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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
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@TheChart, TRUE?!?!?!!!?!
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sofuckingaggravating.gifAZDuck said:@TheChart, TRUE?!?!?!!!?!
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. -
I already knew that the real "chart" says not going for it on 4th and one in opponent territory is FS. That still doesn't bother me as much as it showed Oregon that we are their little bitch.
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How about the emotional boost your team gets, when your coach says "We're better than them, and if we don't get it, our defense will stop them" response?
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. -
You guys, it's just sooo hard you know? To get a win against anybody it's just so hard in this era of college football.
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*maff
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This. The perception of not going for it, meant more than what any chart said. I think subconsciously it affected the team.RoadDawg55 said:I already knew that the real "chart" says not going for it on 4th and one in opponent territory is FS. That still doesn't bother me as much as it showed Oregon that we are their little bitch.
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You guys don't understand the emotion of the game.
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"I don't disagree with you, and I'm not saying you're wrong, but I'm going to write 53,000 equivocal words disagreeing with you."
*Paraphrasing -
There is no chart for that situation. It was just not a smart move by peterman, and I said when that happened during the game that if we don't think we can get a yard against Oregon's defense the game is over.
Really bad decision.
