There's precedent -- albeit not much of it -- that justifies that hope.
Despite baseball's deep-seated roots, one wouldn't expect many historical examples of a team coming back to finish first after being down by so much this late in a season. However, according to the Elias Sports Bureau, four clubs in Major League history -- the 1951 Giants, 1964 Cardinals, 1995 Mariners and 2007 Phillies -- were able to accomplish what the Giants aspire to do: Make the playoffs despite trailing by six or more games with 20 regular-season contests remaining.
As long as there's precedent, there's hope.
"The last thing we can do is cash in and start thinking about plans for the offseason," Giants outfielder Cody Ross said. "That's the worst thing you can possibly do. Just keep battling and anything can happen. ... It's been done before, and it'll be done again."
Three weeks remain in the regular season, and yet the only tight race for a postseason berth appears to be in the American League West, where the Rangers lead the Angels by 3 1/2 games.
Meanwhile, the Giants have their six-game deficit; the Cardinals and Giants are behind by 7 1/2 games in the NL Wild Card race, while the Rays trail the AL version by eight. The White Sox sit eight games back of the AL Central-leading Tigers, with the Indians 8 1/2 games back.
None of them have more than 23 games remaining, which doesn't speak well to their chances of making miracle comebacks. In fact, since 1900, only the resurgent '07 Phillies made it to the playoffs despite being at least seven games out of a playoff spot -- be it with a division or Wild Card lead -- with 22 games remaining.
But if it's inspiration those clubs seek, then it's inspiration history can provide.
Here are a lucky seven examples:
2010 Giants: It was just last year when the eventual World Series champs went from six games back on Aug. 28 to overtake the Padres in the NL West. The Giants won six of seven prior to a season-ending three-game series against the Padres, then beat San Diego on the final day to win the division, avoiding a Padres sweep that would have forced a one-game tiebreaker.
2009 Twins: The Twins are, according to Elias, the only team to stand seven or more games out of a division lead the morning of Sept. 7 and go on to win their division. Through 136 games, they were 68-68, seven games behind the AL Central-leading Tigers and 11 games -- and three teams -- behind the Wild Card-leading Red Sox. Then they won 11 of 12 from Sept. 13-26, finished the regular season with four straight wins and beat a Tigers team that finished 11-15 in a 163rd game.
2007 Phillies: The Phillies got some help, as this was the year of that great Mets collapse, but they had to get hot to take advantage. With 17 games remaining on Sept. 12, the Phillies trailed New York by seven games. Then they went bananas, winning 13 of those games, including four of their last five, while the Mets dropped six of their last seven games to give up the NL East on the final day.
2007 Rockies: For Wild Card hopefuls, the '07 Rockies are perhaps the only team that inspires hope. No team has won the Wild Card after being further than four games back with 140 completed, but the Rockies made an incredible comeback. With Clint Hurdle at the helm, Colorado was 4 1/2 games back of the Wild Card lead and had three teams to jump on Sept. 15. Then it won 14 of its last 15 to edge out the Padres by one game and enter the playoffs -- eventually advancing all the way to the World Series.
1995 Mariners: Since the divisional era began in 1969, Elias says there's only one team that was seven or more games behind in its division at the start of September and went on to win it. That's these guys. In what was the first year of the Wild Card, the '95 Mariners made a roaring comeback. Seattle went from 7 1/2 back of the California Angels at the start of the month to AL West champs by winning a one-game playoff against the Angels in the Kingdome. Seattle wasn't done with its theatrics, as the division title enabled Ken Griffey Jr.'s thrilling walk-off slide at home in the AL Division Series, in which the Mariners won three straight to overcome a 2-0 series deficit against the Yankees.
1964 Cardinals: This was before divisional play, so if the Cardinals wanted to make the playoffs -- the World Series, that is -- they had to win the entire National League outright. That's exactly what Lou Brock, Bob Gibson and Co. did despite being 8 1/2 games behind with 27 to go on Sept. 5. As the Phillies lost 10 games in a row and blew a 6 1/2-game lead with 12 to play, the Redbirds went 19-8 to finish the season -- winning eight in a row at one point -- and jumped the Phillies and Reds to make the World Series, which they won by beating the Yankees in seven.
1951 Giants: The Giants resided in New York back then, and they had no business winning a pennant. Not when you consider that they stood 13 games out of first place on Aug. 11, then -- with a mere 16 games remaining -- six behind the Brooklyn Dodgers on Sept. 13. At that point, they reeled off 13 wins in their next 14 contests, then beat their crosstown rivals in the final game of a best-of-three series -- on Bobby Thomson's "Shot Heard 'Round the World."
Alden Gonzalez is a reporter for MLB.com. Read his columns and his blog, listen to his podcast and follow him on Twitter. Chris Haft contributed to this report. This story was not subject to the approval of Major League Baseball or its clubs.