Why does Gandalf think baggins is right for the job?

Gandalf never gives a real reason for his choice. When questioned by the dwarves he says, You asked me to find the fourteenth man for your expedition, and I chose Mr. Baggins. Just let any one say I chose the wrong man or the wrong house, and you can stop at thirteen and have all the bad luck you like, or go back to digging coal."

Gandalf believes that Bilbo is the man for the job based upon his ancestry and the man he thinks him to be. No other explanation is given.

You asked me to find the fourteenth man for your expedition, and I chose Mr. Baggins. Just let any one say I chose the wrong man or the wrong house, and you can stop at thirteen and have all the bad luck you like, or go back to digging coal."