This line of thinking makes the assumption that ambition is a necessary prerequisite for efficacy. I'm not exactly in a position to qualify this statement, but I would guess that the people who make the greatest positive changes in the world weren't necessarily setting out to have a huge impact, they were just doing what they knew to be right.
Because everyone loves statistically unproven case studies, I offer Penny Arcade. PA launched a webcomic in 98. Five years later, they launched Child's Play - a charity that has raised ~$9M to fund research and facilities for children's hospitals.
When asked about it, Mike mentioned that, when they started Child's Play, neither of them were parents so they didn't know how effective their efforts would be, they just knew it was the right thing to do.