Game theory, or, trading points & yards for victory

[xmarkd400x]

When thinking about this, I'm reminded of a story. I forget the source, so I'll paraphrase here. If you don't know what Mancala is, replace the word 'bean' with 'point', and you'll understand the story.

There was a computer AI (artificial intelligence) competition to create the best Mancala player. The competition was a tournament that pitted the AI players against each other.

In the final game, there were two players that had not lost a game. The first player had won all of it's games by large margins. The second player had won all of it's games by exactly one bean. Everyone thought that player one would win because it's margin of victory was so large. Not much was thought about the second player, who won each game by a single bean.

To everyone's surprise, the second player won the final match by exactly one bean. The first player had an algorithm to maximize the amount of points it scored per turn. The second player had an algorithm to ensure that, after both players had taken a turn, the second player had more beans.

I think this story provides a good basis to discuss how the Patriots play once they have established a lead and are attempting to protect it. Attempting to maximize the margin of victory may or may not be the best strategy for winning games. I'd argue that it is not, using the above story as an example.

Take the end of the Jets game for example. The Patriots were not attempting to maximize the margin of victory. They were attempting to ensure that, after both teams had a turn (possession), the Patriots were ahead. In this case time was more important than points or yards.

 

[Fencer]

Not a close analogy.

In football, most of the state of the game is reset at the end of each drive. The big exceptions to that rule are:

• Score (duh)
• Clock
• Starting field position of next drive
• What you have "in reserve" (unused plays, rested players, etc.)

Still, for most of the game, the strategy pretty much amounts to "We're going to do out best to maximize the expected outcome of this particular drive."

You can be aggressive or conservative on particular PLAYS, in line with down, distance, and so on, as well as general orientation. The analogy is a bit closer there (e.g., grind-it-out may be a better strategy than big-play). Still, the whole point can easily be overblown.

 

[patsfaninpittsburgh]

When thinking about this, I'm reminded of a story. I forget the source, so I'll paraphrase here. If you don't know what Mancala is, replace the word 'bean' with 'point', and you'll understand the story.



I think this story provides a good basis to discuss how the Patriots play once they have established a lead and are attempting to protect it. Attempting to maximize the margin of victory may or may not be the best strategy for winning games. I'd argue that it is not, using the above story as an example.

Take the end of the Jets game for example. The Patriots were not attempting to maximize the margin of victory. They were attempting to ensure that, after both teams had a turn (possession), the Patriots were ahead. In this case time was more important than points or yards.

The problem is:

There is way too much fixation on yards in the 2011 NFL. I believe this is a result of fantasy football and Madden. Also, yards is a "legacy" measurement.

As Fencer said, situational football, situational football.

We have played two and will play a third talented, gaff prone team.

Look at San Diego the past two weeks. Big time deep throw TD's. That's not how to play them yet teams still do and get lit up with some less yards.

Situational football has different strategies so the macro picture is arbitrary.

 

[Brady'sButtBoy]

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...

 

[ewg_gestalt]

I think this story provides a good basis to discuss how the Patriots play once they have established a lead and are attempting to protect it. Attempting to maximize the margin of victory may or may not be the best strategy for winning games. I'd argue that it is not, using the above story as an example.

Take the end of the Jets game for example. The Patriots were not attempting to maximize the margin of victory. They were attempting to ensure that, after both teams had a turn (possession), the Patriots were ahead. In this case time was more important than points or yards.

Actually, I think this misses the point of game theory a little bit. The primary idea of game theory is that the "player"—in this case, the OC or DC—assigns a "value" to each outcome, in terms of what they think the value of that outcome. These outcomes are not necessarily equivalent: for instance, one coach might consider an incompletion to be of lower value than a run for a loss, while another might consider a defensive PI call to be better than a first down via the running game.

The goal of game theory is then to maximize the value to a player, subject to the fact that there are many possible "moves" (plays that can be called), and also to the fact that the opponent's moves—and the values that he assigns to the outcomes—are potentially unknown. In the case you described, the winning algorithm appears to have assigned the same value to any algorithm that put it in the lead, rather than being a "greedy" algorithm that tried to simply score as many points as possible, and weighted scoring X points to be worth more than scoring less than X points.

As you said, though, the Patriots' decisions at the end of the game were predicated on plays that ran down the clock being "worth more" than plays that led to quick points being added. The goal was just to get more points on the board, not to get them on the board in X time or less. If the lead had been one or two points, however, I doubt you would have seen the same "ground and pound" drive—you would have seen something designed to put points up, and then try to kill off the clock in an ensuing drive.

 

[Fencer]

Actually, I think this misses the point of game theory a little bit. The primary idea of game theory is that the "player"—in this case, the OC or DC—assigns a "value" to each outcome, in terms of what they think the value of that outcome. These outcomes are not necessarily equivalent: for instance, one coach might consider an incompletion to be of lower value than a run for a loss, while another might consider a defensive PI call to be better than a first down via the running game.

Well, if the opposing coaches disagree on the value of an outcome, one is probably in error -- football is about as close to a zero-sum game as there is.

Part of the Moneyball idea was the discovery that certain intermediate outcomes -- e.g. a walk -- tended to have different value than was previously assumed.

 

[ewg_gestalt]

Well, if the opposing coaches disagree on the value of an outcome, one is probably in error -- football is about as close to a zero-sum game as there is.

Part of the Moneyball idea was the discovery that certain intermediate outcomes -- e.g. a walk -- tended to have different value than was previously assumed.

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.

 

[Joker]

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

 

[Fencer]

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.

Fair enough, except that I think your word "have" is misleading. It should instead be something like "estimate".

Also, I recall BB as getting more praise and benefit of the doubt than you seem to, not least because it happened to work.

 

[Wides]

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

 

[ay-yo]

Part of the Moneyball idea was the discovery that certain intermediate outcomes -- e.g. a walk -- tended to have different value than was previously assumed.

I can't help but think of Woodhead when the movie talked about players who performed but didn't "look the part".

 

[moosekill]

I agree in that somehow the media has started putting lots of value on yards allowed and points scored. I imagine it has a lot to do with fantasy football and vegas.

If a team is up by 17 points with 2 minutes to go and gives up a 95 yard touchdown drive that uses up 1 1/2 of those minutes, who cares?

If there is 5 minutes left and a team up by 7 uses 4 of those minutes to drive down the field and score a field goal, they win. If another team had thrown a deep interception instead there is a good chance they lose.

In both of those cases the team has accomplished its goal, to win, but at the expense of fantasy football fans or vegas gamblers. I would rather have a win, but because these other groups are affected, it becomes news for ESPN to whine about. When it becomes news we have some morons here complain about how many yards the Patriots allowed in a 3 score victory, or about a 9 point victory rather than a 13 point win.

 

[patsfaninpittsburgh]

I agree in that somehow the media has started putting lots of value on yards allowed and points scored. I imagine it has a lot to do with fantasy football and vegas.

If a team is up by 17 points with 2 minutes to go and gives up a 95 yard touchdown drive that uses up 1 1/2 of those minutes, who cares?

If there is 5 minutes left and a team up by 7 uses 4 of those minutes to drive down the field and score a field goal, they win. If another team had thrown a deep interception instead there is a good chance they lose.

In both of those cases the team has accomplished its goal, to win, but at the expense of fantasy football fans or vegas gamblers. I would rather have a win, but because these other groups are affected, it becomes news for ESPN to whine about. When it becomes news we have some morons here complain about how many yards the Patriots allowed in a 3 score victory, or about a 9 point victory rather than a 13 point win.

Not to mention giving up 504 yards to the Raiders yet holding them to season low scoring.

Just think, Oakland had with 59 minutes 32 seconds played scored 13 points.

Kinda like in the movie "Patton" where Patton shows up at II Corps HQ and kicks the guy sleeping. Patton asks what he's doing and gets the emphatic, "I'm trying to sleep".

Patton tells him to go back to it because he's the only guy who knew what he was trying to do.

 

[patfanken]

Great thread. I wish I was smart enough to participate in it. But I am smart enough to appreciate it and give it a bump

 

[ewg_gestalt]

I agree in that somehow the media has started putting lots of value on yards allowed and points scored. I imagine it has a lot to do with fantasy football and vegas.

Points scored does matter—but also one does have to evaluate the situational context. Nothing in football happens in a complete vacuum.

As for yards, those are, as you said, even less valuable as a complete measure. Yards per point, on the other hand, does have some value as a production statistic. Giving up 95 yards for a FG or giving up 20 yards for a TD? I know which one the Pats would rather have done on Sunday.

If a team is up by 17 points with 2 minutes to go and gives up a 95 yard touchdown drive that uses up 1 1/2 of those minutes, who cares?

Anybody who has bet on a spread of 11, I guess. :bricks:

Fair enough, except that I think your word "have" is misleading. It should instead be something like "estimate".

It's a semantic point. I could just as easily have said "assigns" or "estimates" or "assumes" or whatever. The key point is

 

[ewg_gestalt]

The key point is

What I meant to say was: "The key point is that teams may not view the same results as having the same values, which in turn makes finding the best strategy tougher."

One other thing of note: game theory normally assumes rational intent and actions on the part of the players. When that doesn't happen, game theory more or less breaks down.

 

[Joker]

yeah...uh...if "game theory" had any use whatsoever in evaluating real time NFL football players,then it would have been used to identify a Mike Singletary as a high first round pick as opposed to a Vernot Goatston who was selected SIXTH overall...of course, the classic "game theory is horsesh!t" proof is Tom freakin' Brady.

Game theory, spreadsheets, zero sums,40 times, cone drills...all useless when it comes to the size of the heart in a player's chest.Come up with a "theory" that identifies heart and YOU could become the sports world equivalent of Steve Jobs....I'm not going to hold my breath though.

 

[Fencer]

yeah...uh...if "game theory" had any use whatsoever in evaluating real time NFL football players,then it would have been used to identify a Mike Singletary as a high first round pick as opposed to a Vernot Goatston who was selected SIXTH overall...of course, the classic "game theory is horsesh!t" proof is Tom freakin' Brady.

Game theory, spreadsheets, zero sums,40 times, cone drills...all useless when it comes to the size of the heart in a player's chest.Come up with a "theory" that identifies heart and YOU could become the sports world equivalent of Steve Jobs....I'm not going to hold my breath though.

You, Sir, do not understand what game theory is.

Anyhow, it's applicability to football is on the level of coaching. 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.

 

[moosekill]

yeah...uh...if "game theory" had any use whatsoever in evaluating real time NFL football players,then it would have been used to identify a Mike Singletary as a high first round pick as opposed to a Vernot Goatston who was selected SIXTH overall...of course, the classic "game theory is horsesh!t" proof is Tom freakin' Brady.

Game theory, spreadsheets, zero sums,40 times, cone drills...all useless when it comes to the size of the heart in a player's chest.Come up with a "theory" that identifies heart and YOU could become the sports world equivalent of Steve Jobs....I'm not going to hold my breath though.

Joker I usually enjoy your comments, but I think I am talking about something completely different than you are in this thread, maybe I misunderstand it a a bit.

I agree, it is very difficult to value heart, and as such certain media Einsteins, and some teams put huge amounts of stock in those numbers. Just exactly the same as some of those same people put huge stock in yards allowed and such.

The problem is there are times it is much better for a team to give up yards, or allow a score, when that action uses up time on the clock. There are times a run that has a low chance of a large gain is a much better play than a pass. Just like there are times it makes sense to go for it on 4th and 2 from your own 30. Some people will never be able to grasp this, some will.

 

[Joker]

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.

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." Great players MAKE great plays...great coaches put these great players in a position to use their experience and superior athletic ability to MAKE PLAYS, It is NOT rocket science.

I will now bow out of this thread, because, as I've admitted, I have zero clue how "game theoretic analyses" has any real life application in a real time football game. Carry on Einsteins and Steinmetzes....