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Basic Football Math: 4th and 1
FremontTroll
Member Posts: 4,744
It looks like I missed out on a riveting argument over whether punting on 4th and 1 from your opponents' 39 yard line is EVER a good decision in the game of football.
Rumor has it that there are two sides to this argument. I am hear to dispel those rumors.
Announcers like to talk about field position without any understanding of how much any given portion of field is worth. But every yard does have a value- a value that is not exactly linear. Here is the thing- we don't even have to do the difficult math. Its already been done: http://outsidethehashes.com/?p=199; http://outsidethehashes.com/wp-content/uploads/2011/08/NCAA-Exp-Pts-1st-and-102.png
Now this data is based on 2010 and encompasses all levels of offenses or defenses. So it should approximate what an average offense can do against an average defense.
Luckily for us the two teams playing at midnight Eastern time on Saturday night were almost perfectly matched with the Oregon offense/UW defense being the stronger of the two matchups and UW having a small advantage on both sides of the ball with the caveat being that with Adams and Carrington back UO's offense is likely significantly better than its results to date.
Oregon's offense is 24th in the nation in opponent-adjusted yards per play. UW's defense is 15th.
Oregon's defense is 81st in the nation in opponent-adjusted yards per play. UW's offense is 64th.
Not surprisingly the over/under was 58 points which is almost exactly average for an NCAA football game.
Now onto the 3rd grade math. If we wanted to be fancy we could construct a formula to find the break-even point that would be something like ((Probability of converting) * (expected points of 1st and 10 field position)- ( 1-(probability of converting) * (expected points of opponent's 1st and 10 field position) = Expected points of opponent's 1st and 10 after punt.
(now is the time to consult the chart linked above. I will give Tequilla and Petersen the benefit of the doubt and assume that nothing could go wrong with the punt like a botched snap or block and Cobra will punt inside the 10 100% of the time with no touchbacks.)
Expected value of 1st and 10 inside your opponent's 40 yard line: 3 points.
Expected value of 1st and 10 for your opponent on their own 40: 1.5 points.
Expected value of 1st and 10 for your opponent on their own 10: 0 points.
x*3-(1-x)*1.5=0
x*3=(1-x)*1.5
x*2=1-x
x*2+x=1
x*3=1
x=.33
Therefore if you can make the 1st down more than 1/3 tries then going for it on 4th has positive expected value.
The average NCAA team converts 4th and 1 over 70% of the time: http://blog.minitab.com/blog/the-statistics-game/calculating-the-probability-of-converting-on-4th-down
IF UW could convert that 4th and 1 70% of the time then the value of going for it would be:
.7*3- (1-.7)*1.5
=1.65 points.
Meaning UW gave up 1.65 points of expected value by punting.
Now it is possible that UW's chances of converting were somewhat below average even against a weak Oregon defense. But there IS NO POSSIBLE WAY to massage the numbers to make punting become a good decision. There is no "other side to the argument."
UW gave up value by punting. It wasn't close. And the fact that they were already down 6-0 after one Oregon possession makes a bad decision even worse.
Tequilla Long; Didn't Read summary: Chris Petersen left his balls in Boise. He is not the savior.
Rumor has it that there are two sides to this argument. I am hear to dispel those rumors.
Announcers like to talk about field position without any understanding of how much any given portion of field is worth. But every yard does have a value- a value that is not exactly linear. Here is the thing- we don't even have to do the difficult math. Its already been done: http://outsidethehashes.com/?p=199; http://outsidethehashes.com/wp-content/uploads/2011/08/NCAA-Exp-Pts-1st-and-102.png
Now this data is based on 2010 and encompasses all levels of offenses or defenses. So it should approximate what an average offense can do against an average defense.
Luckily for us the two teams playing at midnight Eastern time on Saturday night were almost perfectly matched with the Oregon offense/UW defense being the stronger of the two matchups and UW having a small advantage on both sides of the ball with the caveat being that with Adams and Carrington back UO's offense is likely significantly better than its results to date.
Oregon's offense is 24th in the nation in opponent-adjusted yards per play. UW's defense is 15th.
Oregon's defense is 81st in the nation in opponent-adjusted yards per play. UW's offense is 64th.
Not surprisingly the over/under was 58 points which is almost exactly average for an NCAA football game.
Now onto the 3rd grade math. If we wanted to be fancy we could construct a formula to find the break-even point that would be something like ((Probability of converting) * (expected points of 1st and 10 field position)- ( 1-(probability of converting) * (expected points of opponent's 1st and 10 field position) = Expected points of opponent's 1st and 10 after punt.
(now is the time to consult the chart linked above. I will give Tequilla and Petersen the benefit of the doubt and assume that nothing could go wrong with the punt like a botched snap or block and Cobra will punt inside the 10 100% of the time with no touchbacks.)
Expected value of 1st and 10 inside your opponent's 40 yard line: 3 points.
Expected value of 1st and 10 for your opponent on their own 40: 1.5 points.
Expected value of 1st and 10 for your opponent on their own 10: 0 points.
x*3-(1-x)*1.5=0
x*3=(1-x)*1.5
x*2=1-x
x*2+x=1
x*3=1
x=.33
Therefore if you can make the 1st down more than 1/3 tries then going for it on 4th has positive expected value.
The average NCAA team converts 4th and 1 over 70% of the time: http://blog.minitab.com/blog/the-statistics-game/calculating-the-probability-of-converting-on-4th-down
IF UW could convert that 4th and 1 70% of the time then the value of going for it would be:
.7*3- (1-.7)*1.5
=1.65 points.
Meaning UW gave up 1.65 points of expected value by punting.
Now it is possible that UW's chances of converting were somewhat below average even against a weak Oregon defense. But there IS NO POSSIBLE WAY to massage the numbers to make punting become a good decision. There is no "other side to the argument."
UW gave up value by punting. It wasn't close. And the fact that they were already down 6-0 after one Oregon possession makes a bad decision even worse.
Tequilla Long; Didn't Read summary: Chris Petersen left his balls in Boise. He is not the savior.
Comments
Why can't UW just bring in an intern to handle this shit? Doesn't UW have a statistics program? Hold a one-day seminar where the intern teaches the coaches basic fucking probabilities and then provides charts for their future consultation.
I have never understood how coaches can get such basic shit wrong routinely. Stubbornness and sticking to ways things were always done is deeply ingrained in the profession. I thought Petersen was different but he is not.
Say what you want about Chip, but he would have gone for it on his OWN 39 in that situation. I miss having a REAL coach.
*Paraphrasing
Really bad decision.
The math changes depending on the score and game dynamics but in the 1st quarter at 0-6 its really very fucking simple math.
I think it should...which makes the decision all the more easier. I agree that anytime you penetrate (rofl) the opponents 40 you should almost never punt. Especially if you got a good defense, like UW has.
It was kind of funny because UW was injured and getting mercilessly stomped but they had a statistician looking at the game and scribbling notes furiously while Bill Walton waxed about big data blah blah blah. So from that I assume you do have someone to do this stuff, but he's probably ignored by Pete and Romar probably has no idea what he's talking about.
The reason it is perceived as cowardly is because it is so obviously the wrong decision that any football player, coach, or fan knows intuitively that it was a bitch move without even thinking about the math. Everyone knows that you are very likely to convert a 3rd or 4th and 1 to go because they've personally witnessed hundreds or thousands of similar situations. Everyone knows that the 30 or so yards of field position aren't so valuable as to just give up possession.
If football were played in a universe where converting a 4th and 1 was equivalent to the rolling a 6 on one roll of a die then there would be no emotional detriment to punting.
To me, the situation is like game theory in poker ... if I'm playing a hand and I'm a 55/45 favorite in the hand, then if I'm playing thousand of hours/hands and continually get put in that spot, then I'm an idiot for not leveraging that advantage. If I'm looking at a single instance, then perhaps I can find a better spot.
And really, that's the point that I was trying to make. Given the game/score situation, I was ok with the idea of punting knowing that the odds of Oregon scoring were far reduced with the extra 30 yards to go. I liked the chances that we could force a 3 and out (which we did before Wooching fucked it up on the punt) ... and who knows whether or not we could have forced a turnover there.
This team has shown throughout the year that they generally play better in the 2nd half than the 1st ... so given that situation and what I've seen all year, the decision to punt to me worked in parallels with the idea of shortening the game.
Now, if you give me an offense like TCU, Stanford, Baylor, etc., then I'm going to say that going for it is just fine.