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

Froob · Nov 5, 2015

Bruins29 said:
Yep, they seem to win it every game.

Coingate?

"And back in 2015 the Patriots were accused of weighted coins which coined the term coingate."

Bruins29 · Nov 5, 2015

So there is a 50% chance of 19 out of 25 flips coming up heads. Ok, makes sense.

Where did he get that .00723 whatever number then?

Pujo · Nov 5, 2015

strngplyr said:
It's also ********.

It's still a 50% chance every game. I don't care what the probability of doing it over an extended period of time is, it doesn't work that way.

Every game is 50%.

.0073 is simply there for effect and isn't meaningful to the actual results in any way, shape, or form.

No, while you're right that any game is 50/50, the chances are that over a large number of tosses, you should get close to an even number of heads and tails. With 25 flips there are 2^25=33,554,432 possible outcomes (e.g, HHHHHHHHHHHHHHHHHHHT, HHHHHHHHHHHHHHHHHHTT, etc). The chances of getting exactly 19 heads is 25 choose 19 = 177,100, the chances of getting 20 heads is 25 choose 20 = 53,130, etc. We add up all the possibilities from 19 to 25, which equals 245,506, then divide that the total number of possibilities (the 33 mil. number, which gives us 0.0073...). This isn't despite each flip being independent, it's precisely because of it (otherwise you'd have to calculate the odds using conditional probabilities). So yeah, the Pats are pretty lucky, but 25 coin flips isn't that large of a sample size. If they got 76/100 heads (same % of heads, but over more flips), that might be fishy.

Pujo · Nov 5, 2015

Bruins29 said:
So there is a 50% chance of 19 out of 25 flips coming up heads. Ok, makes sense.

Where did he get that .00723 whatever number then?

I explained it a bit in the above post, but this is the exact formula:

Rob0729 · Nov 5, 2015

People don't understand probability. As other people point out, the variables change on all these flips which means the 50-50 probability is way out the window.

Whitt25 · Nov 5, 2015

I expected something about our cleats or the grass in our stadium, but okay. Whatever.

I forget that coin tosses determine who wins games in the end, not the actual plays themselves. Forget anyone making clutch catches or stops or forcing turnovers. Nope, just calling heads or tails.

Pujo · Nov 5, 2015

Rob0729 said:
People don't understand probability. As other people point out, the variables change on all these flips which means the 50-50 probability is way out the window.

I'm not sure what you're saying here, but a fair coin should have close to 50-50 odds. If you flipped it 1,000 times you're very likely to get close to (but not exactly) 500 heads (it's pretty simple to calculate the standard deviation, but I'll skip it here). With 25 flips, though, it's a lot less certain - the law of large numbers really only applies to large numbers.

Bruins29 · Nov 5, 2015

Froob said:
"And back in 2015 the Patriots were accused of weighted coins which coined the term coingate."

I dont think I remember that....cause the Pats are tied to so much BShttp://data:image/jpeg;base64,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

PlainOldEd · Nov 5, 2015

Bruins29 said:
the probability of winning it at least 19 times in 25 tries is 0.0073. That's less than three-quarters of one percent.

That is 1 in 7,300 if my math is correct, which is ****ed up.

I am no mathematician, but this doesn't seem right to me. First off, wouldn't it be 1 in 730? but even that seems wrong. If you flipped a coin multiple times you would expect that over time you would win about 1/2 but if you calculate the odds of flipping a coin 25 times and winning 12 or 13 I believe it comes out to around 15%. Again, I'm not a math guy but I suspect this is a case of fuzzy math....
You know the old saying that goes something like this... ?

There are Lies, Damn Lies and Statistics.

Rob0729 · Nov 5, 2015

Pujo said:
I'm not sure what you're saying here, but a fair coin should have close to 50-50 odds. If you flipped it 1,000 times you're very likely to get close to (but not exactly) 500 heads (it's pretty simple to calculate the standard deviation, but I'll skip it here). With 25 flips, though, it's a lot less certain - the law of large numbers really only applies to large numbers.

There are plenty of variables to consider:

Did the Pats always call heads or tails? If they didn't call the same side of the coin each time then it isn't 50-50.
Did the opposing teams in games at Gillette (the away team calls the coin flip) always call the side of the coin opposite of what the Pats always call? Say if the Pats always call heads on the road and the away team called heads and it landed on tails, the Pats winning the coin flip was actually statistically a loss since probability is 50-50 that it will always land on heads or tails not whether the Pats win the coin toss if they don't have exclusively the same side of the coin.
Did each ref flip the coin the same way? If one refs flips the coin and the coin spins a lot in the air while another ref flips the coin and it doesn't spin at all, that will affect the probabilities of how the coin lands. The 50-50 probability is only when the coin is flipped exactly the same every time.
Were any of the flips in extreme wind or rain? Extreme weather can affect a coin flip.

Those are just some examples of variables affecting the outcome. The 50-50 thing is not a constant. If you flip a coin 10 times, odds are good you will not get 5 heads and 5 tails. Variables will always affect the probability unless you can recreate each flip perfectly down to the detail.

Beethree · Nov 5, 2015

The odds of outliers occurring are high over the long haul. Flip a coin 10 times. Write down the results.
Congratulations!!! The odds of flipping a coin and getting that exact permutation of heads and tails is 1 in 1024. That is smaller than the "impossible" probability given in the article. Less than 1/10th of 1%.

Froob · Nov 5, 2015

Bruins29 said:
I dont think I remember that....cause the Pats are tied to so much BS

http://data:image/jpeg;base64,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

Im foreshadowing. Foreshadowgate?

Bruins29 · Nov 5, 2015

PlainOldEd said:
I am no mathematician, but this doesn't seem right to me. First off, wouldn't it be 1 in 730? but even that seems wrong. If you flipped a coin multiple times you would expect that over time you would win about 1/2 but if you calculate the odds of flipping a coin 25 times and winning 12 or 13 I believe it comes out to around 15%. Again, I'm not a math guy but I suspect this is a case of fuzzy math....
You know the old saying that goes something like this... ?

There are Lies, Damn Lies and Statistics.

I was wrong. I had several posters explain it to me....granted since then its gone off the rails into something beyond worth trying to follow.

PlainOldEd · Nov 5, 2015

Bruins29 said:
I was wrong. I had several posters explain it to me....granted since then its gone off the rails into something beyond worth trying to follow.

I wasn't meaning to call you out, I only read the first page of posts before I commented and honestly I wasn't sure whether you were right or wrong. My point was just that they make it sound like it should be 50/50, when in fact in a small sample like that the chances of getting 50/50 results are somewhere around 15%.

Satchboogie3 · Nov 5, 2015

As I mentioned, stretches like these happen. The Jets are 4 for their last 14 on the coin flip. That means opposing teams won 10 of 14, which would be a probability of 0.089. Yes, off by a order of magnitude compared to the Pats... but that's the first team I looked at!

I mean, you could look at split this up however you want. The Bengals have only won 3 of their last 11 coin flips. So if you look at both the Jets and Bengals last 11 games, they've won a total of 6 out of 22. The odds of that is 0.026. None of this means anything because of sample sizes.

And speaking of sample size: How does he come up with 25 tosses? That's starting at game 2 last season. Could it because the Pats lost the previous 5 tosses? 19 out of 30 becomes a much less hysteria-inducing 0.100 probability. Going back further:
29 out of 50 for 0.161 probability. So while they are on a good run, they came out of a bad run (10 for 25) and have just 4 more wins (out of 50) than expected.

PlainOldEd · Nov 5, 2015

Pujo said:
I explained it a bit in the above post, but this is the exact formula: View attachment 11149

what is 13 out of 25 run through the same formula?

lurker1965 · Nov 5, 2015

I'm not 100% sure but in a group of 32 the likelihood of 1 getting this sort of result is like 20% or something. BTW, get Belichick on Penn & Teller's Fool Us - that would be an awesome trick.

A Defiant Goose · Nov 5, 2015

Hey, f**k math to be honest

Satchboogie3 · Nov 5, 2015

Well, it is possible to beat the odds on the coin toss in the long run. I doubt the Patriots do it simply because the reward is way too low for what would be a pain in the ass amount of time/analysis, but they could analyze the video/outcomes of each refs coin flips and run it through a simulator to find a possible bias. The problem is that your sample size is small and any bias found would likely only been seen over a vast sample size, likely much larger than the amount of games you coach over the coarse of a career.

That said, in the unlikely event that the Patriots DO look to find bias in the coin tosses and have actually had success exploiting that, it's not against the rules. It would be rather brilliant (but likely a waste of time and money).

Pujo · Nov 5, 2015

Rob0729 said:
There are plenty of variables to consider:

Did the Pats always call heads or tails? If they didn't call the same side of the coin each time then it isn't 50-50.

Did the opposing teams in games at Gillette (the away team calls the coin flip) always call the side of the coin opposite of what the Pats always call? Say if the Pats always call heads on the road and the away team called heads and it landed on tails, the Pats winning the coin flip was actually statistically a loss since probability is 50-50 that it will always land on heads or tails not whether the Pats win the coin toss if they don't have exclusively the same side of the coin.

Did each ref flip the coin the same way? If one refs flips the coin and the coin spins a lot in the air while another ref flips the coin and it doesn't spin at all, that will affect the probabilities of how the coin lands. The 50-50 probability is only when the coin is flipped exactly the same every time.

Were any of the flips in extreme wind or rain? Extreme weather can affect a coin flip.

Those are just some examples of variables affecting the outcome. The 50-50 thing is not a constant. If you flip a coin 10 times, odds are good you will not get 5 heads and 5 tails. Variables will always affect the probability unless you can recreate each flip perfectly down to the detail.

None of those are relevant to the odds of the flip. The odds are that a fair coin thrown fairly lands on heads are always 50/50. That doesn't mean that you will have an even number of heads and tails, but over a large number of throws (much larger than 25) you'll be damn close. If you're not just counting heads but instead are counting "successes" (the statistical term), which we'll define as "whatever the Pats called as the coin was thrown", the odds are still 50/50, regardless of whether the Pats called heads, tails, there's wind, rain, etc. Even though those do affect the toss, they're not predictable (given a fair coin and a fair toss) by the team making the call. Obviously if you could perfectly model the dynamics (wind, rain, etc.,) then you could predict the coin toss perfectly, but AFAIK, nobody's managed that, and unknown variables that work symmetrically (i.e., just as likely to cause an otherwise heads-falling coin to become tails as they are to cause a tails-falling coin to become heads) don't affect the odds.

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

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