Bob Paduchik, who runs President Bush's reelection campaign in Ohio, likes to measure his progress with numbers. Here's one he cited with satisfaction: 175,000.

That was the number of new and presumably Republican voters his network of field organizers and volunteer activists had helped register, enabling them to cast ballots in the presidential election, as of late last month.

Or so he claimed.

J.B. Poersch, Paduchik's counterpart on John F. Kerry's campaign, paused when the 175,000 figure was recited to him. "That's a lot of voters," he noted coolly. Then his face soured, and he shook his head. "Uh-uh," he said emphatically, dismissing the GOP assertion as fantasy. "That's not the case."

Or maybe it is the case. This is the season of bluster in Ohio, the most battled over of battleground states, where every campaign is making boasts about its organizational prowess, and worrying anxiously about whether the boasts of opponents can be believed. Some liberal groups not affiliated with the Kerry campaign are asserting that they have registered 300,000 or even more voters, in a field organization campaign of unprecedented scope and intensity.

No matter the true figure, every poll that comes out in Ohio between now and Nov. 2 should include an asterisk -- or perhaps even a question mark. On all sides, this year's field operations are devoted to overturning the assumptions of pollsters -- about who will vote, and how many -- to the advantage of either Bush or Kerry, in ways that could produce an Election Day surprise.

For now, the Ohio ground game is kicking up plenty of dust, but the reality behind the fervent and sometimes contradictory boasts of who is winning is hard to discern. Not all of the claimed registrants are reflected in the latest official releases from the secretary of state's office, where information can lag coming in from 88 counties. Registration ends Monday, and no effort has been made yet to determine how many of the applications are duplicates of people already registered. Election officials, and even activists with the groups, acknowledge that a significant fraction of the 300,000 Democratic applications do not reflect new voters, much less represent a guarantee that these people will get to the polls.

In the meantime, registration efforts are generating controversy, including investigations over illegal registration of dead people and a Democratic lawsuit and petition drive accusing Secretary of State J. Kenneth Blackwell (R) of narrowly interpreting rules in a bid to suppress Democratic votes.

For all the confusion, it is clear that, cumulatively, the efforts of the Bush and Kerry campaigns combined with the activities of independent groups mark this year as by far the most extensive ground battle ever in Ohio politics. In a state where voters know they are special -- thanks to 20 electoral votes and a history of backing every presidential winner since 1964 -- this year there is more of everything: volunteers enlisted, doors knocked upon, telephones rung, yard signs planted.

Amid the frenzy, a question looms: What is all this activity really good for?

The rarely spoken secret, even among the leaders of the Ohio ground game, is that no one is really sure.

"A really good ground game will get three to four percentage points," said Paduchik, a 38-year-old veteran of Ohio GOP politics. "We've never had a grass-roots organization like this in the state of Ohio," he noted, a novelty that means no one can say, "What's going to be real on Election Day?"

One person who insists his efforts will prove real -- and possibly decisive -- is Steve Bouchard, who is organizing the state for America Coming Together (ACT). Well funded from labor unions and deep-pocketed liberal benefactors, ACT is one of the new independent groups that seems especially large in Ohio and other swing states. ACT has saturated the state with legions of paid activists, an effort that by law must be uncoordinated with Kerry but that is aimed at getting him elected.

During a visit to ACT's local office here, near the campus of Case Western Reserve University and not far from the Cleveland Clinic hospital, Bouchard said, "If we are neck-and-neck on November 1st, then we are going to win on November 2nd."

Though opposite in their political beliefs, Bouchard and Paduchik share a common stripe in the profession of politics. Historically, field organization is the rump end of the campaign horse -- neither as lucrative, nor as glamorous, as other specialties such as media consulting and polling that attract more attention in news coverage of campaigns, and from candidates themselves.

"It's not really sexy," Paduchik acknowledged of his field operation, with a smile. Others in politics "think of us as the ground-pounders -- the infantry -- people who don't do a lot of thinking."

Paduchik's Ohio roots set him apart from the leaders of the Kerry and ACT ground operations. In part because Democrats have fared so poorly in Ohio statewide elections over the past dozen years, the party now typically imports its political talent for presidential elections. Kerry's Poersch, who helped run the state for Al Gore in 2000, is on leave from his job as chief of staff to Sen. Jack Reed (D-R.I.). ACT's Bouchard, whose wife and children are back home in Northern Virginia, is a New Hampshire native who has run field operations for former presidential candidate Wesley K. Clark and Virginia Gov. Mark R. Warner.

There remain plenty of agnostics among Ohio political experts, some of whom are skeptical about the impact of a ground operation on an election's outcome in a large state. The most important factors, by this reckoning, will continue as in earlier years to be the ads voters see on television, and larger dynamics that will play out nationally -- which this year include events in Iraq and the debates.

"Every election year, there's a claim that an unprecedented level of new voters will be brought out," said Eric W. Rademacher, co-director of the University of Cincinnati's Ohio Poll. He noted that usually such pre-election boasts fall flat. This year, he added, he is confident the ground organizing on both sides "will eclipse any previous efforts," but he said that from a pollster's "analytic standpoint, the real question is, 'Will one side do a better job?' "

Democrats believe they have the edge. ACT said it has registered 88,000 people in Ohio, and that its partners in a coalition of dozens of liberal groups known as America Votes have brought in 215,000 more, for a total of about 300,000, ACT Ohio spokesman Jess Goode said. In the days after Paduchik made his boast of 175,000 new voters, Republicans say they added about 25,000 more. Registering is an easy task in Ohio; more than 7.5 million of Ohio's 8.1 million voting age residents have done it.

Voter registration, however, is only one part of field work. Kerry's Ohio campaign, according to people working on it, has done little voter registration, aware that independent groups such as labor unions, MoveOn.org and ACT are targeting Democratic precincts for this. But Kerry's campaign, though it was far later in hiring staff and getting organized than Bush's, has come alive in recent months. In coordination with the state and national Democratic parties, the campaign has hired 77 full-time field organizers. On any given night, about 16,000 Kerry volunteers are working in the state, according to data released by the campaign. At phone banks, these volunteers have called more than 1.8 million voters, and knocked on more than 93,000 doors, the campaign said.

Paduchik's operation cites its own numbers. The Bush campaign says it has recruited 69,000 Ohio volunteers, and has installed precinct chairmen -- in charge of shooing neighbors to the polls -- in each of Ohio's 12,000 precincts. These volunteers have made nearly 1.4 million phone calls and knocked on 225,000 doors as of Friday night.

Although the GOP and Democratic operations use similar tactics of door knocking and phone banks, they do have some important differences in strategy. One is the relative significance they assign to swing voters -- people who have not made up their mind for whom to vote, or who are "soft" in their support. The Bush operation, while making nods to persuading uncommitted voters when it finds them, is fundamentally organized around the traditional field mission of identifying committed supporters and getting them to the polls on Election Day.

The Kerry operation, and to a degree the work at ACT, devotes more effort to voter persuasion. Kerry strategists say their data on uncommitted voters suggest that they are more likely to be younger and female. Once people are identified in databases as potential, but undecided, Kerry voters, the campaign tries to pepper them with calls and visits, which may include the distribution of pamphlets on issues the potential voters have identified as important. Poersch said the sheer number of volunteers available, combined with technological advances in tracking voters, allows field work to devote more effort to uncommitted voters than in years past.

Bouchard said ACT's doorstep interviews highlight the challenge for Democrats in reaching uncommitted voters: how to raise questions about Bush's record, particularly in Iraq, without sounding defeatist. "I do think there's a conflict for people: If you question the war, are you undermining the efforts of our troops?" he said. "We bring a service to undecideds, we're bringing them information."

Some polls suggest there are very few undecideds left. The latest Ohio poll showed an 11-point lead for Bush, with just 1 percent still up for grabs. Other polls have shown the margin tighter.

Poersch said he believes the election is closer than public polls indicate. And he said he keeps his enthusiasm high by focusing on the fundamental faith of all field organizers, that victory will flow inevitably from a certain number of yard signs, door knocks and phone calls. "If we reach our goals," he said, "we win."

Bob Paduchik, far left, the Bush campaign manager in Ohio, discusses the president's next visit to the state with, from left, executive director Darrin Klinger, and volunteers Capera Clement of Dallas and Les Williamson of Mississippi. Volunteers work the phones and help distribute campaign stickers and signs at Kerry headquarters in Columbus, Ohio.