4th and 1 at the 2, up by 10......

[SouthGeorgiaBillsFan]

Let's just say that's just very wrong. Very.

 

In earlier posts I did post a more detailed, though still summary, analysis. From my own standpoint, I've been studying this kind of thing independently for several years - it's a small hobby - and I'll admit that I do have comprehensive data on literally thousands of NFL and college games. I'm not an "expert", but my hobby has led me to subject my methodology to academics I respect, and I'm reasonably confident in most of it.

 

However, there are better sources - several academic works (cited previously in the thread) have been published on this topic as well. The math tends to get a little hairy, but the conclusions are easy to understand and appreciate. For those who aren't very math-oriented, I also posted some links to a few graphs that demonstrate some interesting results ... though I suppose it is possible for some to look at such things, turn away, and summarily decry LIES! LIES!

 

Actually, part of what makes it interesting to really study these issues is the vitriol it elicits when the numbers show something contrary to what some think is "football sense."

 

In my first post in this thread, I actually stated that I would have gone for it. I cited my belief that only the Bills could actually squander a 10 point lead in that situation. Already, my path to the same conclusion was different from yours, but immediately that ruled out your theory of "Actually, part of what makes it interesting to really study these issues is the vitriol it elicits when the numbers show something contrary to what some think is "football sense,"' at least in regards to me.

 

What you failed to recognize was that I was merely calling into question the validity of statistics based arguments in regards to situational football theory. I was doing this, not according to your presumptive reasoning of "Actually, part of what makes it interesting to really study these issues is the vitriol it elicits when the numbers show something contrary to what some think is "football sense,"' but rather because the entire logical premise upon which you are making your argument is fundamentally flawed. Observe:

 

1. Your "probabilities" supposedly reflect the odds at which a possible outcome will occur. Because those odds are fundamentally based on what has already happened, they do not reflect the odds of the situation that has yet to happen. For example, unless you have included the number of times that an untied shoelace has contributed to a complete pass, then your probabilities by default have a margin of error equal to the proportion of the times an untied shoelace actually caused a change of outcome in the play versus the number of plays from which the probabilities are derived. Since you are not including probabilities of every possible dynamic that could affect the outcome of the game, they are not an accurate reflection of the odds that a situation will occur in that game.

 

2. How can you feel comfortable basing your entire decision making logical model on these probabilities when you know that there is at least some discrepancy (and quite possibly large discrepancies, and you know it) in your stated probabilities and what the actual odds are? That is a logical fallacy, plain and simple.

 

Conveniently for the likes of you who perpetuate these kinds of flawed arguments, numbers and logic intimidate most people, and they are quite happy to just regurgitate your entirely fabricated BS without question, thinking that they sound smarter and more educated in the process. But there will always be someone like me, waiting to poke holes in every theory, and ready to pick apart such baseless and insulting conclusions.

[SouthGeorgiaBillsFan]

To further illustrate my point, let us observe the example of poker:

 

It is a raging argument whether it is more effective in poker to "play the odds" or "play by feel." The truly successful poker players all have one thing in common: they incorporate both. It is absolutely necessary to know the odds of a given scenario (in the case of hand odds we don't have to even worry about unaccounted for dynamics, since we are talking about a simple system of cards being dealt from a limited deck), but ANY good poker player knows that you cannot merely bet the odds. The reason for this is because anyone ELSE who is familiar with how odds work know how to easily manipulate your odds.

 

In a poker game, there are 2 important types of odds. You have the pot odds, and you have the hand odds. The pot odds represent the percentage of all times at which you must win the given pot in order to break even on those pots. The hand odds represent your chance of drawing the winning hand.

 

The argument exists in the idea that as long as you only bet when your hand odds are better than the pot odds, the laws of probability dictate that you should always come out ahead. This seems logically sound at first glance. But there are several unaccounted dynamics that debunk this belief. If the opposing player knows you are betting odds, he can bluff you. Typically betting a pot sized bet completely throws of the logic of the system, as the guy believes he is betting much worse pot odds than he actually is. Therefore, the logic dictates that he must fold. Most good players cannot be easily bluffed this way consistently, and therefore we know that the ones who truly understand how the odds work in poker realize that there is a time to throw the odds out the window and bet your gut.

 

The point being that any idiot can manipulate statistics to make them tell a story according to his design, and thus they have little actual validity in any argument regarding situational football theory.

[Booster4324]

So then why are you using expected points numbers that don't account for the end of the game in your original posts? And why aren't you accounting for the non-linear behaviour of points in terms of wins (and relying on average points)? Your analysis would suggest that we were better off going for it if we were down by 2 pts as well, which is ABSURD!

 

These are two fundamental flaws to your math, and you havn't addressed (or attempted to address) them at all. The guy you talked too who is converting things to win% has it right, that is all we are concerned about with that decision, but I don't trust his numbers saying that a team up by 13 with 2 minutes left only wins 96% of the time.

 

Nice post. Are you really a newbie? If so, please post more.

 

 

Disbelief of a data point (i.e. the 96% number) is somewhat unassailable (I suppose it can be believed or not), but that number itself is sort of secondary in this situation. The question is more which decision, at the time its made, yields the highest probable winning percentage - regardless of what those actual %s are.

 

Please post the stats that prove the 96% number. We do not have to go into it dropping from 98% to 96%. Just the stats that proves that teams up by 13 and less than 2 minutes remaining win 96% of the time.

 

In earlier posts I did post a more detailed, though still summary, analysis. From my own standpoint, I've been studying this kind of thing independently for several years - it's a small hobby - and I'll admit that I do have comprehensive data on literally thousands of NFL and college games. I'm not an "expert", but my hobby has led me to subject my methodology to academics I respect, and I'm reasonably confident in most of it.

 

This should prove to be fairly simple for you. It is a complete softball.

[MRM33064]

To further illustrate my point, let us observe the example of poker:

 

It is a raging argument whether it is more effective in poker to "play the odds" or "play by feel." The truly successful poker players all have one thing in common: they incorporate both. It is absolutely necessary to know the odds of a given scenario (in the case of hand odds we don't have to even worry about unaccounted for dynamics, since we are talking about a simple system of cards being dealt from a limited deck), but ANY good poker player knows that you cannot merely bet the odds. The reason for this is because anyone ELSE who is familiar with how odds work know how to easily manipulate your odds.

 

In a poker game, there are 2 important types of odds. You have the pot odds, and you have the hand odds. The pot odds represent the percentage of all times at which you must win the given pot in order to break even on those pots. The hand odds represent your chance of drawing the winning hand.

 

The argument exists in the idea that as long as you only bet when your hand odds are better than the pot odds, the laws of probability dictate that you should always come out ahead. This seems logically sound at first glance. But there are several unaccounted dynamics that debunk this belief. If the opposing player knows you are betting odds, he can bluff you. Typically betting a pot sized bet completely throws of the logic of the system, as the guy believes he is betting much worse pot odds than he actually is. Therefore, the logic dictates that he must fold. Most good players cannot be easily bluffed this way consistently, and therefore we know that the ones who truly understand how the odds work in poker realize that there is a time to throw the odds out the window and bet your gut.

 

The point being that any idiot can manipulate statistics to make them tell a story according to his design, and thus they have little actual validity in any argument regarding situational football theory.

 

Again, the point is that basic concept of "pot odds" may not be the sole factor, but is certainly relevant in the process - or ought to be - and subject to being quantified.

 

As to whether these concepts have little actual validity in "situational football theory", we disagree. I (obviously) think they are highly relevant.

[BuffOrange]

To further illustrate my point, let us observe the example of poker:

 

It is a raging argument whether it is more effective in poker to "play the odds" or "play by feel." The truly successful poker players all have one thing in common: they incorporate both. It is absolutely necessary to know the odds of a given scenario (in the case of hand odds we don't have to even worry about unaccounted for dynamics, since we are talking about a simple system of cards being dealt from a limited deck), but ANY good poker player knows that you cannot merely bet the odds. The reason for this is because anyone ELSE who is familiar with how odds work know how to easily manipulate your odds.

 

In a poker game, there are 2 important types of odds. You have the pot odds, and you have the hand odds. The pot odds represent the percentage of all times at which you must win the given pot in order to break even on those pots. The hand odds represent your chance of drawing the winning hand.

 

The argument exists in the idea that as long as you only bet when your hand odds are better than the pot odds, the laws of probability dictate that you should always come out ahead. This seems logically sound at first glance. But there are several unaccounted dynamics that debunk this belief. If the opposing player knows you are betting odds, he can bluff you. Typically betting a pot sized bet completely throws of the logic of the system, as the guy believes he is betting much worse pot odds than he actually is. Therefore, the logic dictates that he must fold. Most good players cannot be easily bluffed this way consistently, and therefore we know that the ones who truly understand how the odds work in poker realize that there is a time to throw the odds out the window and bet your gut.

 

The point being that any idiot can manipulate statistics to make them tell a story according to his design, and thus they have little actual validity in any argument regarding situational football theory.

 

So what's the connection again? The Bucs jumped offsides on purpose because they were goading us into going for it? If you wee a Bucs fan do you want us to go for it there? I think you're lying if you say yes.

 

I'm not an originator of this idea, but it's pretty clear that job preservation plays a much larger role in a lot of coaches decisions (not just Jauron's) than putting their team in the best position to win. That Bellichick (and Shannahan as far as anyone knew last yr) are/were considered both fire-proof and 'gamblers' is great evidence of this.

 

Furthermore I saw Marvin Lewis (tied with Brad Childress as the worst gameday coach in football) say on NFL Network when questioned about statistical analysis - make some smug comment about the mathematician's mortgage not being on the line.

Well yah Marvin, that sort of proves the point - when you're thinking about your mortgage you're not giving your team the best chance to win. Because when you punt/kick and lose it's always the player's fault, but everyone blames you when you make the correct "gambling" decision and lose.

[MRM33064]

Please post the stats that prove the 96% number. We do not have to go into it dropping from 98% to 96%. Just the stats that proves that teams up by 13 and less than 2 minutes remaining win 96% of the time ..... This should prove to be fairly simple for you. It is a complete softball.

 

I really started this analysis as a good faith attempt to analyze the decision using some objective metrics, and somehow it all fell apart. Some folks got it.

 

In any case, as I pointed out, the 96% figure didn't come from my data, so people are free to assume it's entirely made up and/or falsified. (Actually, I don't think anything about this is particularly easy or "softball.") In the very low probability (pun intended) that the question was a sincere attempt to learn a little more, I'd point you to this link, which I think is helpful. It's a good summary (or what I think is a good summary of the concepts. http://www.advancednflstats.com/2008/08/win-probability.htm.

 

Also, FWIW, I provided a few other references on this as well, if you can request from me via private message if you're interested. There are also several other forums that spend time analyzing these type questions, though they're not Bills-focused, obviously.

 

That's it on this ... until the next 4-and-? ...

[DonInBuffalo]

FWIW, I did poll a football-savvy statistician on this and his conclusion was that going for it was indeed the better move, but that the decision itself wasn't particularly consequential on those facts.

 

The gist of his response: At that time in the game, with a 10 point lead, his numbers showed that the Bills had close to a 98% chance of winning. Deciding to go for it would've pushed the chance of winning almost all the way to 100%. Deciding to attempt a FG instead reduced the chance of winning, but only reduced it to about 96%.

 

So, his conclusion was that attempting a FG reduced our chances of winning, but not dramatically.

 

Going for the 4th-and-1 earlier in the game had a bigger positive impact, probability-wise, than the negative impact of the erroneous decision to kick the FG at the end.

There are some fundamental flaws in your logic. The biggest one is that you're making inappropriate statistical conclusions. (or phrasing those conclusions very poorly) The only point in the game where anybody knew what the probability of the Bills winning the game was when it was over. Any time prior to that, all you can do is estimate the probability based on a variety of factors. One estimate could be based on what other teams did in similar circumstances. That is presumably what you did above. However, that estimate doesn't take into account a myriad of factors that are unique to the specific Bills game in question. The most obvious factor is the most if not all of the players and coaches are different than all the other games that were used to make your estimate. So your estimate is at best a very rough guess.

 

When coaches make decisions they do so not just based on probabilities, but strategy as well. Here are some of the strategic reasons to kick the FG in that situation:

- If you go for it and fail, it's a momentum swing that could spark the other team. Going for it and failing would also deflate the enthusiasm of the crowd.

- Knowing that the opponent has to score two TDs allows you to adjust your defensive strategy accordingly. You really don't care if they score on the first drive, as long as they have to use all (or virtually all) of the remaining time. You can play prevent and make them dink and dunk their way down the field.

 

Strategic reasoning can't always be quantified. I can't think of any straightforward way to quantify what I listed above.

 

Your statistical reasoning continued to be flawed when you presumed what the probability of the Bills making it if they went for it. Again, because all the players and coaches are different than your sample, any estimate of the probability of making it is going to be at best a rough guess.

 

One of the most important strategic principles involved in protecting a lead is to eliminate (or at least limit) the number of unknown or random elements. In this case, going for it adds a random element (the outcome) , so from a strategic point of view the proper choice is to eliminate that element by kicking the FG, which is essentially a sure thing.

[DonInBuffalo]

I really started this analysis as a good faith attempt to analyze the decision using some objective metrics, and somehow it all fell apart. Some folks got it.

 

In any case, as I pointed out, the 96% figure didn't come from my data, so people are free to assume it's entirely made up and/or falsified. (Actually, I don't think anything about this is particularly easy or "softball.") In the very low probability (pun intended) that the question was a sincere attempt to learn a little more, I'd point you to this link, which I think is helpful. It's a good summary (or what I think is a good summary of the concepts. http://www.advancednflstats.com/2008/08/win-probability.htm.

 

Also, FWIW, I provided a few other references on this as well, if you can request from me via private message if you're interested. There are also several other forums that spend time analyzing these type questions, though they're not Bills-focused, obviously.

 

That's it on this ... until the next 4-and-? ...

That site has some interesting content, but again people need to be careful how they interpret the results of their calculations. For example, on this page:

http://www.advancednflstats.com/2009/09/4t...udy-part-1.html

We don't have such clear-cut options and we don't know the probabilities and payoff values of our decisions. But in football, we do.

That's a complete crock. Put simply, the only event in a football game with a known probability is the coin flip.

[WaterlooBills]

That site has some interesting content, but again people need to be careful how they interpret the results of their calculations. For example, on this page:

http://www.advancednflstats.com/2009/09/4t...udy-part-1.html

That's a complete crock. Put simply, the only event in a football game with a known probability is the coin flip.

 

I agree that MRM is infering things he shouldn't be, but I do believe that this sort of analysis can be used to create an excellent model for 4th down decisions, and that almost no matter what, it will show that NFL coaches punt/kick FGs way too much. The problem is that all of the current stuff relies on past history, which while usefull, is not perfectly accurate. By averaging across all games, that data starts with the assumption that both teams are equal with historically average offenses, defenses, ST play, etc., which is never actually correct. I have yet to see anyone try to correct this sort of analysis for these factors (and I believe that once someone does that some NFL will start using it).

 

I have also yet to see anyone really translate pts to win%, especially in super late game situations as MRM is doing. For example, the 4th down article he has linked uses data from the 1st and 3rd quarters only (and hence, tries to ignore the effect of the end of the game). Correcting for time left, timeouts remaining and score for late game situations is extremely difficult.

 

Finally, MRM, expected points to win% is non-linear not because it is discrete, but because some pt leads are virtually equivalent, especially when one of the teams is unlike to score for the other team to win (as was the case on this play). For example, there was no difference to us being up by 1 pt or 2 pts, 5 pts or 6 pts, yet our win% would shoot through the roof if we were up by 9. This is even more difficult to correct for as the average pts idea breaks down. Early in the game, maximizing expected points will translate almost perfectly to winning%, but not near the end.

[San Jose Bills Fan]

Kudos to you guys. I didn't know we had a Mensa forum here at TSW.

 

Can't keep up but from afar it seems like the Bohr-Einstein debates. Good stuff.

[Ramius]

There are some fundamental flaws in your logic. The biggest one is that you're making inappropriate statistical conclusions. (or phrasing those conclusions very poorly) The only point in the game where anybody knew what the probability of the Bills winning the game was when it was over. Any time prior to that, all you can do is estimate the probability based on a variety of factors. One estimate could be based on what other teams did in similar circumstances. That is presumably what you did above. However, that estimate doesn't take into account a myriad of factors that are unique to the specific Bills game in question. The most obvious factor is the most if not all of the players and coaches are different than all the other games that were used to make your estimate. So your estimate is at best a very rough guess.

 

When coaches make decisions they do so not just based on probabilities, but strategy as well. Here are some of the strategic reasons to kick the FG in that situation:

- If you go for it and fail, it's a momentum swing that could spark the other team. Going for it and failing would also deflate the enthusiasm of the crowd.

- Knowing that the opponent has to score two TDs allows you to adjust your defensive strategy accordingly. You really don't care if they score on the first drive, as long as they have to use all (or virtually all) of the remaining time. You can play prevent and make them dink and dunk their way down the field.

 

Strategic reasoning can't always be quantified. I can't think of any straightforward way to quantify what I listed above.

 

Your statistical reasoning continued to be flawed when you presumed what the probability of the Bills making it if they went for it. Again, because all the players and coaches are different than your sample, any estimate of the probability of making it is going to be at best a rough guess.

 

One of the most important strategic principles involved in protecting a lead is to eliminate (or at least limit) the number of unknown or random elements. In this case, going for it adds a random element (the outcome) , so from a strategic point of view the proper choice is to eliminate that element by kicking the FG, which is essentially a sure thing.

 

Excellent post.

 

I'll also add in that this guy's "stats and percentages" do not take into account other factors such as a team "forcing" more big play attempts because they are down by more. If Tampa is down by 10, then can work into field goal range and kick the fG before trying an onsides kick. If they are down by 13, they are forced to score a TD before the onsides. Knowing you need to put the ball in the endzone in a hurry as opposed to getting into FG range is going to cause the opposing team to take more chances, and make more high-risk decisions in an effort to get the ball downfield. This directly benefits the defense, but cannot be accounted for in whatever jackass statistical analysis someone tries to apply to an NFL game.

[MRM33064]

do believe that this sort of analysis can be used to create an excellent model for 4th down decisions, and that almost no matter what, it will show that NFL coaches punt/kick FGs way too much ..... Finally, MRM, expected points to win% is non-linear not because it is discrete, but because some pt leads are virtually equivalent, especially when one of the teams is unlike to score for the other team to win (as was the case on this play). For example, there was no difference to us being up by 1 pt or 2 pts, 5 pts or 6 pts, yet our win% would shoot through the roof if we were up by 9. This is even more difficult to correct for as the average pts idea breaks down. Early in the game, maximizing expected points will translate almost perfectly to winning%, but not near the end.

 

Very sharp critique, and FWIW, I agree with the vast majority of it - especially the big picture, which is well summarized in the first sentence and is probably the most important takeaway. If/when a similar situation presents, I really hope you take the time to post an analysis. I think this can be a tool to help improve a team's decision-making and, ultimately, its chances to win.

 

(BTW, on the specific situation, I do think it'd be entirely reasonble to interpret the win% differential just as might be implied by what Waterloo said; that is, even if we could all stipulate to the 96% (for sake of argument) the win % may be sufficiently high enough at that point either way so as make the decision inconsequential, especially when factoring in error.)