Crazy thought of day: Cowboys should have missed extra point on purpose with 2:32 left so they'd be up 3, not 4

wejo wrote: The guys of that site write for the Washington Post and are pretty smart so hopefully Rojo gets a response.

Being pretty smart doesn't mean they know what they are doing. Being a writer for the Washington Post means that there is a 74% chance that they are wrong. ;-)

"In no other branch of mathematics is it so easy for experts to blunder as in probability theory" - Martin Gardner

go for 2 wrote:

I think kicking the extra point was smart given the Lions had Prater kicking indoors with a career long of 64 and a season best of 52 this year

This. Looking at the averages and statistics is one thing, but don't forget about who's on the field.

wejo wrote:

Stats guys have shown coaches don't go for it enough. Look at it yesterday 4th and 1 in the 4th on about the 40 and the Lions punted. I'm almost certain a computer would say to go for it.

The issue I have with applying historical stats is that they have no bearing on the current situation. For example, looking at the past doesn't take into consideration how effective the current team is on offense, the opposing team on defense, etc.

Surprise! wrote:

Huge difference between being risk adverse and not going for a 4th down play and intentionally missing an extra point to put the other team within a field goal instead of a touchdown.

AVERSE.

OK brosjo. It is January 5th and you two scamps have already used up all the allotment for thinking that your itsy bitsy brains can handle in a year. You are now officially allowed to be unencumbered by the thought process for the next 360 days.

fixer wrote:

Surprise! wrote:

Huge difference between being risk adverse and not going for a 4th down play and intentionally missing an extra point to put the other team within a field goal instead of a touchdown.

AVERSE.

Thank you grammar fairy!

Perhaps statistically, but in real life -- no. Imagine the head coach who has the chance to go up 4, purposely misses the extra point, only to have the opposing team tie them on a late field goal and win in overtime. Can you imagine how he'll ever explain that? Professional suicide. You look too bad if it goes sour. Even if it's statistically worse to go up 4, nobody's gonna blame you if the other team scores a late touchdown to win. They'll just credit the other team.

I am going to have to use some old reasoning skills and explain this to everyone. First let address the calculator results. The calculator is wrong and does not reflect reality. There something called error variance in stats. The stats suggesting 3 points are better than 4 points reflect a statistical anomaly. With further acquisition of more data that anomaly will likely be erased. Lets look at the data provided by the calculator. With 2:32 left to play with a 3 point plus differential you have an 82% chance to win but with 4 pt plus you have only a 75% chance to win. Lets examine more numbers here: now with 5 pt plus 80%, with 6 pt plus 76%, with 7 pt plus 83%.These percents jump around quite a bit without a clear direct pattern. The error variance is VERY HIGH and these are not accurate measures that reflect reality. Does anyone really think that with 2:32 left in the game your chance to win when up by 3 is 82% but if you are up by 7 you are only 83%!Huge error variance results in misleading data. These differences are not significant but with acquisition of more data it may become more accurate.Stat Sign, You were on the right path. End of thread.

statistical significance wrote:

rojo wrote:

the Cowboys had a 74% chance of winning the game up 4 with 2:32 left. I f they'd been up just 3, their win percentage would have been 82%.

Without knowing more about the data the model is pulling from, you can't know if 74% is significantly different from 82%. Did the calculator provide you with standard deviations, or just probabilities?

Les wrote:

Perhaps statistically, but in real life -- no. Imagine the head coach who has the chance to go up 4, purposely misses the extra point, only to have the opposing team tie them on a late field goal and win in overtime. Can you imagine how he'll ever explain that? Professional suicide. You look too bad if it goes sour. Even if it's statistically worse to go up 4, nobody's gonna blame you if the other team scores a late touchdown to win. They'll just credit the other team.

Yes, this is another good point. The decision would not pass the real life test. If Jason Garrett made the decision to blow the extra point and then they ultimately lost by the other team tying the game with a field goal and subsequently winning, he'd be fired and would never get another head coaching job again. If they just lost because of the normal reasons, he would still have a good job in the NFL.

This is a good example of the difference between empirical and theoretical probability.

Past history may tell us that being down 4 has lead to more victories than being down 3, but math tells us it is better to be down 3.

Out of the universe of possible combinations of play calls, only a portion will be successful. The number of successful combinations when you're down 4 is x. The number of successful combinations when you're down 3 is the entire set that makes up x, plus others.

You have more options down 3, so your probability of winning is higher. Regardless of how you treat your fourth downs (or how past coaches have treated their fourth downs), the probability is what it is.

Rojo, even though your stats are true, if the opposing team knows what you're up to, they can easily foil it. Your stats basically say when down 3 points, teams win 19% of the time vs. 26% when they are down 4 points. This means you're saying the offensive strategy is wrong, and they should be going for the touchdown when down 3 points rather than kicking the field goal as they normally opt to.

malmo wrote:

. Being a writer for the Washington Post means that there is a 74% chance that they are wrong. ;-)

And that is 50% less than if they wrote for a conservative publication. ;-)

(also:

"Aw, you can come up with statistics to prove anything, Kent. Forfty percent of all people know that."

Homer Jay Simpson )

Dragon Runner wrote:

Yes, this is another good point. The decision would not pass the real life test. If Jason Garrett made the decision to blow the extra point and then they ultimately lost by the other team tying the game with a field goal and subsequently winning, he'd be fired and would never get another head coaching job again. If they just lost because of the normal reasons, he would still have a good job in the NFL.

It's worse than that. Think of the "winning" scenarios after you intentionally miss the extra point.

1) The other team drives down the field and then misses the field goal.

Fans conclusion: You made the bonehead decision to intentionally miss the extra point, and you only won because the kicker luckily missed the field goal.

2) The other team drives down the field, makes the field goal, and then your team wins in overtime.

Fans conclusion: Your team saved you by winning in overtime when you could have won in regulation if you had just kicked the extra point.

There is NO scenario where the coach comes out looking good after intentionally missing the extra point.

That quote from John Maynard Keynes seems spot on for this situation.

Correct.

Fundamentally it comes down to this. Rojo is relying on the opinion of someone who has not shown his data, nor the algorithm behind the calculations, that gives that says a 3 point lead is marginally more probable to hold than a 4 point lead.

Lets say I have two garbage bags each full of 1000 ping pong balls. From one bag I pick out 100 balls. I count 74 white ones and 26 black ones. From the other I pick out 100 balls. I count 82 white ones and 18 black ones. Through observation I have determined that the first bag has a 74% chance of picking white balls and an 82% chance of picking white balls out of the second bag. Therefore it must be more probable that I can pick a white ball by selecting picks out of the 2nd bag.

Am I correct? it's completely unknowable. Are there 740 white balls in the first bag? Don't know. Are there 840 in the second bag. Don't know as well....the only thing that is known is the ratios of white to black balls after drawing 100 of them out of each bag on one trial off 100.

If I pick ten balls from the 2nd bag and the mix is 5 black and 5 white does that mean my calculations are all wrong? Again, it's unknowable.

Now lets say I count out 740 white/260 black balls and put them in a bag. I also count out 820 white/180 black balls and put them in another bag.

From the first bag I draw 100 balls. From the second bag I draw 100 balls. How many white balls have I drawn in each bag? It’s unknowable. If I put all of the balls back in the bags and draw them again the count is also unknowable. The same with each subsequent drawing. The only thing that's certain is that as I draw more balls the aggregate bag counts will continue to approach the actual ratios of white to black balls in the bags.

Rojos logic is akin to saying that someone uncovered a statistic by looking at past NFL games that when a team scores 34 points they win 82% of the time. The same study found out that if they score 35 points they win only 74% of the time. So by his logic, 34 points is better than 35, aand when a team scores a touchdown and has 34 points it’s better to miss on the extra points since it’s empirically proven that 34 points has a higher winning percentage than 35. FAIL.

just putting this here wrote:

What you've done isn't correct.

Even keeping your assumption that overtime means a 50% probability of winning, the expression for the probability of winning when down 3 would be T3 + F/2. And when down 4, it's T4.

1-T4 is probability of LOSING.

The Cowboys were the ones making the supposed decision (go up 3 or 4) so logically I was talking about their chances of winning. You are talking about the Lions' chances of winning.

1-(F+T3)/2 is not meaningful. For one thing, you've assumed that a touchdown could lead to overtime

That's true, but it was late at night, whereas your above error was made during the day.

But even beyond that, you've made an assumption that this is the last possession of the game. You can't assume that.

I explicitly stated that assumption on the implied grounds that it's close enough to zero to be negligible with 2 minutes left, which it is. Unless they scored a TD, already an unlikely event since they don't have to, the Lions would surely run down the clock before their FG attempt.

So, the revised probability of Cowboy victory at 3 points ahead is (just using T for the sake of clarity)

1 - (F + T) {don't tell me the Lions might score twice!}

+ F/2 {home field advantage won't be enough to matter}

= 1 - T - F/2

The magic website says that equals 0.82. If so,

T + F/2 = 1 - .82 = .18

F + 2T = .36

Is this realistic in light of the points-per-drive averages I linked before? Twelve teams had a scoring % better than that even during regulation, with punting an option:

The expected long term result of the offense's drive can be expressed as

3F + 7T

If rojo's source is correct, this equals

3(.36 - 2T) + 7T = 1.08 + T

Since surely F >= T, we have

.36 = F + 2T >= T + 2T = 3T

.12 >= T

for a maximum expected score of 1.20, among the worst points-per-drive for any team in regulation during 2014. Basically your correction helped my argument. Good looking out.

About that homefield advantage, even if the Cowboys had a .60 chance of winning OT, you'd have

T + .40F = .18

2.5T + F = .45, an expectation of

3(.45 - 2.5T) + 7T = 1.35 - .5T, and since T can't be less than zero, thus a drive expectation of at best 1.35 - still very low.

More simply, since few people will read all that, suppose fate set the chance of a Lion TD at 0, which should maximize the Cowboys' chances. To have an 82% chance of winning, they'd need the Lions' chance of a FG to be only 0.36 - barely one in three - or a significant overtime advantage. I can't find stats on this, but I doubt many NFL defenses are 2 for 3 in that situation or that many teams are much better than .50 in OT.

If there are any more errors, I don't care, it's still better to be up by 4.

I would put rojo on my coaching staff. I would ask his opinion and then do the opposite. There is a 92% chance that anything rojo says is incorrect. Dude is over 40 years old and has the spelling, grammar and math skills of a particularly dimwitted kindergartner.

opposition wrote:

I would put rojo on my coaching staff. I would ask his opinion and then do the opposite. There is a 92% chance that anything rojo says is incorrect. Dude is over 40 years old and has the spelling, grammar and math skills of a particularly dimwitted kindergartner.

Um, my calculator shows that rojo has an 8.2% chance of being right.

You can argue that there is not enough historical outcome information for it to provide a useful prediction of future outcomes. I hope your not arguing that historical outcome information is always useless.

If there were a million cases in the past when there were teams on the 20-yard-line with 2:32 left and behind by either 3 or 4 points, the outcome of those games would provide useful information for estimating outcome probabilities for the next time that situation arose.

Calculus wrote:

opposition wrote:

I would put rojo on my coaching staff. I would ask his opinion and then do the opposite. There is a 92% chance that anything rojo says is incorrect. Dude is over 40 years old and has the spelling, grammar and math skills of a particularly dimwitted kindergartner.

Um, my calculator shows that rojo has an 8.2% chance of being right.

Rojo has a 4.7% chance of being able to watch TV and drink Dr. Pepper at the same time.