This election cycle, members of the student group Yale for Change spent countless hours traveling to battleground states, phone-banking and door-knocking for Sen. Barack Obama. Their efforts appeared to pay off Tuesday as voter turnout soared nationwide and the Democratic presidential nominee won the presidency.

But according to a model developed by Yale professors to assess the effectiveness of campaign techniques, their tens of thousands of phone calls made and doorbells rung probably spurred no more than a few hundred extra voters to go to the polls.

As many as 11 million more Americans voted Tuesday than in the 2004 presidential election, according to data compiled by the United States Elections Project at George Mason University. But based on a 2002 study on ‘get out the vote’ efforts by Yale political science professors Donald Green and Alan Gerber and then-postdoctoral associate David Nickerson, Yale for Change’s efforts may not have accounted for more than about 430 of those 11 million new voters.

In the study, the three professors carried out a series of door-to-door canvassing experiments in six American cities, from Bridgeport to St. Paul, Minn. The professors found that during a local election, each face-to-face contact with a voter increased his or her chance of voting by seven percent. Their results also suggested that every 12 face-to-face contacts garner one additional vote.

Although the study was done on local elections, Nickerson, now a political science professor at Notre Dame, said that if individuals are targeted because they are unlikely to vote, even in a high turnout election, the study’s conclusions could still be generally applied to this year’s presidential campaign.

Gerber agreed, though he said the equation would have to be modified slightly. He estimated that, for presidential elections, each contact increases an individual’s chance of voting by four percent. Given that, it would take 20 face-to-face contacts to get one additional voter to the polls, Gerber said.

But Gerber’s research did not address instances where canvassers attempted to sway voters; it only predicts the increase in overall turnout from mobilization efforts.

Yale for Change did both in New Hampshire, said Yale College Democrats president Ben Shaffer ’09. Canvassing in Philadelphia last weekend consisted solely of mobilization, Yale for Obama co-director Jacob Koch ’10 said.

All told, Yale for Change’s records show students involved with the group knocked on over 23,000 doors and logged over 50,000 calls between the start of school and Election Day. After subtracting canvassing that involved persuasion, the number of doors knocked for the purpose of mobilization is 17,825. Shaffer said only a third to a half of homes visited resulted in a face-to-face contact, bringing the number of voters reached down to about 5,940.

Given Gerber’s ratio, it is likely that their canvassing efforts resulted in an overall increase in turnout of about 297 votes.

Additionally, Gerber said that his team calculated that for every 400 pieces of campaign literature distributed, one more voter goes to the polls. Literature dropped by Yale for Change, then, brought in an additional 40 votes. Gerber then said an additional 100 votes should be added to the total to account for indirect effects of face-to-face contacts, bringing the final tally to 437 votes gained for Obama in both Pennsylvania and New Hampshire. In Philadelphia alone, the number is about 271 votes.

As for the calls, Gerber said that in a presidential election one additional vote could be won after 100 successful phone conversations in which the volunteer actually spoke with the voter. Ben Lazarus ’10, co-director of Yale for Change, said his organization does not have complete records of which of the 50,000 calls made went to voicemail. Gerber said he doubted whether voicemail messages were “worth very much at all,” as he put it, and therefore could not assess the total impact of calls made.

Michael Jones ’11, who went door-to-door for Obama in Milford, N.H., said that despite the low statistical effect of canvassing on turnout, such campaigns can have far-reaching repercussions.

“The numbers tell one story, but when you leave literature on the door maybe someone you didn’t even intend to reach will read it. Maybe it gets picked up by some 13-year-old kid who can’t vote now, but develops an interest in politics or becomes a lifelong Democrat,” Jones said. “You may never know the effect you’re having.”

Yale for Obama volunteer Sam Brill ’10 said while he thought it “honestly impossible” to pinpoint the number of votes Yale for Change won, he argued that there was another benefit of doing the work.

“What’s important, and what Obama has shown, is a lot of this election was about getting people engaged for the first time,” Brill said. “Literally hundreds of people that I knew became part of history.”

Nora Caplan-Bricker contributed reporting.