Game theory, or, trading points & yards for victory

[Fencer]

I have NEVER heard an NFL coach in my sixty years of being a rabid fan EVER say "my middle linebacker acted on instructions based on game theoretic analyses."

That's just because they didn't phrase it that way.

Coaches try to arrange their defenses so that at least the top two choices for the offense are equally good (or equally bad). Why? Because if one choice were CLEARLY best, then they could improve the defense by shading the defense a little more against that choice, even at the cost of increasing vulnerability against any other decision.

And what I've just said comes straight from the fundamental theorem of game theory, the Minimax Theorem, first proved by John von Neumann.

 

[ewg_gestalt]

I get that Moosekill...I've always thought of it as real life application of one's experience in the arena of NFL football leading to singularly important game winning decisions. What Belichick did taking that safety, for example, had ZERO to do with some over caffeinated lab rat running simulations on an MIT computer.

Fencer is right...I don't understand it as it is presented here...

With rare exceptions, a player acts on game theory only to the extent that they're doing what they're coached to do, with their instructions being explicitly or, much more likely, implicitly based on game theoretic analyses.

Something to think about—Bill Belichick might have found some use for game theory-based analyses over the years, and he certainly wouldn't be averse to using it, if he found it helpful:

Is game theory real? Ask Bill Belichick's Patriots. - October 31, 2005

 

[Joker]

jeezus krist...some guy with a fortunemail.com account writes this bullshyt and you take his word for it?

Besides game theory's world-historical and business significance, it's worth noting, especially at this time of year, that it actually does apply to games. A scholarly paper by Berkeley economist David Romer showed that NFL coaches punt too often on fourth down. Patriots coach Bill Belichick, the league's most successful coach in recent years, read the paper and later stunned fans by running on fourth and one--successfully--in the AFC championship game two years ago. In baseball, a study by an economist and a mathematician examined why American League batters get beaned more often than National Leaguers (short answer: The designated-hitter rule leaves pitchers less afraid of retaliation). As poker has exploded in popularity, some of the new champs have been computer-savvy game theoreticians.

So all hail the Nobel committee for reminding us of the power and pervasiveness of game theo--er, deep strategy. At long last, it's time to get past the name and appreciate the science behind it. As the committee recognized, this stuff works.

FEEDBACK [email protected]

Bill better use that paper for spare toilet paper IF he, indeed , read this garbage. I do not believe this for one second....and, if he did, he made a huge mistake relying on it later on when he ran for it on 4th down in Indy territory and Faulk got stopped.Or did you forget THAT game?

 

[Fencer]

Something to think about—Bill Belichick might have found some use for game theory-based analyses over the years, and he certainly wouldn't be averse to using it, if he found it helpful:

Is game theory real? Ask Bill Belichick's Patriots. - October 31, 2005

By the way ... my doctorate is in game theory, and I used to eat lunch frequently with Tom Schelling.

 

[Joker]

yeah and I stayed at a Holiday Inn last night...

 

[chris_in_sunnyvale]

What is game theory vs. simple strategy? Where is the line drawn?

When I think game theory, I think:

1. Pats strategy vs. the Rams in SB36. Play nickel and dime all game, daring the Rams to have the patience to run the ball the whole game, taking the ball out of Kurt Warner's hands. Two benefits: If the Rams bite and run the ball, the byproduct is longer possessions which (a) gives the Pats opportunities to get turnovers (more plays run by St. Louis) and (b) fewer possessions the Rams have the ball, reducing scoring opportunities and keeping the game within reach; If Martz's ego gets the best of him, the Rams will be throwing into the strength of the Pats' D.

2. Jets strategy vs. the Pats last January. See #1.

Regards,
Chris

 

[Joker]

Game theory really had a HUGE IMPACT in the playoff game two years ago when Ray Rice took the snap on the first play from scrimmage and rumbled 73 yards...great "theory"...the only thing being uttered post game was "game dreary".

 

[VJCPatriot]

Football is a zero-sum game in terms of the outcomes, but clearly teams have different values: otherwise, why the complete shock in the intentional safety in Denver way back when? The die of surrendering points for field position was looked at as BB losing his mind, at least at first.

A major difference between baseball and football is that there are so many more incremental outcomes in football, which makes the analysis process much more challenging.

Without the intentional safety we probably lose that game. Giving up 2 points intentionally and making it much less likely that they score 7 was the right call.

Game theory certainly has a place to be discussed because football is a game won by points and strategy as much as it is on the field. Running out the clock is just one example of a strategy that doesnt maximize points at all, rather it helps ensure that you end up with more points than the opponent by the time the game ends.

 

[Joker]

show me one instance in the history of NFL football where game theory came into play when an All Pro middle linebacker breaks his responsibilities because he recognizes a play that HE, using his ALL PRO ability , can blow up...a play that most other linebackers cannot even SEE, much less blow up...and on the other side of the ball you have "game theory!!!!" that leads to the calling of THAT play which is HUMILIATED and BLOWN UP by the actions of a SUPERIOR PLAYER WITH SUPERIOR INSTINCTS.

What you "game theory" cultists are doing is cherry picking plays in certain games to support your "theory".This theory has so many holes it should be a screen door.

 

[FreeTedWilliams]

I think that it is more situational football than game theories....

The Pats only loss can be directly attributed to them Pats not taking what they had and going for more.

The final drive of the Jets game reminded me of two other great drives.

The one in the 2007 AFC champship game, when the Pats ran the last seven minutes off the clock and never gave the ball back to the Chargers

and Clock killin Corey Dillon, who can forget Corey running over the Colts to seal that game.

Lets face it it was more important on that drive to eat up the clock and kick a field goal than score a TD quickly. The Pats got the ball up by 6 with 7:13 left in the game. By the time the drive was over the Pats had a nine point lead, the Jets were out of timeouts and their was a minute left on the clock.

Say if the Pats had scored a quck TD and given the ball back to the Jets with five minutes left all their timeouts and Pats up by 13 (less than 2 TDs). Which situation would you rather have? I say the first one, everytime.

I think offensively your intent is to score a touchdown everytime you get the ball reagrdless of how you do it, but at the end of the game, clock management becomes a much bigger issue.

In the Bills game the Pats were in a position to go up by ten points with 7 minutes left, and Brady threw a pick at the ten yardline. Imagine what the outcome of that game would have been, if they ran BJGE two more times, ran another minute or so off the clock and gave the ball back to the Bills with say 5 minutes left and the Pats up by ten? If they did they woudl be 5-0 right now, and with the AFC East bascially sewed up already.

 

[Fencer]

yeah and I stayed at a Holiday Inn last night...

Are you calling me a liar?

If so, please go eff yourself.

 

[Fencer]

What is game theory vs. simple strategy? Where is the line drawn?

There is no such line. Game theory is not something from which one can draw mathematically rigorous conclusions; with the rarest of exceptions. But it's a great organizing principle for thinking about strategy.

 

[Joker]

It was an off the cuff remark....not aimed at you....and you are educated in this field?...well then, that explains why you find it so easy to interlace this theory with the real world playing of a game. I do not have expertise in YOUR educational field of interest, but I do have a B.S. Engineering ,BU '73. Curious that you'd get so angry that you'd post "go eff yourself"...I could easily respond "kill yourself first" but I will not do that because this thread is just a topic, not a condemnation of you, your life's work or any other paranoid delusions you are suffering from.

 

[JR4]

All this is very interesting. We have some guys here with a lot of good background.

Question: how much do the Game theory specialist think
Ernie Adams, BB's man with the numbers , plays in formulating
decisions/strategy during the game?

 

[Urgent]

Some folks seem to be defining a trade-off: football is either won by game theory, or great execution of plays. It can't be both.
That's a goofy proposition.
Pretty similar to saying football is either won by good offense or good defense. It can't be both.

Here's a direct example of game theory in football. This is derived from Nash, who was a leading thinker in game theory until his beautiful mind imploded. We have Nash and Von Neumann to thank for the Prisoner's Dilemma, the classic game theory dilemma.

Go back in time 10 years to make this a bit more relevant.

Steroids are no good for you. They have dangerous side effects. Although they provide a significant advantage in strength and ability to recover from fatigue, often ligaments and tendons cannot take the stresses created by more powerful muscles, leading to injuries.

Steroids also lead to bigger, faster athletes in contact sports. The collisions of bigger, faster athletes lead to more serious injuries.

Further, lots of kids see those bigger, faster athletes and want to emulate them. Because athletes take steroids, kids take steroids.

So the league encourages you not to take steroids, but doesn't have an effective testing program.

You have two options:
Cooperate with the league, and resist steroids
Defect from the league, cheat, and take steroids

Let's look at your choices:
If no one else takes steroids: if you take steroids, you have a significant advantage over other players and can quickly become a starter with a huge salary; if you do not take steroids you will be a back-up player for several years and make a lower salary but your long-term health outlook is much better
If many other players take steroids (or, similarly, if the guy you are competing with for a spot takes steroids): if you take steroids, you are at parity with everyone else and can make the team but at the risk of your long-term health; if you do not take steroids you will be released for some player that did and will live a longer, poorer life

So, in your individual situation, it's always to your short term advantage to take steroids. However, from everyone's point of view, it's better if no one takes steroids. The best outcome for everyone is the first option.

Game theory, however, encourages you to defect. That's pure game theory applied to football.

Game strategy is an application of that, where you are maximizing the probability of a win. Straight probability says: if you average 6 yards per pass attempt and 4 yards per run attempt, always pass. Game theory says: if you always pass, the opponent will prepare to always defend the pass, and your average per pass will drop. So game theory will encourage you to maximize the mix of run and pass, for example, to maximize your probability of a win.

Of course proper execution is important. In the example above, if you improperly ingest the steroids, they will not have the intended effect.

Game theory has absolutely nothing to do with selecting players in the draft. The fact that Ryan Leaf failed and Tom Brady thrived has nothing to do with game theory.

Game theory is also quite different than statistical analysis. Moneyball is about statistical analysis. Everyone can see that a .300 hitter with 50 home runs a year is valuable. However, if you cannot afford those players, statistical analysis will enable you to identify undervalued assets to improve the number of wins you can achieve on a limited budget. Both are analytic tools, but otherwise not related.

 

[patsfaninpittsburgh]

It was an off the cuff remark....not aimed at you....and you are educated in this field?...well then, that explains why you find it so easy to interlace this theory with the real world playing of a game. I do not have expertise in YOUR educational field of interest, but I do have a B.S. Engineering ,BU '73. Curious that you'd get so angry that you'd post "go eff yourself"...I could easily respond "kill yourself first" but I will not do that because this thread is just a topic, not a condemnation of you, your life's work or any other paranoid delusions you are suffering from.

Maybe his remarks are the result of you:

Admitting you know squat about the subject.

Having promised to no longer comment.........

Continually to make make stupid, flippant comments in the thread.

Many articles state the BB continually challenges the status quo and challenges subordinates to come up with something different.

Perhaps "fencer" can comment, but my guess would be that game theory would probably predict it's not smart to give up an 81 yard TD run.

 

[BradyFTW!]

this is all pure garbage....one of you "experts" quantify heart and maybe I'll begin to listen

All discussions of this nature require a token luddite. Never change, Joker, you fill the role admirably

 

[Joker]

All discussions of this nature require a token luddite. Never change, Joker, you fill the role admirably

yeah...I love it when I'm threatened to be hunted down and hanged or deported to Australia.

Tell you what, I'll buy into this entire gossamer winged, fragile butterfly theory. I'll take my life's savings and go to Vegas and bet heavily ,using "game theory". I checked with a cousin and he said they'd(the casinos) would welcome me with open arms...use any theory I want. Now, if I end up living in a truck, down by the river then I'm going to blame some of the people in this thread...and that is something I do not forgive...

 

[Urgent]

yeah...I love it when I'm threatened to be hunted down and hanged or deported to Australia.

Tell you what, I'll buy into this entire gossamer winged, fragile butterfly theory. I'll take my life's savings and go to Vegas and bet heavily ,using "game theory". I checked with a cousin and he said they'd(the casinos) would welcome me with open arms...use any theory I want. Now, if I end up living in a truck, down by the river then I'm going to blame some of the people in this thread...and that is something I do not forgive...

Actually, given your reference, I believe the threat would be "shot in the head by a police officer, found hung in your cell, or hit by a bolt of lightning", not deportation, but great reference.

However, not all theories are the same thing. Don't confuse game theory with the butterfly theory, chaos theory, string theory, the theory of gravity or evolution, or any others. They are different things. Unrelated.

There have been a couple interesting examples of real game theory here.
Run vs. pass.
Points vs. time.
Steroids.

Other applications to the NFL?

 

[Joker]

Sorry for being unclear...the first reference was what really happened to the Luddites in England 150 years ago.

the second paragraph was a weak attempt at reconstructing that famous Godfather quote by working in a Chris Farley reference.

I do not doubt that game theory has a valid place in a football teams overall philosophy. How it relates to predicting outcomes before a contest is what I have a hard time wrapping my mind around. A MLB sees an offensive lineman show a tell that he recognizes as tipping off a play in the B gap, yet on this play the MLB's responsibility is the A gap. Game theory predicts that the MLB will shirk responsibility and plug the B gap, stuffing the run, bringing up 4th down and winning the game????

Really????? Like I said, this is the FIRST TIME in my life I have ever heard that game theory predicts outcomes of plays and games. I always thought that ,when trying to distill a game down to its' core that it is four or five PLAYS that determine the outcome of a game...I mean, Belichick has iterated and reiterated this ad nauseum.At one point does game theory predict that Eli Manning ,in the grasp,will escape with no call ending the down because of referee failure? Is there even any relation whatsoever between game theory and referee calls,funny bounces,playing conditions,a team's physical integrity/injuries,team harmony/disharmony...I mean, I can go on for a few hours here...and yet I'm supposed to swallow this "game theory" hook ,line and sinker or be branded an idiot, a Luddite, told to GFM and "Continually to make make stupid, flippant comments in the thread." (which in itself is a ludicrous butchering of basic English).

If this so called uber theory is the NEW paradigm, then I'm guessing all the experts in this thread can easily explain which defensive philosophy will prevail from game to game,read and react or attack...then I can go to Vegas and become a gajillionaire using these tried and true game theory axioms.