When the rallies have ended, when the tour buses have been idled, when the TV airwaves are finally free of campaign commercials come Tuesday night, Scott Brown and Elizabeth Warren will test a political theory.
Will a Democratic candidate get a boost into office from the higher voter turnout that historically occurs in Massachusetts in a presidential year?
That is not to say that Warren, a Harvard Law School professor and consumer advocate, has not worked for the right to replace Brown as the state’s junior US senator.
After all, she outraised all other congressional candidates in the country, endured the learning curve as a first-time political candidate, and battled Brown during three televised debates.
But it underscores one of the reasons her party leaders have had confidence about retaking the seat Brown stunned them by winning in a special election nearly two years ago, when the Republican upset Democrat Martha Coakley to replace the late Senator Edward M. Kennedy.
It also explains why Brown has approached the race as he has, and why he is hoping to buck history when the votes are tallied.
Before the Democrats had even recruited Warren to run, they were confident about unseating Brown because the 2012 election would coincide with a presidential race.
While they admitted being overconfident about Coakley’s prospects in 2010, they felt she was victimized not just by a lackluster campaign, but also because her race was the only one on the ballot.
It became a focal point nationally for party opponents, especially Tea Party members who hoped to block President Obama’s health care law.
In that special election, Brown got 1.168 million votes, or 52 percent of the total cast. Coakley got 1.059 million, or 47 percent.
All told, 2.249 million votes were cast. Brown ended up with 109,000 more than Coakley. Yet a little more than a year earlier, in the 2008 general election, Obama was on the ballot in Massachusetts.
The Democrat beat Republican presidential nominee John McCain by a margin of 61 percent to 38 percent, with Obama getting 1.904 million votes and McCain 1.109 million.
Most significant: A total of 3.103 million votes were cast — 854,000 more than in the Brown-Coakley special election.
Democrats argued that if those extra votes were split by the same 61 percent to 38 percent ratio seen in Obama’s win over McCain, and then added to the Republican and Democratic totals from the 2010 special election, a Democratic candidate — now Warren — would beat Brown by a margin of 1.580 million votes to 1.493 million votes.
That explains why Brown has served the way he has the past two years and run the way he has against Warren.
The senator has embraced occasions when he could break ranks with his fellow Republicans and vote with the Democrats.
On the stump, he has trumpeted a Congressional Quarterly analysis naming him the second-most bipartisan member of the Senate.
Brown and Warren both have run TV ads showing them alongside the Democratic president, the opposite of Republican candidates elsewhere in the country.
The risk for Warren in her party’s numerical analysis is two-fold: The turnout on Tuesday may not match the intensity of 2008, and Democrats could split their votes between Obama for president and Brown for senator.
A Globe poll last week enumerated both dangers.
Obama led Republican presidential nominee Mitt Romney by 52 percent to 38 percent, a sizable lead but about half the margin the president had in a similar poll in September.
Meanwhile, the poll showed Brown and Warren tied at 47 percent, when likely voters leaning toward one candidate or the other were nudged into making a pick between the two.
Among those who said they would vote for Romney for president, only 5 percent said they would also vote for Warren for senator. But among those who said they would vote for Obama for president, 14 percent said they would vote for Brown for senator.
That is his hope as he seeks his first full Senate term. And it explains why Brown’s final TV ad does not mention that he is a Republican, but closes with the admonition to “vote the person, not the party.”