The problem with going for it on 4th down is, even if they get a 1st down that does not garauntee they'll score TD later in the drive, but it does garauntee you'll run more time off the clock to get your next score and that next score could very well be a FG anyway or another 4th down try.
I have no clue how you can put accurate mathmaticall odds on that.
If you listen to these people who try using mathmatical odds like this, most will tell you that going for it on 4th down is almost always the right play anyway, but what they fail to understand is, going for it on 4th down creates "high voalitilty", get'em and your chances may improve dramatically, fail and your chances go down dramatically.
Just because the league average is for example 60%, that does not mean you'll convert them each game at 60%, sometimes you might convert them at 80% and sometimes at 38%, see, "high voalitility", get 80% and you'll win far more than not, get 38% and you lose far more than not, but when averaged together at the end of a season it may be 60%.
3 point shooting in the NBA is a similar thing, it's "high voalitility", shoot 50% like the Celtics did against the Heat and your chances to win are dramtically increased, but shoot 25% or whatever it was like the Celtics did against the Cavs and your chances go down quite a bit.
3 point shooting is a "high voalitility" stratergy and it's one reason you'll rarely see teams who shoot many, many 3's win the title.
I would rather coach a "low voalitility" statergy myself.
The problem with going for it on 4th down is, even if they get a 1st down that does not garauntee they'll score TD later in the drive, but it does garauntee you'll run more time off the clock to get your next score and that next score could very well be a FG anyway or another 4th down try.
I have no clue how you can put accurate mathmaticall odds on that.
If you listen to these people who try using mathmatical odds like this, most will tell you that going for it on 4th down is almost always the right play anyway, but what they fail to understand is, going for it on 4th down creates "high voalitilty", get'em and your chances may improve dramatically, fail and your chances go down dramatically.
Just because the league average is for example 60%, that does not mean you'll convert them each game at 60%, sometimes you might convert them at 80% and sometimes at 38%, see, "high voalitility", get 80% and you'll win far more than not, get 38% and you lose far more than not, but when averaged together at the end of a season it may be 60%.
3 point shooting in the NBA is a similar thing, it's "high voalitility", shoot 50% like the Celtics did against the Heat and your chances to win are dramtically increased, but shoot 25% or whatever it was like the Celtics did against the Cavs and your chances go down quite a bit.
3 point shooting is a "high voalitility" stratergy and it's one reason you'll rarely see teams who shoot many, many 3's win the title.
I would rather coach a "low voalitility" statergy myself.
It was 4th and goal from the 6
Absolutely, I think Belichick was right. I dare you to find anybody thats studied math at a high level that disagrees.
ps You still haven't told me what you think the probabilities are for 18? 15? 11?
How can you even have an opinion on the subject without at least an estimate on the probs?
It was 4th and goal from the 6
Absolutely, I think Belichick was right. I dare you to find anybody thats studied math at a high level that disagrees.
ps You still haven't told me what you think the probabilities are for 18? 15? 11?
How can you even have an opinion on the subject without at least an estimate on the probs?
OK. You're obviously not very perceptive. Read my username closely. It will tell you exactly where I'm from. Hint: It makes it difficult to say the Cowboys did anything right.
You're clearly slow so I'll spell it out for you.
Obviously it would have been better to have the FG than the missed attempt.
But that wasn't the question. The question is which is worth more in that situation. 3 points or 1 play from the 6 yard line for a shot at 7.
Now think back to the end of the game. You're lining up to do an onside kick down 6 points. I offer you either 6 points or one play from the 6 yard line. Which do you pick?
OK. You're obviously not very perceptive. Read my username closely. It will tell you exactly where I'm from. Hint: It makes it difficult to say the Cowboys did anything right.
You're clearly slow so I'll spell it out for you.
Obviously it would have been better to have the FG than the missed attempt.
But that wasn't the question. The question is which is worth more in that situation. 3 points or 1 play from the 6 yard line for a shot at 7.
Now think back to the end of the game. You're lining up to do an onside kick down 6 points. I offer you either 6 points or one play from the 6 yard line. Which do you pick?
" I guess arguably this whole thing should have been about the difference between 15 and 12/10, but that would have just confused the math and I think most people reading this are confused enough as it is."
This is my point with you.
" 12 to 11 is important because it gets you the ability to use a fg and a 2 point conversion, but you still need the two point conversion. That makes 11 to 10 a much more important jump. "
Anything that is important is desireable. You should always keep the option open since you're playing for the tie either way. Sitting on 11 gives you that option.
Unlike some other people on this site, I think you're close to getting it. You just need a little more help.
Perhaps it would help if you got a spreadsheet and put the variables in there. Put in a probability for a 2. A probability for a touchdown when you need a touchdown. A probability for a touchdown or a field goal when you need it. The probability of winning in overtime and the probability of holding the Giants scoreless. Try to work it through and see which gives you the greater chance of winning.
I've been asking other people to do this. I don't think they can do it and I'm basically mocking them for saying one's more valuable than the other than the other with absolutely no clue how much either is worth. Its like hearing an argument over whether you should give up 10 Zambian Kwacha for 10 Brazilian Real without ever looking at an exchange rate table.
Anyway, in your case, I really think you can do it. I mean that in all seriousness. You're almost there. Do you have Excel on your computer? Try to do it and see what you come up with.
" I guess arguably this whole thing should have been about the difference between 15 and 12/10, but that would have just confused the math and I think most people reading this are confused enough as it is."
This is my point with you.
" 12 to 11 is important because it gets you the ability to use a fg and a 2 point conversion, but you still need the two point conversion. That makes 11 to 10 a much more important jump. "
Anything that is important is desireable. You should always keep the option open since you're playing for the tie either way. Sitting on 11 gives you that option.
Unlike some other people on this site, I think you're close to getting it. You just need a little more help.
Perhaps it would help if you got a spreadsheet and put the variables in there. Put in a probability for a 2. A probability for a touchdown when you need a touchdown. A probability for a touchdown or a field goal when you need it. The probability of winning in overtime and the probability of holding the Giants scoreless. Try to work it through and see which gives you the greater chance of winning.
I've been asking other people to do this. I don't think they can do it and I'm basically mocking them for saying one's more valuable than the other than the other with absolutely no clue how much either is worth. Its like hearing an argument over whether you should give up 10 Zambian Kwacha for 10 Brazilian Real without ever looking at an exchange rate table.
Anyway, in your case, I really think you can do it. I mean that in all seriousness. You're almost there. Do you have Excel on your computer? Try to do it and see what you come up with.
OK. You're obviously not very perceptive. Read my username closely. It will tell you exactly where I'm from. Hint: It makes it difficult to say the Cowboys did anything right.
You're clearly slow so I'll spell it out for you.
Obviously it would have been better to have the FG than the missed attempt.
But that wasn't the question. The question is which is worth more in that situation. 3 points or 1 play from the 6 yard line for a shot at 7.
Now think back to the end of the game. You're lining up to do an onside kick down 6 points. I offer you either 6 points or one play from the 6 yard line. Which do you pick?
OK. You're obviously not very perceptive. Read my username closely. It will tell you exactly where I'm from. Hint: It makes it difficult to say the Cowboys did anything right.
You're clearly slow so I'll spell it out for you.
Obviously it would have been better to have the FG than the missed attempt.
But that wasn't the question. The question is which is worth more in that situation. 3 points or 1 play from the 6 yard line for a shot at 7.
Now think back to the end of the game. You're lining up to do an onside kick down 6 points. I offer you either 6 points or one play from the 6 yard line. Which do you pick?
I'm just curious.
What do you think the probability was that the Cowboys eventually won the game if they were down 15 at that point?
What would it be at 11? at 18?
Can you give a rough outline of how you got to those probs?
Math does matter and decisions like this one are a little bit more complicated than just counting to 3.
Not to rub it in because I'm sure you lose a lot of money betting on sports but I've yet to meet a winning sports bettor that was bad at math or a losing one that was good at it.
I make money on sports. You lose money at sports. Ask yourself why?
I'm just curious.
What do you think the probability was that the Cowboys eventually won the game if they were down 15 at that point?
What would it be at 11? at 18?
Can you give a rough outline of how you got to those probs?
Math does matter and decisions like this one are a little bit more complicated than just counting to 3.
Not to rub it in because I'm sure you lose a lot of money betting on sports but I've yet to meet a winning sports bettor that was bad at math or a losing one that was good at it.
I make money on sports. You lose money at sports. Ask yourself why?
Which of the following is more likely...
Gruden's way.
Kick a short field goal (98%)
+
Get an onside kick (10%)
+
Drive 35 yards into field goal position with 40 seconds and no timeouts (25%)
+
Kick a long field goal (70%)
+
Win in Overtime (50%)
Multiply all of these together and you get 0.86%.
Gruden really legitimately thinks that is more likely than Phillips way.
Convert one 6 yard pass and win the game (about 40%).
Which of the following is more likely...
Gruden's way.
Kick a short field goal (98%)
+
Get an onside kick (10%)
+
Drive 35 yards into field goal position with 40 seconds and no timeouts (25%)
+
Kick a long field goal (70%)
+
Win in Overtime (50%)
Multiply all of these together and you get 0.86%.
Gruden really legitimately thinks that is more likely than Phillips way.
Convert one 6 yard pass and win the game (about 40%).
Unlike some other people on this site, I think you're close to getting it. You just need a little more help.
Perhaps it would help if you got a spreadsheet and put the variables in there. Put in a probability for a 2. A probability for a touchdown when you need a touchdown. A probability for a touchdown or a field goal when you need it. The probability of winning in overtime and the probability of holding the Giants scoreless. Try to work it through and see which gives you the greater chance of winning.
I've been asking other people to do this. I don't think they can do it and I'm basically mocking them for saying one's more valuable than the other than the other with absolutely no clue how much either is worth. Its like hearing an argument over whether you should give up 10 Zambian Kwacha for 10 Brazilian Real without ever looking at an exchange rate table.
Anyway, in your case, I really think you can do it. I mean that in all seriousness. You're almost there. Do you have Excel on your computer? Try to do it and see what you come up with.
Unlike some other people on this site, I think you're close to getting it. You just need a little more help.
Perhaps it would help if you got a spreadsheet and put the variables in there. Put in a probability for a 2. A probability for a touchdown when you need a touchdown. A probability for a touchdown or a field goal when you need it. The probability of winning in overtime and the probability of holding the Giants scoreless. Try to work it through and see which gives you the greater chance of winning.
I've been asking other people to do this. I don't think they can do it and I'm basically mocking them for saying one's more valuable than the other than the other with absolutely no clue how much either is worth. Its like hearing an argument over whether you should give up 10 Zambian Kwacha for 10 Brazilian Real without ever looking at an exchange rate table.
Anyway, in your case, I really think you can do it. I mean that in all seriousness. You're almost there. Do you have Excel on your computer? Try to do it and see what you come up with.
OK. You need to read the post a little bit closer. Gruden (actually I think it was Jaworski but I thought it was Gruden when I heard it) said after they got to six points "If only they had kicked the field goal" it would now be 3 points. Implicit in that statement was the assumption that everything else would have gone the same way as it did. I recognize that assumption is faulty. But lets just run with it a second. Plus he said it not me.
Obviously with everything else playing out the way it did, the Cowboys would have been up by a point if they made it. The way I look at it, if you are going to assume everything else plays out the same, it proves that Phillips did make the right decision. If they had made it, they would have won the game. If they kicked, they would still be in desperation mode as the kick wouldn't have helped much. Even with his own assumption in place and the ability to revisit it with the knowledge of the future scores, he still thought kicking was the right move. I found it to be a ridiculous statement and I still do.
Lets step back and look at this from a more macro level.
Have you ever seen a situation when a team could kick a field goal but goes for a touchdown and misses and eventually loses by 3 points or less? What did the announcers say about it?
Whenever this happens, they talk about it endlessly. Often, they completely ignore the game at hand in order to keep talking about it. In the post game press conference, there are no other reasons presented for the loss. Thats the only one. The coach could have kicked and he didn't. Talk radio lines light up all day Monday with people's anger.
Have you ever seen a situation where a team could kick a field goal but goes for a touchdown and makes it and eventually wins by a 4 points or less? What did the announcers say about it?
Absolutely nothing. They never mention the play the rest of the day. When the team ultimately wins, other factors are always presented. Nobody ever acknowledges that the coach's "gamble" (actually a well calculated +EV risk) was a key factor in the victory.
How often does a team kick and then eventually lose by 4 or less? How often do you hear about it then?
Perfect example:
Opening weekend.... The Redskins took points off the board and then didn't score. They won anyways, but Collinsworth couldn't shup up about it the rest of the game. If they lost, you knew that would be the reason and every newspaper in the country would put "Shanahan gambles game away" in the headline.
The very next night, the Ravens took 3 points off the board and replaced them with 7. They ultimately won by a single point. I watched all the postgame shows and read a lot of papers the next day. Not one single reporter focused on it. Nobody acknowledged that this was a key to the victory.
I bet you watched that game. Do you remember them doing it? Do you remember anybody talking about it? I bet somehow you blocked it out from your memory because nobody else made any sort of big deal. I can guarantee you they did it and the Ravens would have likely lost if they didn't.
For reasons that I don't at all understand, its like the announcers have some sort of pact to never mention these calculated risks unless they fail. I think the coaches pick up on that and say..."I know the odds are in my favor but I really don't want the blame if it doesn't work" so they wimp out. Since nobody does it, it becomes even more of a story when somebody does.
As somebody that does study the math and knows the truth, I can tell you that the "gamble" works both in theory and in practice.
Far far more teams have ultimately lost games they could have won because they didn't gamble than because they did. Smart fans need to start noticing this and doing a few of their own calculations.
You say you know math well and you would run circles around me. Great. Go for it. Calculate the probability that the Cowboys win the game when they are down 15 at that point. At 11. At 18.
I'll even make it easy on you. I'll let you round the 18 probability down to 0. It wasn't zero and that helps my case but I'll still let you do it for simplicity.
If it was the wrong decision, it should be easy to prove with a statement like "They had a 4% probability at 11 and a 3% probability at 15. 40% of 4% < 3%" But you can't make that statement. Can you? You know why...because its not true.
Nearly any way you calculate it, whatever number you calculate for their prob at 15, their prob at 11 was four times higher.
I've been called "stupid", "idiotic" "a moron", etc. etc. but nobody has presented anything near a coherent argument as to exactly where I'm wrong. You said you were going to run circles around me. Start running!!!
OK. You need to read the post a little bit closer. Gruden (actually I think it was Jaworski but I thought it was Gruden when I heard it) said after they got to six points "If only they had kicked the field goal" it would now be 3 points. Implicit in that statement was the assumption that everything else would have gone the same way as it did. I recognize that assumption is faulty. But lets just run with it a second. Plus he said it not me.
Obviously with everything else playing out the way it did, the Cowboys would have been up by a point if they made it. The way I look at it, if you are going to assume everything else plays out the same, it proves that Phillips did make the right decision. If they had made it, they would have won the game. If they kicked, they would still be in desperation mode as the kick wouldn't have helped much. Even with his own assumption in place and the ability to revisit it with the knowledge of the future scores, he still thought kicking was the right move. I found it to be a ridiculous statement and I still do.
Lets step back and look at this from a more macro level.
Have you ever seen a situation when a team could kick a field goal but goes for a touchdown and misses and eventually loses by 3 points or less? What did the announcers say about it?
Whenever this happens, they talk about it endlessly. Often, they completely ignore the game at hand in order to keep talking about it. In the post game press conference, there are no other reasons presented for the loss. Thats the only one. The coach could have kicked and he didn't. Talk radio lines light up all day Monday with people's anger.
Have you ever seen a situation where a team could kick a field goal but goes for a touchdown and makes it and eventually wins by a 4 points or less? What did the announcers say about it?
Absolutely nothing. They never mention the play the rest of the day. When the team ultimately wins, other factors are always presented. Nobody ever acknowledges that the coach's "gamble" (actually a well calculated +EV risk) was a key factor in the victory.
How often does a team kick and then eventually lose by 4 or less? How often do you hear about it then?
Perfect example:
Opening weekend.... The Redskins took points off the board and then didn't score. They won anyways, but Collinsworth couldn't shup up about it the rest of the game. If they lost, you knew that would be the reason and every newspaper in the country would put "Shanahan gambles game away" in the headline.
The very next night, the Ravens took 3 points off the board and replaced them with 7. They ultimately won by a single point. I watched all the postgame shows and read a lot of papers the next day. Not one single reporter focused on it. Nobody acknowledged that this was a key to the victory.
I bet you watched that game. Do you remember them doing it? Do you remember anybody talking about it? I bet somehow you blocked it out from your memory because nobody else made any sort of big deal. I can guarantee you they did it and the Ravens would have likely lost if they didn't.
For reasons that I don't at all understand, its like the announcers have some sort of pact to never mention these calculated risks unless they fail. I think the coaches pick up on that and say..."I know the odds are in my favor but I really don't want the blame if it doesn't work" so they wimp out. Since nobody does it, it becomes even more of a story when somebody does.
As somebody that does study the math and knows the truth, I can tell you that the "gamble" works both in theory and in practice.
Far far more teams have ultimately lost games they could have won because they didn't gamble than because they did. Smart fans need to start noticing this and doing a few of their own calculations.
You say you know math well and you would run circles around me. Great. Go for it. Calculate the probability that the Cowboys win the game when they are down 15 at that point. At 11. At 18.
I'll even make it easy on you. I'll let you round the 18 probability down to 0. It wasn't zero and that helps my case but I'll still let you do it for simplicity.
If it was the wrong decision, it should be easy to prove with a statement like "They had a 4% probability at 11 and a 3% probability at 15. 40% of 4% < 3%" But you can't make that statement. Can you? You know why...because its not true.
Nearly any way you calculate it, whatever number you calculate for their prob at 15, their prob at 11 was four times higher.
I've been called "stupid", "idiotic" "a moron", etc. etc. but nobody has presented anything near a coherent argument as to exactly where I'm wrong. You said you were going to run circles around me. Start running!!!
OK. You need to read the post a little bit closer. Gruden (actually I think it was Jaworski but I thought it was Gruden when I heard it) said after they got to six points "If only they had kicked the field goal" it would now be 3 points. Implicit in that statement was the assumption that everything else would have gone the same way as it did. I recognize that assumption is faulty. But lets just run with it a second. Plus he said it not me.
OK. You need to read the post a little bit closer. Gruden (actually I think it was Jaworski but I thought it was Gruden when I heard it) said after they got to six points "If only they had kicked the field goal" it would now be 3 points. Implicit in that statement was the assumption that everything else would have gone the same way as it did. I recognize that assumption is faulty. But lets just run with it a second. Plus he said it not me.
Thank you for at least trying to figure this out. I can't believe how many people on this site are willfully ignorant.
There are a whole lot of variables involved. I could explain how to do a really good calculation but it will get very complicated very quickly.
Basically, when you do this you get x% probability you score 0..they score 0. y% you score 7 they score 0...etc...etc.
One way to simplify it is to quickly knock out all of the scenarios where it doesn't matter whether you go for it or not.
Obviously, if Dallas managed to score 5 more times they win no matter what. If Dallas scores only once more they lose no matter what.
The remaining scenarios are:
1. Dallas scores 2 TDs. Giants score none.
2. Dallas scores 2 TDs. NY scores FG.
3. Dallas scores 1 TD and FG. Giants score none.
Lets compare the relative strength of all scenarios at -15 and -11.
1. At -11, DAL wins 100% of the time. At -15, DAL wins 24% (48% 2 pt conv * 50% OT win)
2. At -11 DAL wins 50% of the time. At -15, DAL wins 0% of the time.
3. At -11 DAL wins 24% of the time, At -15, Dal never kicks the FG, they go on 4th from FG range and score the TD about 25% of the time. At that point they still need the 2 and OT so overall prob is 24% * 25%.
You'll notice that in scenarios 1 and 3, -11 is 4 times more likely to lead to a win than -15. In scenario 2, a win is a considerable possibility at -11 and impossible at -15.
So you really need to ask yourself how likely are each of these scenarios. All of them are fairly unlikely but hey you already knew Dallas was in a lot of trouble no matter what.
The big thing to remember is that in scenario 1 and 3, -11 is 4 times better than -15. In scenario 2, its infinitely better.
So basically assume that Dallas gets two more scores is X.
The real question is how likely is it that NY scores a field goal between now and the end of the game.
I'd say thats about 50%. So with the 2 tds
at -11: Dallas' win prob is (1 * 0.5) + (0.5 * 0.5) = 0.75x
at -15: Dallas win prob is (0.24 * 0.5) = 0.12x
So basically you end up with Dallas winning the game when they score twice more 75% of the time when they go for it and only 12% of the time when they don't.
Solving for x is considerably more complicated but its actually not all that relevant. You can just think of the decision still in terms of X.
I called you up before the play and said I'll give you $63 (75 -12) if they make this. You give me $12 if they don't.
Do you accept the gamble?
I know I would. Those were basically the odds that Phillips faced.
I suppose you could fiddle with the prob the Giants scored a field goal (note they actually did....which made the call look even better in hindsight...not that anyone noticed). You can fiddle with these probabilities a little bit more but it only changes the ultimate conclusion from good to really good.
I continue to dare anyone to come up with actual math on why this was a bad move.
Thank you for at least trying to figure this out. I can't believe how many people on this site are willfully ignorant.
There are a whole lot of variables involved. I could explain how to do a really good calculation but it will get very complicated very quickly.
Basically, when you do this you get x% probability you score 0..they score 0. y% you score 7 they score 0...etc...etc.
One way to simplify it is to quickly knock out all of the scenarios where it doesn't matter whether you go for it or not.
Obviously, if Dallas managed to score 5 more times they win no matter what. If Dallas scores only once more they lose no matter what.
The remaining scenarios are:
1. Dallas scores 2 TDs. Giants score none.
2. Dallas scores 2 TDs. NY scores FG.
3. Dallas scores 1 TD and FG. Giants score none.
Lets compare the relative strength of all scenarios at -15 and -11.
1. At -11, DAL wins 100% of the time. At -15, DAL wins 24% (48% 2 pt conv * 50% OT win)
2. At -11 DAL wins 50% of the time. At -15, DAL wins 0% of the time.
3. At -11 DAL wins 24% of the time, At -15, Dal never kicks the FG, they go on 4th from FG range and score the TD about 25% of the time. At that point they still need the 2 and OT so overall prob is 24% * 25%.
You'll notice that in scenarios 1 and 3, -11 is 4 times more likely to lead to a win than -15. In scenario 2, a win is a considerable possibility at -11 and impossible at -15.
So you really need to ask yourself how likely are each of these scenarios. All of them are fairly unlikely but hey you already knew Dallas was in a lot of trouble no matter what.
The big thing to remember is that in scenario 1 and 3, -11 is 4 times better than -15. In scenario 2, its infinitely better.
So basically assume that Dallas gets two more scores is X.
The real question is how likely is it that NY scores a field goal between now and the end of the game.
I'd say thats about 50%. So with the 2 tds
at -11: Dallas' win prob is (1 * 0.5) + (0.5 * 0.5) = 0.75x
at -15: Dallas win prob is (0.24 * 0.5) = 0.12x
So basically you end up with Dallas winning the game when they score twice more 75% of the time when they go for it and only 12% of the time when they don't.
Solving for x is considerably more complicated but its actually not all that relevant. You can just think of the decision still in terms of X.
I called you up before the play and said I'll give you $63 (75 -12) if they make this. You give me $12 if they don't.
Do you accept the gamble?
I know I would. Those were basically the odds that Phillips faced.
I suppose you could fiddle with the prob the Giants scored a field goal (note they actually did....which made the call look even better in hindsight...not that anyone noticed). You can fiddle with these probabilities a little bit more but it only changes the ultimate conclusion from good to really good.
I continue to dare anyone to come up with actual math on why this was a bad move.
During that whole Belichick thing, I met math people who couldn't believe he was right at first and then ran the numbers to try to refute me and said "wow that surprised me...why don't more coaches go" and I said "Would increasing your probability of winnning the game by 5% be worth listening to a bunch of morons call you a moron?" .
Last post you said you could "run circles around me in any math field". You actually got my hopes up. I've been wanting somebody reasonably smart to come on here and try to argue the other side.
Instead all I got was a bunch of curse words. Oh well....disappointing.
During that whole Belichick thing, I met math people who couldn't believe he was right at first and then ran the numbers to try to refute me and said "wow that surprised me...why don't more coaches go" and I said "Would increasing your probability of winnning the game by 5% be worth listening to a bunch of morons call you a moron?" .
Last post you said you could "run circles around me in any math field". You actually got my hopes up. I've been wanting somebody reasonably smart to come on here and try to argue the other side.
Instead all I got was a bunch of curse words. Oh well....disappointing.
I'm familiar with the volatility argument. At first, it makes a lot of sense. I think its a holdover from the financial industry. A lot of math people worked in finance at some point. Basically, you'd much rather a mutual fund that provided a 10% annual return than one that had a 50% chance at quadrupling and a 50% chance of going to zero. Makes sense in that context.
I don't think its as relevant in football as people think. The problem with worrying about volatility is that one way or another you are going to win the game or you're going to lose the game. Volatility would make sense if a coach could go to the other coach and say "Hey you take 0.6 wins. I'll take 0.4 wins". The other coach would say "OK deal...I was scared I'd lose too". You can't do that. No matter what you do, there is going to be risk. No matter what decision you make, its going to be a gamble. If you have to gamble, you might as well make the bet that gives you the best chance at winning.
Speaking from a pure mathmatical perspective, then every NBA would be better off taking a 3 pt shot every time down court.
A team that shoots 36% on 3's is the same as shooting 54% on 2's and no team in the league can shot 54% or even remotely close to 54% but many teams can shot 36% on 3's.
A 40% shooting team in 3's is the same as 60% shooting on 2's, wow what a huge avantage would that be.
So basically using your theory and the theory of all those that propose going for it on 4th down is best because mathmatically it would be the best stratergy, well taking a 3pt every trip down the court is mathmatically best, but it would not work because of " high voalitility".
Those mathmatical formula's "assume" that a team will produce it's average stat per game put it does not work that way in the real world.
If a NBA team could shot 40% every game then yea go for 3 each time and no-one could ever beat the team, but because you can not shot 40% every game, sometimes you'll shoot above that and sometimes well below, in the end you'll likely win about the same number of games.
A 2 pt shot is "low voalitility", in the long run a better stratergy.
"High voalitility" stratergy puts all your marbles in fewer plays, in other words, the success of a few plays dramtically increases your chances but the failure of a few plays dramatically decreases your chances, "low voalitility" stratergy" spreads your marbles into more baskets, thus giving the better team "more chances" to win.
A good example of this was the Super Bowl when the Saints tried a onside kick in the middle of the game, the Saints realalizing the Colts were the better team needed to use a high voalitility stratergy, they put all their marbles into fewer baskets, get and they chances go up, fail and your chances go down giving the Colts the ball in excellent field position.
This is why coaches don't just go for it on every 4th down play.
I'm familiar with the volatility argument. At first, it makes a lot of sense. I think its a holdover from the financial industry. A lot of math people worked in finance at some point. Basically, you'd much rather a mutual fund that provided a 10% annual return than one that had a 50% chance at quadrupling and a 50% chance of going to zero. Makes sense in that context.
I don't think its as relevant in football as people think. The problem with worrying about volatility is that one way or another you are going to win the game or you're going to lose the game. Volatility would make sense if a coach could go to the other coach and say "Hey you take 0.6 wins. I'll take 0.4 wins". The other coach would say "OK deal...I was scared I'd lose too". You can't do that. No matter what you do, there is going to be risk. No matter what decision you make, its going to be a gamble. If you have to gamble, you might as well make the bet that gives you the best chance at winning.
Speaking from a pure mathmatical perspective, then every NBA would be better off taking a 3 pt shot every time down court.
A team that shoots 36% on 3's is the same as shooting 54% on 2's and no team in the league can shot 54% or even remotely close to 54% but many teams can shot 36% on 3's.
A 40% shooting team in 3's is the same as 60% shooting on 2's, wow what a huge avantage would that be.
So basically using your theory and the theory of all those that propose going for it on 4th down is best because mathmatically it would be the best stratergy, well taking a 3pt every trip down the court is mathmatically best, but it would not work because of " high voalitility".
Those mathmatical formula's "assume" that a team will produce it's average stat per game put it does not work that way in the real world.
If a NBA team could shot 40% every game then yea go for 3 each time and no-one could ever beat the team, but because you can not shot 40% every game, sometimes you'll shoot above that and sometimes well below, in the end you'll likely win about the same number of games.
A 2 pt shot is "low voalitility", in the long run a better stratergy.
"High voalitility" stratergy puts all your marbles in fewer plays, in other words, the success of a few plays dramtically increases your chances but the failure of a few plays dramatically decreases your chances, "low voalitility" stratergy" spreads your marbles into more baskets, thus giving the better team "more chances" to win.
A good example of this was the Super Bowl when the Saints tried a onside kick in the middle of the game, the Saints realalizing the Colts were the better team needed to use a high voalitility stratergy, they put all their marbles into fewer baskets, get and they chances go up, fail and your chances go down giving the Colts the ball in excellent field position.
This is why coaches don't just go for it on every 4th down play.
Thank you for at least trying to figure this out. I can't believe how many people on this site are willfully ignorant.
There are a whole lot of variables involved. I could explain how to do a really good calculation but it will get very complicated very quickly.
Basically, when you do this you get x% probability you score 0..they score 0. y% you score 7 they score 0...etc...etc.
One way to simplify it is to quickly knock out all of the scenarios where it doesn't matter whether you go for it or not.
Obviously, if Dallas managed to score 5 more times they win no matter what. If Dallas scores only once more they lose no matter what.
The remaining scenarios are:
1. Dallas scores 2 TDs. Giants score none.
2. Dallas scores 2 TDs. NY scores FG.
3. Dallas scores 1 TD and FG. Giants score none.
Lets compare the relative strength of all scenarios at -15 and -11.
1. At -11, DAL wins 100% of the time. At -15, DAL wins 24% (48% 2 pt conv * 50% OT win)
2. At -11 DAL wins 50% of the time. At -15, DAL wins 0% of the time.
3. At -11 DAL wins 24% of the time, At -15, Dal never kicks the FG, they go on 4th from FG range and score the TD about 25% of the time. At that point they still need the 2 and OT so overall prob is 24% * 25%.
You'll notice that in scenarios 1 and 3, -11 is 4 times more likely to lead to a win than -15. In scenario 2, a win is a considerable possibility at -11 and impossible at -15.
So you really need to ask yourself how likely are each of these scenarios. All of them are fairly unlikely but hey you already knew Dallas was in a lot of trouble no matter what.
The big thing to remember is that in scenario 1 and 3, -11 is 4 times better than -15. In scenario 2, its infinitely better.
So basically assume that Dallas gets two more scores is X.
The real question is how likely is it that NY scores a field goal between now and the end of the game.
I'd say thats about 50%. So with the 2 tds
at -11: Dallas' win prob is (1 * 0.5) + (0.5 * 0.5) = 0.75x
at -15: Dallas win prob is (0.24 * 0.5) = 0.12x
So basically you end up with Dallas winning the game when they score twice more 75% of the time when they go for it and only 12% of the time when they don't.
Solving for x is considerably more complicated but its actually not all that relevant. You can just think of the decision still in terms of X.
I called you up before the play and said I'll give you $63 (75 -12) if they make this. You give me $12 if they don't.
Do you accept the gamble?
I know I would. Those were basically the odds that Phillips faced.
I suppose you could fiddle with the prob the Giants scored a field goal (note they actually did....which made the call look even better in hindsight...not that anyone noticed). You can fiddle with these probabilities a little bit more but it only changes the ultimate conclusion from good to really good.
I continue to dare anyone to come up with actual math on why this was a bad move.
Thank you for at least trying to figure this out. I can't believe how many people on this site are willfully ignorant.
There are a whole lot of variables involved. I could explain how to do a really good calculation but it will get very complicated very quickly.
Basically, when you do this you get x% probability you score 0..they score 0. y% you score 7 they score 0...etc...etc.
One way to simplify it is to quickly knock out all of the scenarios where it doesn't matter whether you go for it or not.
Obviously, if Dallas managed to score 5 more times they win no matter what. If Dallas scores only once more they lose no matter what.
The remaining scenarios are:
1. Dallas scores 2 TDs. Giants score none.
2. Dallas scores 2 TDs. NY scores FG.
3. Dallas scores 1 TD and FG. Giants score none.
Lets compare the relative strength of all scenarios at -15 and -11.
1. At -11, DAL wins 100% of the time. At -15, DAL wins 24% (48% 2 pt conv * 50% OT win)
2. At -11 DAL wins 50% of the time. At -15, DAL wins 0% of the time.
3. At -11 DAL wins 24% of the time, At -15, Dal never kicks the FG, they go on 4th from FG range and score the TD about 25% of the time. At that point they still need the 2 and OT so overall prob is 24% * 25%.
You'll notice that in scenarios 1 and 3, -11 is 4 times more likely to lead to a win than -15. In scenario 2, a win is a considerable possibility at -11 and impossible at -15.
So you really need to ask yourself how likely are each of these scenarios. All of them are fairly unlikely but hey you already knew Dallas was in a lot of trouble no matter what.
The big thing to remember is that in scenario 1 and 3, -11 is 4 times better than -15. In scenario 2, its infinitely better.
So basically assume that Dallas gets two more scores is X.
The real question is how likely is it that NY scores a field goal between now and the end of the game.
I'd say thats about 50%. So with the 2 tds
at -11: Dallas' win prob is (1 * 0.5) + (0.5 * 0.5) = 0.75x
at -15: Dallas win prob is (0.24 * 0.5) = 0.12x
So basically you end up with Dallas winning the game when they score twice more 75% of the time when they go for it and only 12% of the time when they don't.
Solving for x is considerably more complicated but its actually not all that relevant. You can just think of the decision still in terms of X.
I called you up before the play and said I'll give you $63 (75 -12) if they make this. You give me $12 if they don't.
Do you accept the gamble?
I know I would. Those were basically the odds that Phillips faced.
I suppose you could fiddle with the prob the Giants scored a field goal (note they actually did....which made the call look even better in hindsight...not that anyone noticed). You can fiddle with these probabilities a little bit more but it only changes the ultimate conclusion from good to really good.
I continue to dare anyone to come up with actual math on why this was a bad move.
it comes down to time and the number of possession you will have , down 3 scores , you have to kick the field goal , stupid not kicking it at that point in the game .
the only reason the giants ended up with only a 6 point win , is that they didnt play the game correctly ...........no team with 3:20 left in the game up by 18 throws the ball , there was no purpose to do that .
it comes down to time and the number of possession you will have , down 3 scores , you have to kick the field goal , stupid not kicking it at that point in the game .
the only reason the giants ended up with only a 6 point win , is that they didnt play the game correctly ...........no team with 3:20 left in the game up by 18 throws the ball , there was no purpose to do that .
Of course, 2 is better than 3. But the bottom line is that not all scores are equal. Take the FG there and you are really still depending on 5 scores.
In addition to the 2 touchdowns, you also need the 2 point conversion, your defense to provide a 0 socre to the Giants and a score in overtime. That is an absurd amount to ask for.
Gamble and get a touchdown and you are just two scores away from winning the game.
You make fun of my posts and my math but I see you have yet to take me up on my challenge.
What do you think are the odds on each of the 5 things you need to happen in order to win the game after you kick?
Go ahead and post your own numbers. Prove I'm wrong.
Of course, 2 is better than 3. But the bottom line is that not all scores are equal. Take the FG there and you are really still depending on 5 scores.
In addition to the 2 touchdowns, you also need the 2 point conversion, your defense to provide a 0 socre to the Giants and a score in overtime. That is an absurd amount to ask for.
Gamble and get a touchdown and you are just two scores away from winning the game.
You make fun of my posts and my math but I see you have yet to take me up on my challenge.
What do you think are the odds on each of the 5 things you need to happen in order to win the game after you kick?
Go ahead and post your own numbers. Prove I'm wrong.
Speaking from a pure mathmatical perspective, then every NBA would be better off taking a 3 pt shot every time down court.
A team that shoots 36% on 3's is the same as shooting 54% on 2's and no team in the league can shot 54% or even remotely close to 54% but many teams can shot 36% on 3's.
A 40% shooting team in 3's is the same as 60% shooting on 2's, wow what a huge avantage would that be.
So basically using your theory and the theory of all those that propose going for it on 4th down is best because mathmatically it would be the best stratergy, well taking a 3pt every trip down the court is mathmatically best, but it would not work because of " high voalitility".
Those mathmatical formula's "assume" that a team will produce it's average stat per game put it does not work that way in the real world.
If a NBA team could shot 40% every game then yea go for 3 each time and no-one could ever beat the team, but because you can not shot 40% every game, sometimes you'll shoot above that and sometimes well below, in the end you'll likely win about the same number of games.
A 2 pt shot is "low voalitility", in the long run a better stratergy.
"High voalitility" stratergy puts all your marbles in fewer plays, in other words, the success of a few plays dramtically increases your chances but the failure of a few plays dramatically decreases your chances, "low voalitility" stratergy" spreads your marbles into more baskets, thus giving the better team "more chances" to win.
A good example of this was the Super Bowl when the Saints tried a onside kick in the middle of the game, the Saints realalizing the Colts were the better team needed to use a high voalitility stratergy, they put all their marbles into fewer baskets, get and they chances go up, fail and your chances go down giving the Colts the ball in excellent field position.
This is why coaches don't just go for it on every 4th down play.
Thank you for starting to think about it from a purely math point of view. The volatility argument is actually pretty relevant. The reason why NBA teams don't shoot a 3 every shot is game theory. There isn't a guy open every shot. To a certain extent, you need to take what the defense gives you. The "3 only strategy" only works when you actually can convert 40% of the shots. The NFL analogy is the prevent defense. I know its hated but there is a logic behind the prevent. The offense should (and if there was no prevent) would throw a bomb on every play when they are behind.
You mention whether a team should prefer a high volatility or low volatility game. It brings up a very good point and helps me make my case. The greater your chance of winning the game, the lower volatility you want it. If the ref called the coaches and said, "we're bored with this....every play I'm going to award a TD to whoever performs the best" the Cowboys would obviously cheer and the Giants would obviously boo. There is only one win to go around. If the Giants want low volatility, the Cowboys want high volatility.
Bottom line, the lower your chance of winning the more risks you need to take. You really don't see this in the NFL. Coaches should be getting desperate a whole lot earlier. But they just don't want to get blown out so they do incredibly stupid things like kick FGs down 18. Instead of getting mad at them, most people seem to get mad at the guys that actually try to win.
Stop and think about it. You'll see I'm right. I know I making a big deal of this but its really a bigger issue. In my opinion, this is the biggest problem in football. Basically, teams give up too early. They disguise it by saying they are "just staying in the game" but in truth the coach is just narrowly lowering the losing margin.
When guys like Belichick and Phillips actually think about how to win and challenge the order, we really need to focus on what happened and why.
Volatility is a very good point. From now on, watch a game and say "If I was Team A would I want high volatility or low" Do the same for the other one. The answer needs to be the opposite for the other team.
Speaking from a pure mathmatical perspective, then every NBA would be better off taking a 3 pt shot every time down court.
A team that shoots 36% on 3's is the same as shooting 54% on 2's and no team in the league can shot 54% or even remotely close to 54% but many teams can shot 36% on 3's.
A 40% shooting team in 3's is the same as 60% shooting on 2's, wow what a huge avantage would that be.
So basically using your theory and the theory of all those that propose going for it on 4th down is best because mathmatically it would be the best stratergy, well taking a 3pt every trip down the court is mathmatically best, but it would not work because of " high voalitility".
Those mathmatical formula's "assume" that a team will produce it's average stat per game put it does not work that way in the real world.
If a NBA team could shot 40% every game then yea go for 3 each time and no-one could ever beat the team, but because you can not shot 40% every game, sometimes you'll shoot above that and sometimes well below, in the end you'll likely win about the same number of games.
A 2 pt shot is "low voalitility", in the long run a better stratergy.
"High voalitility" stratergy puts all your marbles in fewer plays, in other words, the success of a few plays dramtically increases your chances but the failure of a few plays dramatically decreases your chances, "low voalitility" stratergy" spreads your marbles into more baskets, thus giving the better team "more chances" to win.
A good example of this was the Super Bowl when the Saints tried a onside kick in the middle of the game, the Saints realalizing the Colts were the better team needed to use a high voalitility stratergy, they put all their marbles into fewer baskets, get and they chances go up, fail and your chances go down giving the Colts the ball in excellent field position.
This is why coaches don't just go for it on every 4th down play.
Thank you for starting to think about it from a purely math point of view. The volatility argument is actually pretty relevant. The reason why NBA teams don't shoot a 3 every shot is game theory. There isn't a guy open every shot. To a certain extent, you need to take what the defense gives you. The "3 only strategy" only works when you actually can convert 40% of the shots. The NFL analogy is the prevent defense. I know its hated but there is a logic behind the prevent. The offense should (and if there was no prevent) would throw a bomb on every play when they are behind.
You mention whether a team should prefer a high volatility or low volatility game. It brings up a very good point and helps me make my case. The greater your chance of winning the game, the lower volatility you want it. If the ref called the coaches and said, "we're bored with this....every play I'm going to award a TD to whoever performs the best" the Cowboys would obviously cheer and the Giants would obviously boo. There is only one win to go around. If the Giants want low volatility, the Cowboys want high volatility.
Bottom line, the lower your chance of winning the more risks you need to take. You really don't see this in the NFL. Coaches should be getting desperate a whole lot earlier. But they just don't want to get blown out so they do incredibly stupid things like kick FGs down 18. Instead of getting mad at them, most people seem to get mad at the guys that actually try to win.
Stop and think about it. You'll see I'm right. I know I making a big deal of this but its really a bigger issue. In my opinion, this is the biggest problem in football. Basically, teams give up too early. They disguise it by saying they are "just staying in the game" but in truth the coach is just narrowly lowering the losing margin.
When guys like Belichick and Phillips actually think about how to win and challenge the order, we really need to focus on what happened and why.
Volatility is a very good point. From now on, watch a game and say "If I was Team A would I want high volatility or low" Do the same for the other one. The answer needs to be the opposite for the other team.
Of course, 2 is better than 3. But the bottom line is that not all scores are equal. Take the FG there and you are really still depending on 5 scores.
In addition to the 2 touchdowns, you also need the 2 point conversion, your defense to provide a 0 socre to the Giants and a score in overtime. That is an absurd amount to ask for.
Gamble and get a touchdown and you are just two scores away from winning the game.
You make fun of my posts and my math but I see you have yet to take me up on my challenge.
What do you think are the odds on each of the 5 things you need to happen in order to win the game after you kick?
Go ahead and post your own numbers. Prove I'm wrong.
Of course, 2 is better than 3. But the bottom line is that not all scores are equal. Take the FG there and you are really still depending on 5 scores.
In addition to the 2 touchdowns, you also need the 2 point conversion, your defense to provide a 0 socre to the Giants and a score in overtime. That is an absurd amount to ask for.
Gamble and get a touchdown and you are just two scores away from winning the game.
You make fun of my posts and my math but I see you have yet to take me up on my challenge.
What do you think are the odds on each of the 5 things you need to happen in order to win the game after you kick?
Go ahead and post your own numbers. Prove I'm wrong.
Last post you said you could "run circles around me in any math field". You actually got my hopes up. I've been wanting somebody reasonably smart to come on here and try to argue the other side.
Instead all I got was a bunch of curse words. Oh well....disappointing.
Last post you said you could "run circles around me in any math field". You actually got my hopes up. I've been wanting somebody reasonably smart to come on here and try to argue the other side.
Instead all I got was a bunch of curse words. Oh well....disappointing.
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