Fans decked out in Red Sox gear lined the route, holding signs and cheering for the team. Some couldn't resist a shot at the archrival New York Yankees and former Red Sox star Johnny Damon, who defected to New York after the 2004 championship.
''Johnny Damon is home changing diapers,'' read one sign. ''This is better.''
Another fan held a sign that said, ''A-Rod: Mr. April, Miss October.''
There were some indications Boston fans might even be getting picky about their championships, with 2004 and 2007 coming when the Sox were on the road.
Ortiz said a fan asked him when the team was going to win a World Series at Fenway.
''I told him, 'Dude, it doesn't matter where you win it, as long as you win it,''' Ortiz said.
Red Sox president Larry Lucchino said before the parade that he could not choose which Series win he liked better.
''They're two flavors of ice cream — they both taste good,'' he said. You can't choose among them. I think the next one is going to taste good, too.''
Mayor Thomas Menino acknowledged having the celebration on a week day would inconvenience some businesses and keep school children away, but said players were eager to get home to their families and begin their vacation.
Menino also said a ''rolling rally'' was easier for city officials to manage, because it spread out the crowds. He estimated security would cost $500,000.
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AP reporters Matt Pitta, Ken Maguire and Jimmy Golen contributed to this report.