Gambling on 4th down article

[Runner Runner]

[ QUOTE ]
The fact is that almost all coaches play too safe on fourth and one. Maybe they worry about their job and it is the fault of dumb owners. In any case there is no excuse for a coach to be unaware of these techniques any more than a poker player has an excuse for not knowing card combinations. They might win without that knowledge, but they don't deserve to.


[/ QUOTE ]

This is bang on, but let's not forget the role of the media and the general public in this. Most people are generally way too risk averse. How many times do you see a coach after losing a game get bombarded with questions about why he went for it in a certain spot compared to the amount of questions he gets for why he didn't go for it. The general public's lack of knowledge about a good gamble is the root cause of these coaching mistakes.

[Shoe]

I agree, I always tell my friends I would make a great football coach because I would coach the same way I play Madden. Actually, I would be a terrible coach, but I think I would make a good play caller.

Teams should also go for the surprise onside kick more as well. It succeeds about half the time, I don't know how that isn't +EV.

[maurile]

This topic was first explored in great depth in the absolutely wonderful book, The Hidden Game of Football (http://www.amazon.com/exec/obidos/tg/detail/-/0446514144/).

Subsequently, there was this paper by David Romer: It's Fourth Down And What Does The Bellman Equation Say? (http://emlab.berkeley.edu/users/dromer/papers/nber9024.pdf)

Here is the press release (http://www.berkeley.edu/news/media/releases/2002/08/19_ftball.html) from Berkeley:

UC Berkeley professor gives surprising answer to NFL fourth down question
19 August 2002

By Kathleen Maclay, Media Relations

Berkeley - In a new study, David Romer from the University of California, Berkeley, tackles a topic outside of his usual expertise as an economist -professional football.

In research that would be a welcome assignment to many an armchair quarterback, he reviewed almost 20,000 first quarter plays in 732 regular season games in 1998, 1999 and 2000 that were downloaded from the National Football League Web site. Armed with mathematical, statistical and economic tools, Romer zoomed in on fourth down decision-making and the rarely-questioned consensus that it's usually far better to kick than to go for a first down or touchdown.

Romer's working paper, "It's Fourth Down and What Does the Bellman Equation Say?" pulls off a dramatic turnover of this conventional wisdom.

"The results are striking," he said. "The analysis implies that teams should be quite aggressive...In practice, however, teams almost always kick on fourth down early in the game."

Teams would often fare better if they went for a first down or touchdown on fourth down, Romer said in his research, presented this summer to the National Bureau of Economic Research. The private, nonprofit, nonpartisan research organization is dedicated to promoting greater understanding of how the economy works.

In setting boundaries for his research, Romer decided to look at first-quarter plays to avoid the complications introduced when one team is well ahead of the other, or when the end of a half is approaching. And taking into account that decisions to go for a touchdown on fourth down are so rare, he analyzed the outcomes of third-down plays instead to determine what to expect if teams went for it on fourth down.

Romer started by considering the number of points involved - three for a field goal, seven for a touchdown - and the probabilities of the success of a field goal and the odds of making a first down or touchdown. The catch, Romer said, is to think ahead about what happens next, and what happens after that, and after that - a process summarized by a tool known to economists as the "Bellman equation."

To deal with this complication, Romer focused on 101 situations: a first down on each yard line, a kickoff from the 30-yard line, and a free kick from the 20-yard line following a safety. The Bellman equation and large data set allowed him to estimate an average value in terms of points for each of these situations.

When combined with information about the likely outcomes of kicking and going for it, these point values allowed Romer to determine which decision is better on average as a function of where the team is on the field and how many yards it needs for a first down or a touchdown. Then, he compared these results with the teams' actual choices.

On a team's own half of the field, going for it is better on average as long as there are less than about 4 yards to go for a first down, Romer found. After midfield, teams should generally be even more aggressive, he said.

Yet on the 1,100 fourth downs where Romer found it would be best to go for it, teams kicked 992 times.

Romer realizes that his conclusions run counter to conventional football wisdom. But he argues that the conclusions make sense if one thinks about them.

An example he gives in the paper concerns a team facing fourth and goal on the 2-yard line. The usual strategy is to attempt a field goal, which will almost certainly produce three points. In this situation, however, going for a touchdown has about a three-sevenths chance of success, and so, on average, produces about the same payoff in terms of immediate points. But because trying for a touchdown and failing leaves the opponent with the ball in terrible field position, thinking about what will happen next tips the balance in favor of the aggressive strategy.

Romer is curious why teams are so cautious, even when the rewards of a win, often nationally televised, are so high.

One possible reason may be that the costs of losing as a result of a failed gamble are much higher than the costs of losing due to playing it safe, he said. The coach opting for the play less taken may face jeering and complaining fans, critical sportswriters and sports talk show commentators, and costly reprimands from team owners.

Or maybe, Romer said, teams are really trying to win, but are just exhibiting human imperfection.

While it may seem Romer's work is out of bounds for an economist, it fits, in fact, into the burgeoning field of behavioral economics. So does the scholarship of many of his UC Berkeley colleagues, including Daniel McFadden and George Akerlof, winners of the Nobel Prize in Economic Sciences in 2000 and 2001, respectively.

The academic study of football offers several benefits, he said:

* The analysis demonstrates the ability of mathematical, statistical and economic tools to develop insights into a subject that, at first glance, seems to have nothing to do with those areas.

* Professional football team behavior offers a powerful test of economists' standard assumptions about risks, rewards and decision-making, their theory that people are "good maximizers."

* Football team behavior can help distinguish between competing explanations of failure.

* Football is fun: people like to watch it and talk about it.

Romer said his research was spurred by his own puzzlement, when listening to a football game on the radio, over why there were no questions about strategy on a fourth down.

Doing research on the game hasn't dampened his enthusiasm for the sport. "I probably enjoy it more," he said.

[BarronVangorToth]

[ QUOTE ]
It succeeds about half the time, I don't know how that isn't +EV.

[/ QUOTE ]


Video game EV <> Real life EV

Unfortunately.

Barron Vangor Toth
www.BarronVangorToth.com (http://www.BarronVangorToth.com)
GTA:SA 4Life

[David Sklansky]

Onside kicks need not succeed anywhere near half the time to be a good bet. The EVs in this article, if at all accurate, make that clear.

[BarronVangorToth]

I think part of the joke is that in video games they work a disproportionate amount of the time.... There, they are ALWAYS +EV. In real life, however, yes, probably worth trying more often than they are.

Barron Vangor Toth
www.BarronVangorToth.com (http://www.BarronVangorToth.com)

[maryfield48]

James Surowiecki wrote about the apparent inefficient 4th-down tendencies in the NFL in his book The Wisdom of Crowds. He pointed out though that the research did not take into account the psychological effects of a 4th down conversion/TD attempt, especially a failed one. For example, a successful goal-line stand can boost the confidence of the team on defense. This could translate into better performance later in the game. I don't know how that might be measured, but it should not be ignored.

[Shoe]

[ QUOTE ]
[ QUOTE ]
It succeeds about half the time, I don't know how that isn't +EV.

[/ QUOTE ]


Video game EV <> Real life EV

Unfortunately.

Barron Vangor Toth
www.BarronVangorToth.com (http://www.BarronVangorToth.com)
GTA:SA 4Life

[/ QUOTE ]

I'm not talking about onside kick success from a video game, the half the time stat was from the onside kick success stats that the announcers put up during one of the games. Even when teams are expecting an onside kick, it still succeeds around one-third of the time. If that rate is sustainable, I would think it would be worth doing almost every time. Unfortunately, I cannot find a website with these stats to confirm.

Edit: for the 2004 regular season, onside kicks were successful 23.4% of the time (11 out of 47). It does not say how many of these attempts were "surprise" onside kicks. Also, not sure if that is a big enough sample size.

[gasgod]

[ QUOTE ]
[ QUOTE ]
The fact is that almost all coaches play too safe on fourth and one. Maybe they worry about their job and it is the fault of dumb owners. In any case there is no excuse for a coach to be unaware of these techniques any more than a poker player has an excuse for not knowing card combinations. They might win without that knowledge, but they don't deserve to.


[/ QUOTE ]

This is bang on, but let's not forget the role of the media and the general public in this. Most people are generally way too risk averse. How many times do you see a coach after losing a game get bombarded with questions about why he went for it in a certain spot compared to the amount of questions he gets for why he didn't go for it. The general public's lack of knowledge about a good gamble is the root cause of these coaching mistakes.

[/ QUOTE ]


How many times have you seen a scenario like this play out?

Team is ahead by 4 with 2 minutes left. 4th and 1 on their own 42. The other team is out of time outs, but has a formidable two minute drill.

Of course, instead of playing to win, the coach plays not to lose and punts. Worse yet, he orders a "prevent" defense, and quickly gives back all the yards the punt gained.

Somebody ought to write "The Theory of Football"


GG

[The Dude]

Great topic selection, David. I often marvel at some of the blatant errors made by coaches and managers in different professional sports. Really, how can they not know these things and get to be in the positions they're in?

[Jman28]

Great article Sklansky. I think about this all the time. I'm always baffled by coaches' ack of understanding of simple probability and EV concepts.

-Jman28

[andyfox]

I can't speak for football, as I know little about the sport, but in baseball, the short answer is that the teams are, generally, run by ignoramuses. Many of them simply refuse to acknowledge that knowledge of the game has incrased tremendously in recent years with the advent of sabermetric methods. What used to be taken for granted (about, for example, sacrifices, stolen bases and batting average) has been shown to be worthless. Yet managers and general managers continue to do things the old way beause that's all they know. Baseball, to a large extent, prides itself on its traditions, and some managers continue to manage as if the game was the same as it was when only half as many runs were being scored as are now.

[RunDownHouse]

[ QUOTE ]
Video game EV <> Real life EV

Unfortunately.

[/ QUOTE ]

The success of surprise onside kicks is well over 50%. I want to say its around 70%, but I don't remember the precise number. TMQ often writes on this subject and has a precise stat.

[Shoe]

[ QUOTE ]
I can't speak for football, as I know little about the sport, but in baseball, the short answer is that the teams are, generally, run by ignoramuses. Many of them simply refuse to acknowledge that knowledge of the game has incrased tremendously in recent years with the advent of sabermetric methods. What used to be taken for granted (about, for example, sacrifices, stolen bases and batting average) has been shown to be worthless. Yet managers and general managers continue to do things the old way beause that's all they know. Baseball, to a large extent, prides itself on its traditions, and some managers continue to manage as if the game was the same as it was when only half as many runs were being scored as are now.

[/ QUOTE ]

Please elaborate. Should teams steal more, sacrifice less?

[andyfox]

Basically:

-Stolen bases have very little to do with winning games. Anything less than a 67% success rate is couterproductive.

-Sacrifices don't have much value in a high-offense era. Teams score fewer runs when a sacrifice is successful. For example, a team will score fewer runs with a man on second and one out than with a man on first and nobody out.

-Batting average is a less useful predictor of run generation than on base percentage.

[Guruman]

I think that the article was a little crude numerically, but I really liked the concept of compiling hard statistical data and using it as a resource to assist decision-making on fourth down.

A few things that I think the article left out:
1)game clock
-A team's probability of scoring points most likely goes down dramatically as the clock winds under five minutes (a typical amount of time for a comfortable 80 yard TD drive) A team with a 3 point expectation from its own 40 probably has that expectation drop significantly with only 90 seconds left in the half. This could be easily resolved by compiling statistical data on multiple tables that are referenced by time (eg a table for 5+ minutes, one for 4-5 min, one for 3-4 min, one for 2-3 min, and one for less than 2 min)

2)the effect of field goals.
I think that for simplicity's sake that Mr. Sklansky omitted the many ways that "go for it or punt" is different from "go for it or kick a FG," and this may be to the detriment of the article. Kicking a high percentage field goal can do things like mathematically cause the opposition to need more posessions to win, cause your team to need fewer posessions to win, and cause an opponent to need to convert a 2-point conversion to tie.

Additionally, the field goal effect would tend to inflate the point expectation a team would have while in FG range. Mr Sklansky (again, for simplicity's sake) implied that the point expectations would semi-evenly fall off as the distance from the goal line increased, which would not be the case. FG's would put a soft floor on expectation at around 3 points all the way out until about the 35 yard line (a 45 yard FG attempt). After that distance the expectation would probably drop dramatically.

Also of note is the fact that the consequence of missing a FG attempt is worse than the consequense of going for it and not making the first down since the ball is spotted where the a missed field goal was kicked.

Field goals were not addressed at all in the article and they often come into play when making fourth down decisions.

3)player personnel and stastical sampling
-The cowboys are currently undergoing a major player personnel shift during this offseason that includes changes at QB, RB(not literally but essentially since Julius Jones only played a few games last season) and probably several players on defense. The change in personnel that affects every nfl team during and after the season can have a profound effect on the relevance of the statistical data that any coach can compile.

Overall I like the idea of creating a dataset to help with making fourth down decisions. The process outlined in the article needs some cleaning up imo though.

Good food for thought! /images/graemlins/grin.gif

[DougOzzzz]

There's an article somewhere at football outsiders (http://www.football outsiders.com) that backs up the theory that real life coaches should go for it much more on 4th down. What is odd is not that most coaches use a more conservative strategy - it's that ALL coaches (in the NFL at least) are more conservative than they should be. I severely doubt that all NFL coaches are blind to the fact that a more aggressive approach on 4th down would increase their winning percentage. Clearly, the coaching EV of being aggressive on 4th down is not nearly as good as the game EV.

I remember several years back, when the Cowboys were coached by Barry Switzer. With a couple minutes left, and the score tied, Switzer elected to go for it on 4th and 1 foot from I believe the 30 yard line. Emmitt Smith was stuffed on a run attempt and failed to convert - the Cowboys gave up an easy field goal and Switzer was blasted by the press for his decision. Even Troy Aikman admitted afterwards that it was probably the wrong decision.

The bottom line is the media and fans are going to remember the times you went for it and it didn't work out more often than the times it helped you win. Therefore, even though a more aggressive 4th down approach would improve your winning percentage, the chance that you lose your job is much greater.

Another unrelated example of public opinion vs. actual probabilities is the Super Bowl in 2004. Many people blamed John Fox for Carolina's loss because he went for the 2 point conversion twice in that game and failed to convert both times. Statistical analysis clearly shows that his decision to go for it both times was correct.

[MicroBob]

I do think owners (or AD's in the college game) MAY play a role in keeping coaches conservative.
But I doubt the press has much to do with it.


I've worked in the press...AND with football coaches (coach's film....other stuff...while also working as a reporter at the press-conferences) and I honestly don't think most coaches give a damn what the press thinks or what questions are asked.
Anytime you see a coach get upset in a conference it usually stems from losing a tough game AND/OR being asked the same stupid question for the 27th consecutive time.


They are going to do what they think is best in order to win the game...They just happen to think that coincides with being too conservative on 4th down. And it just happens to be one of the only questions some reporters know how to ask.

"do you think it was a mistake going for it on 4th down?" when they didn't make it strikes coaches as being about as dumb as "do you think it was a mistake raising PF with your AA?" to a winning poker player if he loses the hand on the river.


I believe this aspect of football might change in the future though.

Teams are experimenting with formations and other ideas....and Fisher did some wacky things with his onside kicking with the Titans in a couple of games.


I also believe there are more and more situations where baseball is learning the math and there have been some articles on this.
Bill James and other math-dudes looking at the implications of various plays and presenting their conclusions to some teams for example.

tony Larussa has even done some experimenting with putting the pitcher in the 8th batting spot.


There have also been more and more experiments with having 2 scheduled pitchers for a given game (essentially an 8 or 10 man rotation every 4 or 5 games). This is being increasingly done at the minor-leagues. At first it was done just to get all the prospects a regular amount of work.
Then it was determined that it might not be a half-bad strategy.
Some pitchers get shelled when they reach 80-90 pitches typically. Some last to 100-110 pitches before they are really tired...but usually their pitching is declining a little bit before then.

Why wait UNTIL they are getting hit hard to remove them if past experience shows there is a good chance they will START to get hit hard at such-and-such point of the ball-game and you can remove that pitcher BEFORE he gets in a jam?

Letting the starter stay in UNTL he gets in a jam is a bit silly when you think about it....and it's often-times done with a philosophy of 'he got us this far....let him try to finish it off' since it was tradition for a starter to go as long as possible because early removal denoted failure.


The general idea of 'why are pitching these guys so much?' was a big factor in teams dropping the 4-man rotation.


I agree that most baseball managers and football coaches aren't exactly mathematical geniuses (on that note...neither am I...not even close. do you see why??).

But I think if one looks hard enough one can find examples of where they actually have adjusted to the math, etc.

[MicroBob]

Also - sometimes it's just not so simple as the stats might show.

Just showing that 'the chances of scoring a run are not that much more attractive when stealing a base' is not necessarily relevant.

Often-times, sending the runner is part of a hit-and-run..and it's not just designed to get the runner a head-start but rather is used to move the infielders around and draw attention to the runner. Opening up a hole on the 2nd base side of the infield can make a huge difference in whether the hitter gets a base-hit or not.

Also...if a contact-hitter is at the plate whom you can trust then having a speedster dancing around all over the plce at 1st base who is merely a THREAT to take-off can really distract even the best of pitchers into performing less than optimally.

So....if the chances of getting that run in from 1st base appear to be pretty close to getting it in AFTER a steal of 2nd base it may have more to do with the fact that there was a hit-and-run on there (I'm assuming the study just looks at 'score run AFTER SB' vs. 'score run WITHOUT SB' and perhaps does not consider 'score run if hit-and-run' since hit-and-runs don't show up in the box-score)

....or that the catcher told the pitcher 'look...this guy is a real threat to run so make sure you get the ball to the plate quickly and don't kick too high' (thus decreasing velocity or breaking-action).


General point being...it's not always as straight-forward as it might seem regarding 'stolen-base does not mean enough for run-scoring and therefore should not be attempted as much'.


Again...I don't know too much about the math involved...just a guy who knows a little bit about baseball pontificating from the devil's advocate side.

[InfernoLL]

I think it's reasonable to assume Sklansky realizes there are a lot more factors involved in these decisions than what is discussed in the article. The article had a length limit.

Your point about the game clock can be dismissed. The article stated that the analysis only directly applied when it wasn't near the end of the game.

Field goals are important, but again, the point of the article was to demonstrate the relative simplicity of the analysis of these situations, and how results gained are sometimes very different from what is actually done. Adding field goals to the analysis would be trivially simple.

Your third point is implicit in whatever methods the coaches would have to use to obtain the statistical information necessary to calculate decisions. There would always be some lack of confidence as to how well the data applies to the present situation, but that's part of the game.

[SlantNGo]

It's simple. There's no way you're going to convince the players that going for it on 4th down is mathematically correct. For a poker comparison, think of how many players you want in the pot with pocket aces. The football player wants it heads up because he will win small a large percentage of the time. The poker player wants everyone in because it increases his expectation.

As soon as you go for it on 4th down and fail a couple of times, the players will think you've gone mad and lose confidence in you. Even if a coaching "mastermind" like Belichick, Holmgren or Shanahan was the coach.

[mosch]

[ QUOTE ]
There's no way you're going to convince the players that going for it on 4th down is mathematically correct.

[/ QUOTE ]

If these guys are true professionals, and I believe most of them are, then this should be a non-issue. The idea that all of these highly skilled athletes can't compete if they've had any misfortune is absurd, yet commonly accepted.

[The Dude]

[ QUOTE ]
It's simple. There's no way you're going to convince the players that going for it on 4th down is mathematically correct. For a poker comparison, think of how many players you want in the pot with pocket aces. The football player wants it heads up because he will win small a large percentage of the time. The poker player wants everyone in because it increases his expectation.


[/ QUOTE ]
Am I missing something here? Your example contradicts your point. Oh yeah, and I think you're wrong.

Fans and media will have a much harder time understanding it than the players.

[Guruman]

Infeernoll:
[ QUOTE ]
I think it's reasonable to assume Sklansky realizes there are a lot more factors involved in these decisions than what is discussed in the article. The article had a length limit.

[/ QUOTE ]

I understand that the specifics of a true fourth down EV system would be a little beyond the scope of the article. That said, I still feel that there were a couple of significant factors that would go into such a system that were not addressed.

[ QUOTE ]
Your point about the game clock can be dismissed. The article stated that the analysis only directly applied when it wasn't near the end of the game.

[/ QUOTE ]

Fair enough, though I did offer up a suggestion for dealing with short game clocks.

[ QUOTE ]
Field goals are important, but again, the point of the article was to demonstrate the relative simplicity of the analysis of these situations, and how results gained are sometimes very different from what is actually done. Adding field goals to the analysis would be trivially simple.

[/ QUOTE ]

I disagree about the triviality of FGs for the reasons that I stated above. The fact that you can cause a team to have to score on two seperate possesions to win as opposed to one by making a field goal is a very significant consideration at any point in a tight game. I'd love to see how you would account for this in a purely EV system.
[ QUOTE ]
Your third point is implicit in whatever methods the coaches would have to use to obtain the statistical information necessary to calculate decisions. There would always be some lack of confidence as to how well the data applies to the present situation, but that's part of the game

[/ QUOTE ]

The only point that I was trying to make there was to show how wildly inaccurate statistical samples of any given football team can be based on rapidly shifting personnel. As a further ex:

Dallas' ability to convert a fourth down this year would rely on a couple of key players for success: Julius Jones, Larry Allen, Drew Bledsoe, and possibly Keshawn Johnson or Jason Witten. If any one of those guys goes down, so goes the rating. The converse is of course also true of opposing defensive personnel.

On top of that, there is almost never a large enough sample of 3rd or 4th down plays attempted by any club with the same personnel to be statistically relevant. Last year Arizona led the league with 241 3rd down attempts. New York Giants were at the bottom with 190. Fourth down attempts ranged from 19 to 4.

Anyone in the probability forum will tell you that this is not close to enough of a sample to get a good read on a team's ability to convert, and even a large enough sample would have to assume consistent personnel - a near impossibility in the NFL.

The proof is in the pudding here as well: Third down conversion success rates ranged from 52.3 to 25.1, and fourth down ranged from 73.7 to ZERO! Clearly you cannot accurately determine your team's ability to convert based on a sample of actual game play, so you are reduced to what the coaches do anyway - make an educated guess.

I think that finding an even remotely accurate way to determine fourth down completion odds is the biggest hurdle to clear if a coach wants to create an EV system for determening whether or not to go for it.

[David Sklansky]

"On top of that, there is almost never a large enough sample of 3rd or 4th down plays attempted by any club with the same personnel to be statistically relevant. Last year Arizona led the league with 241 3rd down attempts. New York Giants were at the bottom with 190. Fourth down attempts ranged from 19 to 4.

Anyone in the probability forum will tell you that this is not close to enough of a sample to get a good read on a team's ability to convert, and even a large enough sample would have to assume consistent personnel - a near impossibility in the NFL.

The proof is in the pudding here as well: Third down conversion success rates ranged from 52.3 to 25.1, and fourth down ranged from 73.7 to ZERO! Clearly you cannot accurately determine your team's ability to convert based on a sample of actual game play, so you are reduced to what the coaches do anyway - make an educated guess.

I think that finding an even remotely accurate way to determine fourth down completion odds is the biggest hurdle to clear if a coach wants to create an EV system for determening whether or not to go for it."

The fourth down odds should be determined not from the small sample of your partidcular team's results but rather from the much larger sample of all team's results in the past several years. You of course adjust these numbers based on what you know about your team. But the adjustment would never be nearly as much as the one year statistical extremes that some teams would exhibit by chance.

[maurile]

[ QUOTE ]
I think that finding an even remotely accurate way to determine fourth down completion odds is the biggest hurdle to clear if a coach wants to create an EV system for determening whether or not to go for it.

[/ QUOTE ]
All of your objections are addressed in this article (http://emlab.berkeley.edu/users/dromer/papers/nber9024.pdf).

To find the rate of converting on 4th-and-1, look at the success rate for all 3rd-and-1's and 4th-and-1's over the past several years (adjusting for field position as well, since it's easier to convert at mid-field than near your opponent's goal line). Then do the same for 4th-and-2, then 4th-and-3, and so on. There are enough third down plays to get a sufficient sample for each distance to go.

If anything, using third down as a proxy for fourth down will underestimate the success rate, since teams will always go for it on 3rd down, while they may only go for it on 4th down if they have a particular play in mind that they think will work.

[HelloGoodbye]

Interesting article with major problems in unaddressed variables, do you see why?

Among many things, what he dismisses as decisions made merely by ''feel'', would be quite often more accurately described as decisions made by momentum, which is real, shouldn't be dismissed, and can't be calculated with ''simple math''.

[HelloGoodbye]

"-Sacrifices don't have much value in a high-offense era. Teams score fewer runs when a sacrifice is successful. For example, a team will score fewer runs with a man on second and one out than with a man on first and nobody out."

I'm far from a baseball expert, but the way this is phrased here seems a bit misleading. You would have to take into consideration who was at-bat, which more often than not would be pitcher or poor hitter.

[SlantNGo]

Come on guys, football is a game of egos and heart, not brains... going for it on 4th down early in the game at your own 40 just tells your defense you lack confidence in them. Football is as results-oriented a game as they get... in other sports, in the playoffs, you play 5 games or 7 games. In football, everything comes down to one game. You cannot have a losing session! Gambling on 4th down more is surely the +EV play, but it will "backfire" on you and cause you to lose some games but win more in the long run.

[SlantNGo]

How does my example contradict my point? The poker player takes the +EV play, knowing that it may result in a loss every once in awhile, but he makes up for it with bigger wins. The football player wants the least variance play, hence getting it heads up with Aces to win the small pot more often.

And I agree about the fans and media, but they're not the main problem... even if a high school coach tried this, as soon as he fails three 4th down conversions in a row, the players aren't buying it. That's just the way football is, it doesn't encourage thought. Do something radical, and if it works, you're a genious, it it doesn't, you're fired. I've seen plenty of coaches, even at an amateur level, get canned for doing this less "radical" than going for it early on 4th down.

[ QUOTE ]
Am I missing something here? Your example contradicts your point. Oh yeah, and I think you're wrong.

Fans and media will have a much harder time understanding it than the players.

[/ QUOTE ]

[Shoe]

[ QUOTE ]
Come on guys, football is a game of egos and heart, not brains... going for it on 4th down early in the game at your own 40 just tells your defense you lack confidence in them.

[/ QUOTE ]

Not if your defense understands your strategy going into the game. In fact it might show them that you have confidence in them to stop the opposition even when you miss and give the opponent the ball with good field position.

[SlantNGo]

Definitely... how do you sell that to players who average a 15 on their Wonderlic though? It's a catch-22. I mean, a 30 is not that impressive, and a 10 is literate... I'm not sure any coach in the NFL is good enough to sell that to their defense. These aren't all Joey Harringtons and Alex Smiths.

Speaking of which, Frank Gore from Miami scored a 6! SIX! on his Wonderlic...

[HelloGoodbye]

The problem is that David wants to make a complicated subject into ''simple math''. David talks in his books about passing up +EV plays if it means bigger +EV plays in the future, or passing up edges in ''go broke'' situations, but he doesn't touch upon the majority of those examples in this article.

For example, if you are the much better team it may be better to punt than to go for it, even if the math used here seems to show otherwise. The math here assumes you're trying to win by the most points possible, and not the what it should be, which is to assume you're trying to get the best possible chance of winning by atleast 1.

[Shoe]

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The problem is that David wants to make a complicated subject into ''simple math''. David talks in his books about passing up +EV plays if it means bigger +EV plays in the future, or passing up edges in ''go broke'' situations, but he doesn't touch upon the majority of those examples in this article.

For example, if you are the much better team it may be better to punt than to go for it, even if the math used here seems to show otherwise. The math here assumes you're trying to win by the most points possible, and not the what it should be, which is to assume you're trying to get the best possible chance of winning by atleast 1.

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Well said.

[OrangeKing]

I think there is a lot of merit to the idea that football teams - especially since their seasons and playoffs are shorter than in any other sport - do have an interest in keeping variance low at the expense of some points EV.

Think of the phrase: "defense wins championships." For a long time, I found this silly; after all, offense is, pretty much by definition, just as large an impact as defense on whether or not you win each individual game. However, high scoring offenses tend to increase variance, while tough defenses will reduce variance. In a playoff format where one loss knocks you out, you might be more likely to win the Super Bowl with a team that has a smaller edge over another team, but with a lot less variance in the scores of their games.

[David Sklansky]

"The math here assumes you're trying to win by the most points possible, and not the what it should be, which is to assume you're trying to get the best possible chance of winning by atleast 1."

You missed the sentence that the math assumes early stages of the game with approximately equal scores and equal teams.

[SlantNGo]

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"in the early to middle stages of a game between approximately equal teams when the score is close"

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If this were the case, wins and losses would be decided only by variance. Assuming one team feels they are slightly better than the other team, i.e. add 0.1 to their EV for every situation.

In this case, taking your example, punting on 4th and 1 on the 30 has an EV of -0.9 pts. When your opponent does it, your EV is 1 pt. Rinse, lather, repeat, due to the lower variance, you will win more games, albeit by a closer margin.

Now go for it. 30% of the time, you suffer an EV loss of 3.4 pts (again, subtracting 0.1 for your "edge" over your opponent), while you're opponent is punting everytime, where your EV is 1. Repeat this situation many times, and you actually won't win as many games due to the higher variance, although your average winning margin is increased.

The point I'm trying to make is that variance is MORE important than EV if you believe your team has an edge over the other team. A 16-game season is clearly not the long run. In addition, the way the playoff criteria are set up (better records gain homefield advantage, etc.) further suggests that a lower EV lower variance approach is superior.

On a side note, if you believed you were the underdog, you could take the higher EV play, hoping to get lucky and score a few more wins. If the teams are even, the mathematical analysis is moot; wins and losses will only be determined by variance.

Your current analysis is great if teams played 10,000 game seasons, but I think you're underestimating the importance of minimizing variance in a 16-game season with playoffs.

[SlantNGo]

Actually, I had a change of heart after I wrote that... there is already a "chart" of sort used in football, and that's the 2-point conversion chart. And you're right, it seems more the media than the players who question a failed 2-point conversion that the coach called according to the chart. So I do believe we could see someday, an innovative head coach (most likely a former offensive coordinator) using a 4th down chart to guide him.

[maurile]

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The problem is that David wants to make a complicated subject into ''simple math''.

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This subject has been treated by some pretty advanced math, and the answer is the same as David's.

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The math here assumes you're trying to win by the most points possible, and not the what it should be, which is to assume you're trying to get the best possible chance of winning by atleast 1.

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In the first quarter, getting the biggest lead possible and maximizing your chance to win by at least one are the same thing.

[maurile]

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I think there is a lot of merit to the idea that football teams - especially since their seasons and playoffs are shorter than in any other sport - do have an interest in keeping variance low at the expense of some points EV.

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In the first quarter of a game, this is simply incorrect.

In any event, the way the analysis was done in The Hidden Game of Football, they focused directly on maximizing the chance to win -- not just on simply maximizing immediate point differential.

David got the correct answer: teams irrationally go for it on fourth down too infrequently.

[maurile]

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"in the early to middle stages of a game between approximately equal teams when the score is close"

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If this were the case, wins and losses would be decided only by variance.

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No, it would also be decided according to which coaches make the better decisions. For example, a team that always punts on first down would decrease its chances of winning -- as would a team that always punts on fourth down.