Polling has fundamental issues that can't be solved with statistics. The biggest one is the unknown difference between who responds to the poll and who votes. And poll response areas are very low these days - I've heard well under 1% is common (that is, less than 1 out of 100 individuals contacted by the pollster answer the questions).

Nate Silver nailed this in the 2016 election. He said Trump's victory there was consistent with historically normal polling errors.

What may have been less widely appreciated is these errors are not related to causes like limited sample size that are straightforwardly amenable to statistical analysis. They come from the deeper problems with polling and the way those problems shift under our feet a little bit with each election.