game where one will win and the other will lose will each try to minimize their bad outcomes, and maximize their good outcomes.

A gentleman named John Forbes Nash created a game solution concept for a zero-sum game (one with a winner and loser) that implies two equally matched players, each knowing the best strategies of their opponent, would adopt opposing strategies such that neither could successfully do what would be optimally best. When you get to that point, you're in what's called a Nash Equilibrium. Two tic-tac-toe players that know what they're doing can easily get to a Nash Equilibrium.

Let's think for just a moment about youth football, and the decisions of offensive and defensive coordinators. Without worrying about passing too much, since passing isn't that easy for fifth graders, then as a defensive coach you might choose to defend the outside run, or the inside run, or 'play it safe' and attempt to defend both types of running plays equally well.

As an offensive coach I can choose to run inside or run outside.  On the table below, I've shown what the defense can do on the top column labels, and what the offense can do on the row labels, and within the matrix, what the yardage gain outcome might be given the circumstances.

	D Defends Outside	D Defends Inside	D Defends Both
O Runs Outside	0	5	4
O Runs Inside	5	0	4

There are four downs available to gain ten yards for an offense. But the risks associated with giving possession back to the opposing team on a fourth down failure make three downs the effective opportunity.

Under two out of three scenarios shown in the matrix above, as an offensive coach I can run a successful play. At first blush, that would seem to be pretty good odds. To optimize my chances for a five yard play, I need to 'keep you guessing' so let us presume that I will try to run as often inside as I do outside.

Also notice that your defense can't just sit in a defense-of-both posture. If you do that then I will gain 12 yards every three plays and march down the field.

Given my criteria, your defense would best be served to guess and defend either inside or outside on every first down. Two outcomes would be possible. If you guess correctly, I gain 0 yards. If you guess incorrectly, I gain 5 yards.

So the down and distance for the next play is either 2nd and 10, or 2nd and 5. If the distance is 10, then for both of the next two downs you should play safely against both types of runs, and force my offense into 4th and 2.

If though, you did not guess correctly on first down, you are now defending a 2nd and 5 situation. You should guess again. If you guess correctly on second down, you will force our offense to face a 3rd and 5, at which point you can safely defend against both and inside and outside run and likely force us into 4th and 1. If you guessed wrong for a second consecutive time then you have just allowed me a first down. But you should guess again, and hope you won't be wrong four times in a row.

Unfortunately for most offenses, if the defense guesses correctly even ONCE in any series of three consecutive downs, which they are statistically likely to do, then the offense will encounter a fourth down situation within four to six plays.

By guessing in this manner, your defense minimized risk over a series of three downs, and maximized the chance of creating a fourth-down during the possession. That's Minimax theory at work.

Because it gets really hard to string three first downs together, offenses reach a Nash Equilibrium in the game, and can't score.

Enter the option. (You knew it was coming, didn't you?)

The coolest thing about the triple option is that it tilts the odds in favor of the offense running the right play. The guesswork has been removed. My offense no longer cares whether your defense is defending the inside or outside, until the play has commenced.

Running the triple effectively is like being able to bet at the roulette wheel for both red and black with the same chip. Once the ball gets rolling, you're pretty sure that one or the other is going to work.

I've not just minimized, but actually eliminated the statistical advantage for the defense of defending either the inside or the outside. If you defend the outside, the triple runs inside. If you defend the inside, the option goes outside.

The test of course, especially in youth football, is that the next best strategy for your defense will then be to force my offense (or our coach) into errors. Your defense will try to get us to make the wrong read, or run the wrong version of the option, or defeat our blocks, or make a big play with some type of high-risk strategy that might leave the defense in an otherwise unsound position, but could create a big loss of yardage.

And that's another whole set of circumstances that we would have to draw out, and won't worry about today.

The triple option isn't the exclusive way to apply these game theories to football. Many modern college spread offenses have options on pass patterns as intrinsic components - so depending on how the defense is aligned, a pattern may break off or take off in different directions and timings. Zone read running plays are option running plays from shotgun, and NFL offenses throw quick slants and wide receiver zip passes off called running plays all the time, depending on what the defenses show. These are all more modern ways of using real-time decision making to maximize good outcomes.

These games within games are all Minimax efforts to tilt the Nash Equilibrium out of balance and into the favor of the offense.

To all our players, parents and friends, here's hoping your holidays are maximized for great outcomes, and  don't let the eggnog effect your equilibrium too much.

Ho, ho, ho, Merry Christmas!

What Don't You Know?

"There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don't know. But there are also unknown unknowns. There are things we don't know we don't know." ~ Donal Rumsfeld

This post is about unknown unknowns. It came to mind because I was thinking about the Black team's three losses in 2010.

(I've noticed that I don't dwell on the losses for the other teams quite as much. I think it is because I'm focused more on the improvements among individual players on the Blue and White teams, and can really leave the games at that. But I seem to linger on the losses for the Black team. We did have improvement among many of our players on the Black team as well, but I just wasn't entirely content with that. If you're blessed with a roster full of talent, you'd better win games. We try not to overly emphasize winning, but as I've mentioned before, they do keep score, and we do try to win.)

Anyway, what kept coming to mind thinking about those losses was Don Rumsfeld's famous line about unknown unknowns. His topic was much more serious than mine, but he actually expressed what we went through to some degree as an offensive football team.

In our 6-0 loss in the semifinals of the Basehor Tournament, we knew that we would have to adapt to playing without a couple of key players. We knew that we would not know what type of defense they would be playing, as there had been no opportunity to scout them. But we did not know that we did not know how to handle an eagled scheme with hard-charging defensive ends. By the time we learned that, the game was in the second half. By the time we found something that might have worked against that thing that we didn't know about, we were down to our last possession.

Before our game against SMNW, we knew that their safety would come up to play run support just before the snap. We knew that we would not know until we had a few cracks at their line whether our veer or option would be more effective (turned out to be veer.) But we did not know that we did not know how to handle an overloaded gap blitz. We learned how to handle that in the weeks following that game. But our offense sputtered in that game because we never knew that we hadn't known how to handle a defense like that.

Against Olathe East we knew that we would be playing the best team in our league, and we would need a great effort against them. We knew that we would not know from snap to snap where their safety would line up, and we prepared for multiple possibilities. But we did not know that we needed to know how to attack a team that stacked six players outside our A backs, instead of the more typical four. It wasn't until the following week at practice, after losing to them, that we developed some better strategies to deal with that type of alignment.

By the time we played our final game we could handle defensive ends crashing with a 5-3 eagle under look. We were much more prepared to pick up the occasional blitz, even through an overloaded gap. And though they didn't stack the outside quite as aggressively as Olathe East, our final opponent did shift somewhat to the outside at the expense of their interior defense - and we were in a far better position to exploit that.

There is a temptation to believe that "now we've seen it all." But I'm sure that we haven't. And I'm happy that we learned and adapted to what defenses did against us throughout last season, and that we got better. But I suppose I will always worry about all the things I don't know that I don't know.

No coach can know what those are beforehand of course - that's the nature of the problem. But this off season, I will be thinking about ways to get faster at understanding unexpected tactics and becoming quicker at inventing adjustments.

RAVENS!

NFL Hits

The National Football League is cracking down on high speed hits to the head.

They've enacted a rule this year that prohibits the practice of 'launching' - whereby a player, typically defensive, leaves his feet to dive head first into a player running at some degree of opposite angle. And it isn't just helmet to helmet contact - also now illegal is forearm to helmet, and shoulder to helmet delivered via the launch.

I know why defensive backs do these things. They are trying to intimidate receivers coming over the middle. This practice has actually been a response to the tightening of pass defense rules in the NFL over the years. It used to be difficult to cross the middle, because DB's could grab you on your cut, and linebackers always took a shot at you as you went past. Now with the 5 yard contact rule in the NFL, fast wide receivers achieve very high velocities on their pass patterns. Safeties in zone defenses launch themselves at those crossing receivers because trying to wrap up Larry Fitzgerald or Randy Moss at full speed is mostly futile.

The way to protect wide receivers is to slow them down. The way to slow them down is to eliminate the immensely irritating 5-yard contact rule. Slow receivers down, and the inevitable collisions in football will be less violent.

Another idea would be for the NFL to fine players proportionally according to the force of any given collision. Force is changed momentum over time. Momentum is mass multiplied by velocity. So the force of any collision in football has a lot to do with how fast two guys are going, how big they are, and at what angle they collide (head-on shortens the time for the change in momentum, creating more force - oblique angles create 'glancing blows' that are less forceful collisions.) 

1. Should the NFL compel wide receivers to run routes at certain angles? Do the angles of the routes have any bearing on the increasing or decreasing incidence of injury?
2. Should the NFL consider whether the wide receiver crossed the field with reckless velocity?
3. What should the NFL do about receivers that 'launch' themselves to catch a pass? Is that a reckless disregard for defenders?
4. Maybe the blame for the angle of a given collision that contributes to an excessive force problem should be placed on the coach that drew the route? Or perhaps blame could be placed on the quarterback that threw the poor pass that caused a last-second adjustment and an unfortunate change in angle?

Obviously, they're not going to adopt ANY of those ideas. The owners like passing. But the truth is, if we don't slow receivers down and simply succeed in lowering the target hitting points for defensive backs - which is I think, the goal of the league - we will soon be discovering a rash of different injuries - neck, ribs, knees, etc. - and then the owners will wonder what they ought to do about that.

Ambidexterity is Good Thing

Our White team's right-footed punter, seeing the heavy rush from his right, calmly booted the ball left-footed.

I've never seen that before.



Lesson for football coaches: If in doubt about who you should choose to be your punter, a soccer player is not a bad idea.

Progress

I've had very little chance to watch our Blue team play in games this year, aside from Coach Lee's highlight clip on YouTube a couple of weeks ago.

Last night I began converting the Blue team's DVD (thanks Dave Brown!) from their second game, and am uploading it to our protected site today. It should finish out sometime this afternoon. Click the 2010 Videos link over on the right side of this page to see what we've shot and uploaded this season. The Blue team's game Saturday was against Paola, and I was able to convert all but Paola's last two plays - a halfback pass incompletion, and another halfback pass for a short completion and tackle by Zach O.

Let me give you my quick impresssion - what a difference one year makes!

We knew that the Blue team had some good talent from last year in players like Eddie and Grant, and we knew that we had some brand new kids like Tommy, Dante, Julian, & Jack M. that looked ready to help right away. We also blended in a couple of kids with two years experience in another program, Shawn and Jacob H, and they've been very consistent performers for a relatively inexperienced team.

But do you recall an e-mail I sent to many of you about how excited I was for the second-year guys, and the progress that I thought they might make? Watching film of Jake, Zach, Colby, and Jarid was a real treat for me. Those guys are absolutely breaking out this season for the Blue team.  Michael B is another second year player - albeit this is his first year in the U.S. - and he has ramped way up from where he was this summer.

By moving to three teams, suddenly those guys that were very new last year now have very important roles, and are making key plays for a rapidly improving Blue team. Mix in the brand new tackle football guys - Dillon, Stewart, Halen, and Hunter - all of whom have big roles themselves and are producing, and the Blue team is really coming together.

I really enjoyed watching your game on film Ravens Blue. You were very impressive. All of us are really excited for you guys!

One Block

Our black team gave up a touchdown to SME on a kick return.

It only took one block to spring him (click the pic for a closer look):

Excellent game anyway. And another good weekend for Blue and White as well - Blue with their first win, and White playing a one touchdown game against the highest scoring team in the league. Great job guys!