Thirteen months before Bay State voters go to the polls, the Massachusetts Senate race is already ramping up. The campaigns of Sen. Scott Brown (R) and presumptive Democratic nominee, Harvard professor Elizabeth Warren, both released campaign-style Web videos today.

Warren’s video is a four-minute biographical piece meant to introduce her to voters. Over a montage of old family photos, she tells the viewer about her upbringing and her career. It follows many of the contours of her well-received speech introducing herself to local politicians and labor union officials and activists on Labor Day. A key part of the Warren campaign’s narrative is to emphasize her upbringing in what she has repeatedly called “the ragged edge of the middle class” and how she’s spent her life working for middle-class folks.

“Fighting for middle-class families is in her blood. It’s how she was raised, and it’s who she is,” Warren adviser Doug Rubin wrote in an email to supporters introducing the video. “But there are a lot of people who don’t know Elizabeth’s story, and I need your help to get the word out to every Massachusetts voter.”

Brown’s video, which taps into his campaign’s narrative of the Senator as a regular guy who has the interests of Massachusetts voters at heart, takes footage from his appearance at the Irish Heritage Festival in the Dorchester neighborhood of Boston, which he attended Sunday with former Boston Mayor Ray Flynn (D). The video uses footage of Brown dressed casually in a polo shirt and khaki pants interacting with residents intercut with people on the street talking about how Brown has their back.

“I was looking for a change, and he brought the change that I was looking for. I think he’s one of a kind, and I’m glad he’s here today,” a woman on the street says as the video opens.

“Even though the election is still more than a year away, the DC/Beacon Hill political establishment is already working each and every day to defeat me,” Brown wrote in an email to supporters sharing the video. “They are trying to reverse what you did on January 19, 2010,” he wrote, referring to the date of his upset special election victory for the Senate seat previously held by Sen. Edward Kennedy (D).

Both campaigns will have plenty of resources to help sell their narratives to voters during the next year. Brown had more than $10 million in his campaign account at the end of September. Warren, even though she jumped into the race in September, raised more $3 million by the end of the third quarter.

Meanwhile, in another sign that the campaign in the Bay State is already heating up, Brown today responded to questions about a plagiarized passage that appeared on his website — first discovered by the Democratic group American Bridge 21st Century. Brown told the Boston Globe that the whole issue was “getting a little silly.”

Warren must beat CityYear co-founder Alan Khazei and other candidates in the Democratic primary before she can take on Brown.

Watch Warren’s campaign video:

Watch Brown’s campaign video: