Unsurprisingly, Wlezien and Erikson found that as the campaign goes on, the polls start looking more like the eventual outcome.
But they also found that the rate of this improvement isn't linear. There are some volatile periods of the campaign in which the polls' predictive value surges quite quickly. And there are other, more stagnant periods in which the polls might change, but those changes don't tend to have any lasting impact.
One of those volatile and consequential phases is the one we're in right now. The authors found that around 300 days before the election (mid-January), general election polls are essentially meaningless — their predictive value is close to zero. But by the time we get to mid-April of the election year, polls explain about half the variance in the eventual vote split. And mid-April polls have correctly "called" the winner in about two-thirds of the cases since 1952.