Uh oh, here we go: CBS claims Pats win coin flip at "impossible clip"

PatsWickedPissah · Nov 6, 2015

Some here might like to read Nassim Nicolas Taleb's "Fooled By Randomness" concerning mis-understanding leading to the mis-use of stats by ordinary folks AND professionals.

RelocatedPatFan · Nov 6, 2015

Someone should point out...if 0.73% is impossible, then he should take a flight on any plane. How impossible would it be to be a pilot for more than a couple of years.

Ken Canin · Nov 6, 2015

Any of the anti-Pats message boards taking this seriously? There was in fact a fumble analysis last year at about the same level of rigor that people seemed to take seriously.

Ken Canin · Nov 6, 2015

PatsWickedPissah said:
Some here might like to read Nassim Nicolas Taleb's "Fooled By Randomness" concerning mis-understanding leading to the mis-use of stats by ordinary folks AND professionals.

Haven't read that one, but good books on statistical fallacies include Jordan Ellenberg's How Not To Be Wrong and Sam Savage's The Flaw of Averages. The Ellenberg book is particularly crisply written and interesting.

That said, I doubt most of these Pats analyses are due to misunderstanding of statistics per se; more likely due to tendentiousness.

Having said that, I'm not sure it's actually a good idea to understand statistics and probability, at least at the research level, unless one is actually doing work for which that level of understanding is necessary. It's depressing when one learns enough about the subject to understand that invalid statistical inference techniques permeate contemporary demotic (and even scientific in some fields) discourse.

aluminum seats · Nov 6, 2015

Ken Canin said:
...invalid statistical inference techniques permeate contemporary demotic (and even scientific in some fields) discourse.

Oh man, they were going on and on about that over on the Jets' message board last week.

FourierSeries · Nov 6, 2015

PatsWickedPissah said:
Some here might like to read Nassim Nicolas Taleb's "Fooled By Randomness" concerning mis-understanding leading to the mis-use of stats by ordinary folks AND professionals.

Great book.

I work in finance (and have a math degree) and I see the misunderstanding and misuse of math/stats by professionals on a daily basis. It played a huge role in the 2008 financial crisis. More than most people know.

FourierSeries · Nov 6, 2015

As long as we're on the topic, here's an interesting probability question that has an answer which some may find counter-intuitive. The theory behind it is measure theoretic in nature, but for those with no background in measure theory, you can probably arrive at the answer using a heuristic approach.

Suppose you are playing darts. Someone selects, at random, a specific point on the dartboard and says they will give you $1000 if you hit that specific point with a dart. What is the probability that you win the $1000?

Sicilian · Nov 6, 2015

FourierSeries said:
As long as we're on the topic, here's an interesting probability question that has an answer which some may find counter-intuitive. The theory behind it is measure theoretic in nature, but for those with no background in measure theory, you can probably arrive at the answer using a heuristic approach.

Suppose you are playing darts. Someone selects, at random, a specific point on the dartboard and says they will give you $1000 if you hit that specific point with a dart. What is the probability that you win the $1000?

I'm curious about the answer. Is there somewhere online that breaks it down for an amateur like myself?

bbobbo · Nov 6, 2015

i would say 0%.

the probability of hitting a certain area on a dartboard should be (area of target) / (area of dartboard), assuming you discount all throws which miss the target completely. since a point has no dimensions, it has no area, so the probability of hitting the point would be 0 / (area of dartboard) = 0.

FourierSeries · Nov 6, 2015

Sicilian said:
I'm curious about the answer. Is there somewhere online that breaks it down for an amateur like myself?

The probability of hitting the specific point, or any specific point for that matter, is 0. You can think of the probability as an area. In this case, the area of any specific point is 0 (it has no height or width.)

Another similar example is selecting a real number from the set of all real numbers. Since there are infinitely many real numbers, you have a probability of 0 of selecting any specific real number.

In measure theory, this is described as an event that "almost never" happens. In the dart example, while you will definitely hit a point on the board, you'll "almost never" hit a point which has been specified before hand.

FourierSeries · Nov 6, 2015

bbobbo said:
i would say 0%.

the probability of hitting a certain area on a dartboard should be (area of target) / (area of dartboard), assuming you discount all throws which miss the target completely. since a point has no dimensions, it has no area, so the probability of hitting the point would be 0 / (area of dartboard) = 0.

Yep.

Sicilian · Nov 6, 2015

FourierSeries said:
The probability of hitting the specific point, or any specific point for that matter, is 0. You can think of the probability as an area. In this case, the area of any specific point is 0 (it has no height or width.)

Another similar example is selecting a real number from the set of all real numbers. Since there are infinitely many real numbers, you have a probability of 0 of selecting any specific real number.

In measure theory, this is described as an event that "almost never" happens. In the dart example, while you will definitely hit a point on the board, you'll "almost never" hit a point which has been specified before hand.

Love it. Thank you.

onegameatatime · Nov 6, 2015

The probability that the Patriots would win 19 of the last 25 flips = 1, or 100% ... because it happened.

The name "Brady" is not uncommon compared to many others -- 0.025% of Americans. So what were the chances the Patriots would get a QB named Brady? 0.025% = 0.00025. And yet it happened! Isn't that amazing despite those long odds?

Oswlek · Nov 6, 2015

Rob0729 said:
I guess I could be mixing up my statistics. Been too long since grad school I guess. I will just admit I am wrong and be done with it and not continue hijacking the thread.

I think I know what you were going for, Rob. You were probably thinking of something like a football play, which can have a multitude of possible outcomes and have an infinite number of variables, all of which can have at least a trivial impact. On top of that, the results of each play influence the odds for subsequent plays. The same isn't true of coin flips.

To illustrate, think of a rain variable. It can have a major impact on a game by diminishing visibility, worsening footing, making the ball slicker, altering coach's confidence in certain plays, etc. But no matter how hard it rains it won't make it any more likely that heads will turn up more frequently than tails*. Or, if not, that you can know ahead of time which side will turn up.

Hopefully this makes sense.

* I mean this over an extended period of time. Clearly a drop can influence the spin leading to heads coming up, but the drop would have resulted in tails had the spin been reversed. Rain by itself doesn't make one side more likely to come up than the other.

WinstonSmith · Nov 6, 2015

PatsWickedPissah said:
Some here might like to read Nassim Nicolas Taleb's "Fooled By Randomness" concerning mis-understanding leading to the mis-use of stats by ordinary folks AND professionals.

My brother, a fan, bought the book for me for my birthday. It’s definitely an interesting read but the guy comes across as an insufferable arrogant prick.

Semi OT: A reliable source close to the Patriots claims that McNally gets head and the occasional tail before home games in the unisex bathroom.

sb1 · Nov 6, 2015

Obviously most of the time Kraft paid off some skilled refs in flipping the coin to whichever side the Patriots pick.

supafly · Nov 6, 2015

Satchboogie3 said:
Yes, on a roulette table, the odds of the NEXT spin are independent of the prior (so 46ish% odds with the zero).

If you asked the question "what are the odds of 7 straight reds?", the answer is ~0.0044. So if you thought like the author of the article, you might think "those odds are 'impossible', is something going on?!", neglecting the fact that you expect to see a run like this once every 227 spins, which, if they spin the wheel once a minute, would happen more than 6 times a day on average.

The analysis in the article (0.0073 probability of winning at least 19 of 25 tosses) is correct. The issue is that no analysis on the expected distribution (or confidence interval) was given, which is what tells us what to expect given a certain sample size. As I showed above, 25 coin tosses is WAY too small a sample size to attribute 19 out of 25 to anything but chance. It's within the normal distribution. You expect a very wide range of results with small sample sizes. And of course if you look at the Patriots last 50 or 60 games, the win % comes down closer to 50% and draws further into the middle of the bell curve (normal distribution).

But since it's the Patriots, it can't just be blind luck, it has to be cheating...

Thank you for taking the time to break that down. Much appreciated.

The Brandon Five · Nov 7, 2015

Since the visiting team calls it, the Patriots are obviously playing Jedi mind tricks to get them to call the side they know will not come up.

Ivan · Nov 7, 2015

As long as they win 11 out of every 12 flips the universe is in order.

XLIX · Nov 7, 2015

FourierSeries said:
The probability of hitting the specific point, or any specific point for that matter, is 0. You can think of the probability as an area. In this case, the area of any specific point is 0 (it has no height or width.)

If you consider the tip of the dart a point, then your odds are 0. You can't hit a point with another point.

However, when I throw a dart into a dartboard, it leaves a roughly 1 mm in diameter hole in the board. If you select a point on the board, then it is possible I hit that point because it is possible that the point lies within the 1 mm range I've created.

For example, suppose a computer selected a random number between 1 and 2. Because there are an infinite amount of numbers between 1 and 2, the odds of me guessing it correctly are zero, no matter how many guesses you gave me. But since the range between 1 and 2 is finite, then if I gave a range such as "the number is between 1.1 and 1.2" there would be a 10% chance I was correct.

Uh oh, here we go: CBS claims Pats win coin flip at "impossible clip"

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