Hillary Clinton talks with Ohio voters at Angie's Soul Cafe in Cleveland on Oct. 31. (Melina Mara/The Washington Post)

Sean Trende of RealClearPolitics ran through an experiment on Twitter, meant to demonstrate why big shifts in polling may not actually reflect reality.

Imagine a scenario in which you have one poll a day tracking the presidential election. Let's say the true state of the race is that it is tied, and that poll has a margin of error of 3 points. On Monday, you might get a result in which Donald Trump leads by 4. That's within the margin of error: If the poll estimates that support for Hillary Clinton is 3 points lower than it actually is and 1 point higher for Trump, you get a 4-point spread. The next day, the poll says Trump leads by 1 point. The next day, Clinton is up by 2.

To an outside observer, it looks like Clinton has gained 6 points in two days. In reality, though, we know that the state of the race hasn't changed at all, because that's the rule we set.

Trende's point is that more polls are better because they help smooth out some of the jumping around in the polls. But you don't have to take his word for it. You can let your computer show you how this works.

On this interactive, you can set three variables: what the actual state of the race is, how many polls you want each day and what the margin of error in those polls would be. The more polls, the closer the daily average is to the real state of the race. You'll note that the weekly average — which includes a lot more polls — tends to be closer to the state of the race than an individual day's results, too.

Those dots popping up over and under the horizontal line reflect the daily averages. (Red dots show a Trump lead; blue, Clinton.) They should be distributed about evenly above and below — but they won't necessarily be. Notice, too, that as the dots fill in, it looks like patterns emerge, up and down. Those aren't real movement! We know that because the computer doesn't actually change the real value.

This is only one facet of why polling doesn't necessarily offer the hard-and-clear result that people would like to see. Trende was responding mostly to the sharp decline in the number of polls this year versus 2012, a function in large part of the cost of conducting the surveys.

It's a good thing to keep in mind. Polling is good at giving us a sense of the race. But we're also very good at misinterpreting what we're seeing.