Bilbo was the 14th participant in this expedition.
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I think your referring to Gandalf choosing Baggins as the fourteenth. He really didn't have a reason....... that's just how he chose to do it.......
"Of course there is a mark," said Gandalf. "I put it there myself. For very good reasons. 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."
As for further explanation, the text later cites ( a few paragraphs down)
"So, no one can tell for sure why he did that, but one can think, beyond the shadow of doubt that he 'sensed' that Bilbo is a 'man' for the job."