Something surprising happens when Bernie Sanders starts speaking at his presidential campaign rallies. He doesn’t ingratiate himself with audiences by praising their hometowns, or telling easy jokes, the way many candidates do. He gets right down to business, delivering a searing indictment of American politics, with crusty, to-the-barricades exhortations.

And his admirers lap it up. No one else can send liberals into a fever pitch merely by uttering the words “Glass-Steagall,” the Depression-era controls on banks that Mr. Sanders wants to reinstate.

The Times conducted a video analysis of Mr. Sanders’s Oct. 3 appearance before a crowd of 20,000 people in Boston. Six moments in his 80-minute stump speech particularly revealed his ability to connect with voters.

Battle Cry of an Underdog

It’s the Economy, but You’re Not Stupid

His Values Are Not Republican Values

Billionaires Need Not Apply

Of Guns, Badges and Black Lives

And the World Will Be Better for This

Urging a “political revolution” to upend the American establishment, Mr. Sanders puts his own, wordier spin on President Obama’s campaign message of “Yes we can!” He urges voters not to be practical or pragmatic, but to dream big and aim high.