Game theory, or, trading points & yards for victory

[Fencer]

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.

Fair enough.

I've been assuming that if we're competing to see what location we can get to in a Markov model, that's game theoretic. (I'm biased that way, given the subject of my thesis.) But it's not obvious that the game theory aspect adds much insight.

What's more, the Markov-model aspect is more clearly applicable to player evaluation in baseball than it is in football, where in turn it's probably more clearly applicable than in, say, basketball or hockey.

But play calling and formations? That's very much minimax stuff -- i.e., pure game theory. And of course player evaluation is heavily affected by your views on Xs and Os.

 

[Fencer]

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.

More precisely, they were the result of a particular stupid, flippant comment that appeared to call me a liar.

 

[Joker]

More precisely, they were the result of a particular stupid, flippant comment that appeared to call me a liar.

 

[Fencer]

JoKer just broke new ground -- he's the first member of my Ignore list.

 

[ewg_gestalt]

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????

No. The point of game theory, as applied to football, is not to suggest or predict the actual outcomes of plays. The goal is to allow teams to evaluate different strategies, and to decide what play might be the best for a given situation—or an overall strategy for a game. On the other hand, once the play is called, it's up to the players to execute the play. The two don't have to be in conflict.

 

[Patjew]

This is some interesting stuff about something I know next to nothing about. Can someone provide a one or two sentence definition of game theory?

 

[Urgent]

I would defer to Fencer, whose understanding is far deeper.

But my simple explanation would be:
Game theory is an approach to building a strategy for a two-party game where you maximize your chances of success based on all the possible decisions your opponent could take.

A good example in football is lining up the defense on first down. Basically, the opponent can run or pass. If your opponent tends to run on first down 60% of the time, you want your alignment to be better against the run. But if you stack 11 players around the running back, on the 40% of the time the opponent passes, you lose. So you could use game theory to build an alignment that maximizes your results.

One could use game theory to examine decisions like:

• Whether to punt on fourth and under two
• How often to pass on first down
• Whether to onside kick in the first half
• How often to blitz six men

It's not just the statistical probability; it's an assessment of your strategy relative to your opponent's strategy in each situation.

 

[Urgent]

I think what's interesting about this discussion is the real lack of application of game theory to sports in general.

Nobel Prizes have been awarded multiple times for application in economics. The last 20 years has seen plenty of application to biology. Negotiations training is full of game theory.

Very little has been applied, or at least published, on application to professional sports.

 

[The Scrizz]

I would defer to Fencer, whose understanding is far deeper.

But my simple explanation would be:
Game theory is an approach to building a strategy for a two-party game where you maximize your chances of success based on all the possible decisions your opponent could take.

That's very succinct, to which I would add it does not have to be a two-party game (or a game at all), and 'strategy' would be a good word for describing game theory in relation to football but not necessarily as applied to other pursuits where it is more of a mathematical, scientific undertaking.

But a fair definition for this discussion.

:youtheman: - Note, this smilie was chosen by my daughter and has nothing to do with this post other than, the game theory decision that allowing my daughter to choose the smilie would make my life easier than not allowing her to.

 

[JR4]

I would defer to Fencer, whose understanding is far deeper.

But my simple explanation would be:
Game theory is an approach to building a strategy for a two-party game where you maximize your chances of success based on all the possible decisions your opponent could take.

A good example in football is lining up the defense on first down. Basically, the opponent can run or pass. If your opponent tends to run on first down 60% of the time, you want your alignment to be better against the run. But if you stack 11 players around the running back, on the 40% of the time the opponent passes, you lose. So you could use game theory to build an alignment that maximizes your results.

One could use game theory to examine decisions like:

• Whether to punt on fourth and under two
• How often to pass on first down
• Whether to onside kick in the first half
• How often to blitz six men

It's not just the statistical probability; it's an assessment of your strategy relative to your opponent's strategy in each situation.

This is why I was asking about Ernie Adams, BB's man with the numbers.
How much is he involved? Sitting up there in his booth, does he have a program that, given the current situation, can communicate to BB the best probable defense or offense play?
Assume this program has been fed all kinds of data about the current opponent.
AI programs and computers are so advanced now that answers could be given in seconds. Has football become as highly technical as it it physical?
WAR GAMES!

 

[Fencer]

This is some interesting stuff about something I know next to nothing about. Can someone provide a one or two sentence definition of game theory?

A game, mathematically, is a decision process controlled by two or more entities that have differing objectives.

Game theory is the study of games.

Beyond that:

• If the objectives are STRICTLY opposed to each other, the game is "zero-sum". Examples would include various forms of play and gambling -- board games, card games, sports, etc.
• If the objectives are not strictly opposed to each other, the game is "cooperative" or "non-zero-sum". Examples would include almost everything in the real world -- negotiations, economic competition, war, etc.

 

[kudzif]

xmarkd400x-

I see what you're getting at and I like your analogy, I think there is some truth in your idea that BB may have changed his thinking - the last two games anyway. But I don't think the extra running plays and clock grinding was just a strategy for the Jets. One simply has to look at the Buffalo game (as I'm sure BB and staff have in detail) and say "if" the Pats had played that one as they did this Sunday against the Jets then Brady doesn't throw 4 INTs and the Pats may not be leading the league in scoring and Brady's not on a superhuman TD pace but they are likely 5-0.

Whatever the game - the "situation" always calls for winning. Good post...

The offense is paid to score points , they have to adopt a strategy that allows them to score the most points.Scoring a lot tends to correlate with passing a lot.Teams that run the ball a lot tend not to score a lot of points.Our defense is on a record pace for conceding the most 20+ yard plays in nfl history. This means teams can score on us quickly so slowing the game up won't help the team.Less points combined with our defense equals to more losses.
We should stop trying to make excuses for our atrocious defence. Yards are not the most important defensive stat , but giving up as many yards as we do is unacceptable. I am pretty sure no superbowl winning team has ever conceded yards remotely close to the rate we are doing.

 

[Fencer]

The offense is paid to score points , they have to adopt a strategy that allows them to score the most points.

You want the highest probability of ending the game with more points than your opponent. To a first approximation, your strategy should be to have the highest expected number of points, but there are at least two significant reasons to deviate from the strict form of that approach:

1. Clock-grinding at the end of games with the lead.
2. Protecting against bad turnovers even at the cost of slightly lowering your own scoring potential.