His Congressional logbook lists it as an official state visit, but when U.S. Senator Scott Brown arrived at the Elks Lodge in West Roxbury early on a Friday night in January he was just one of the guys.

He shook hands. He had a beer. He cracked a smile again and again, and leaned back as he talked with party goers gathered to welcome home Massachusetts State Senator Mike Rush.

Rush had just completed an eight-month tour of duty in Iraq with the U.S. Navy. A year after leaving Beacon Hill for Capitol Hill, Brown wanted to be on hand to celebrate his fellow servicemen and former State Senate colleague’s homecoming.

Nevermind that Rush was a Democrat or that Election Day was 11 months away, the self-proclaimed People’s Senator was not going to miss it.

“Scott Brown came early and stayed late,” remembers Lawrence S. DiCara ’71, a former Boston City Councillor, who was at the event that night. “He actually enjoys going to those events. A lot of people in politics don’t.”

More than just enjoyment, former politicians and political science professors say, events like these give Brown a platform to exercise what has become a winning political combination: independent politics and relatability.

Brown’s success rising through local, state, and ultimately federal politics in an overwhelming Democratic state has largely hinged on this confluence of personality and politics, they say.

“The sense that many voters have is that he is like them,” said Boston College political science professor Dennis Hale. “Not born rich, not born lucky. He worked hard to make his way in the world and was a success.”

The formula worked for Brown in January 2010 when his barn coat and moderate stances helped the state senator emerge suddenly to upset Democratic Attorney General Martha M. Coakley. Just two short years later, Brown’s success against Harvard Law School professor Elizabeth Warren next Tuesday may well depend on how believable that formula is this time around.

A SENATOR JUST LIKE YOU

When his S.U.V. slowed to a stop in front of Mr. Bartley’s Gourmet Burgers in Harvard Square one afternoon in late April, Brown looked as if he could have been any other businessman grabbing a quick bite on his lunch break. He wore a shirt, a tie, and a smile, but no jacket.

“What’ll you have?” someone yelled, after Brown was ushered to a seat at the bar.

The Senator smiled. He ordered a themed burger bearing his name, and talked with the fry cook at the grill in front of him. Between bites, french fry in hand, Brown explained that he had been a Bartley’s regular for years. He said that he discovered the joint and the adjacent Hong Kong Restaurant while an undergraduate at Tufts University in nearby Medford.

Brown has an everyman quality rare in politicians, those familiar with the race say. In advertisements, he often sports a Bruins jersey and focuses on his active home life. On the campaign trail he prefers talking with voters about their lives to answering questions from reporters. Brown has been endorsed by retired athletes like former Celtics star Bob Cousy and women’s advocates like Laurie Myers.

“[To voters,] he is like the boy next door, like the guy I could have a beer with—the guy I can trust,” said former Massachusetts Treasurer Joseph D. Malone ’78, a Republican who sought statewide office several times during his career.