> 16 point misses by seasoned pollsters are not accidental.
Not a pollster, but Nate Silver publicly challenged someone on Twitter to a $100k bet over how red Florida would go. IIRC Silver was predicting 3-5% margin, Twitterer said minimum 8%. Trump won by 14%. Even Silver, who lived and breathed analyzing polls and their reliability, made a mistake of that magnitude with his own money on the line. Sometimes the votes don't line up with polling, and sometimes the professionals genuinely don't see it coming.
I think that that is more of an illustration that polls are always about a statistical likelihood and never about an absolute. With a 3-5% margin 14% is not as unlikely as you might think. (It's ~ 1:3).
You need a measure of variance to perform that kind of estimate. There's scenarios where 98% of results land within 3-5% of a value, and the 14% is extremely unlikely. And scenarios where the variance is high, and it's much more likely. (you can also be wrong about what you think the variance is)
As far as I'm aware these poll results have (roughly) a normal distribution, right now the spread between the two extremes in polls with sufficiently high 'N' to be taken into account in most reports differ by 19%.
"standard normal" isn't the same as "normal"; standard normal defines the mean & variance (0 & 1 respectively), but normal distributions can have any mean & variance.
The other issue is that in an election like the US, the results in different states are not independent, decoupled rolls of the dice. i.e. If the results of the first few states lean a few % one way off the polling (within the margin of error) then it's most likely that most of the other states will doe the same.
> 16 point misses by seasoned pollsters are not accidental.
Not a pollster, but Nate Silver publicly challenged someone on Twitter to a $100k bet over how red Florida would go. IIRC Silver was predicting 3-5% margin, Twitterer said minimum 8%. Trump won by 14%. Even Silver, who lived and breathed analyzing polls and their reliability, made a mistake of that magnitude with his own money on the line. Sometimes the votes don't line up with polling, and sometimes the professionals genuinely don't see it coming.