“They’re already there!” she exclaimed. “Do you not know?”

It was the sort of moment that 2020 Democratic candidates have been struggling to obtain: pithy, well received and on brand. People who didn’t watch the Fox News event will be exposed to Gillibrand’s rejoinder, and she and her campaign surely hope she’ll gain contributions and a boost in the polls as a result.

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Why else do these events, really? The two dozen major Democratic candidates vying for spots on the debate stage and in crowded lists used by pollsters each hope that standing in front of a camera and talking will, somehow, spark the sort of thrust that propels candidates into the upper tier of the field. (Gillibrand’s last viral moment, when a young woman walked through a live interview shot to get ranch dressing, didn’t exactly have that effect.)

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They may be hoping in vain. At least 30 town hall events have been hosted by the three main cable news networks (Fox, CNN and MSNBC). With only one exception, most don’t appear to have done much to boost candidates’ chances.

Without further ado, here’s how polling has shifted after each town hall, according to the RealClearPolitics polling average. Each line shows the change relative to the day of the event itself, one week prior and three weeks after, and is colored according to the host network.

(The chart doesn’t include town hall events that took place over the weekend, because it’s too early to determine how those might have affected polling. The dotted line for Sen. Bernie Sanders (I-Vt.) in April is to differentiate from the line beneath it. )

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In most cases, there has been very little change whatsoever. In part, that’s because many of the candidates started out with very low poll numbers and then didn’t see those numbers change. Those candidates who did see big movement were generally ones who are further ahead in the polls.

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A big driver of these shifts, though, is probably campaign announcements. Sen. Kamala D. Harris (D-Calif.) saw a big jump after her January town hall — but she had also just announced her candidacy. Sanders saw a jump after he announced. The most dramatic shifts for Sanders, though, came in polling after April town halls — that happened to coincide with former vice president Joe Biden’s entry into the Democratic race.

So where’s the exception to all of this, the example of a town hall event in which a candidate seems clearly to have benefited? It doesn’t stand out on the chart above, really, but it’s that first CNN town hall with South Bend, Ind., Mayor Pete Buttigieg. He went from zero in the polls to 1.6 percent three weeks later, effectively getting onto the map for the first time. A month after that town hall, he was near 3 percent; another month later, and he was over 6.

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That surge isn’t shown only in polling. Here, for example, is the surge in attention to Buttigieg on Twitter.

That growth was exceptional.

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It’s not hard to suss out why Buttigieg had that moment. It was early in the campaign, before the flood of town halls, and he was then relatively unknown. He leveraged that attention with several interviews over the next few weeks, a format in which he fares well. There were a lot of factors, in other words, that helped him magnify the boost from his CNN appearance.

Other candidates haven’t similarly benefited. It’s not clear whether Gillibrand will, either. (She trails most of the field, including Buttigieg.) National cable attention can be a double-edged sword, as when Gillibrand disparaged the National Rifle Association during her town hall — and the gun group quickly circulated a letter of praise she had sent it in 2008.