GovBeat and The Fix exchanged some thoughts Monday on the state of the Virginia governor’s race. The summer hasn’t been kind to either Republican nominee Ken Cuccinelli, who’s faced questions about his relationship to the CEO of a nutritional supplement company at the center of a developing scandal involving Gov. Bob McDonnell (R), or Democratic nominee Terry McAuliffe, whose former company is being investigated by the Securities and Exchange Commission.

And the two candidates aren’t being kind to each other. After a feint at being positive — both ran early ads introducing themselves to state voters — the two sides have gone relentlessly negative. It’s unlikely that either side will do anything other than try to disqualify the other candidate from now until Election Day.

But beyond the airwaves, both candidates are engaged in a two-front war: First, they have to convince their base voters to show up to the polls. Second, they have to pull those fence-sitters their way. Motivation, in a low-turnout off-year election, plus persuasion, in an incessantly negative race, equals a win.

So, how many people are going to show up to vote? The number of voters who have turned out in governor’s races in Virginia has declined precipitously over the last two decades. When Virginia elected Doug Wilder in 1989, 66.5 percent of registered voters showed up at the polls. Turnout has declined every four years after that; in 2009 just 40.4 percent of registered voters cast a ballot.

Strategists on both sides think that 40.4 percent is a nadir, and that turnout this year will land somewhere between 41 percent and 45 percent. That amounts to about 2.1 million to 2.3 million raw votes. And the voters who decide the election will probably be the ones who know Ken Cuccinelli the best.

Cuccinelli hails from Prince William County; he served as a state senator in neighboring Fairfax County before being elected attorney general. In recent years, Prince William has been one of the best indicators of the state’s overall vote.

Since 2004, Prince William has voted for the winning gubernatorial or presidential candidate every time, and by margins that mirror the statewide total: George W. Bush won it with 52.84 percent of the vote, and won statewide with 53.68 percent. The county was off by just 1.7 percent in the 2005 governor’s race, which Democrat Tim Kaine won. In 2009, McDonnell underperformed his statewide total in Prince William by less than one-tenth of one percentage point.

In all five presidential or gubernatorial years since 2004, the county has been off by an average of just 2.7 percentage points. Democrats tend to do better in Prince William in presidential years, too: Barack Obama won the county by wider margins than he did statewide in both 2008 and 2012. That underscores both the opportunity and the challenge McAuliffe’s campaign faces: The Democratic voters are there — mainly in Neabsco, Woodbridge and Dumphries — but they don’t always turn out. The more Republican precincts in western PWC, Cuccinelli’s base, are more regular voters.

If McAuliffe can persuade those occasional Democratic voters to turn out, he’ll have a big advantage, both in Prince William and statewide. Broadly speaking, higher turnout is better for McAuliffe; the question, of course, is which voters actually head to the polls.

At least one Republican strategist isn’t confident in the math. “I’m not sure that the Cuccinelli strategy, which is a low, low turnout, actually works,” said Tom Davis, the former Republican congressman. “If they get any kind of urban turnout model together, the Democrats are in great shape.”