Not only is luck a huge component but exposure is as well. Granted my recruitment was in the stone ages but I was very lightly recruited due to lack of exposure. I was from a state that was not a hot bed for my sport and my family did not have the time, money, and inclination to travel the summer competition circuit to gain exposure. As a result the interest I received during the traditional recruiting times (prior to senior year) were mostly schools in my region, not near the top of Div I.
When All-American lists and national ranking were compiled after my senior season suddenly I was ranked as high as #2 in the nation in some sources but by that time most schools had filled their recruiting class. Coincidentally the individual ranked #1 was also from a similar background and in my same situation.
Luck became a factor when the school I had already decided to attend (and not compete) had a spot and some money open up due to a transfer situation. I was able to attend the school I had chosen academically that also happened to be in the top ranked conference for my sport and my coach was a multi-time Olympic team coach. The other top ranked athlete also became lucky as he found a similar situation within the same conference. We came from half a country apart and went to different schools but became good friends based on our recruiting backgrounds and luck.
If not for the luck involved I would have never realized my potential and never made the lifelong friends and connections I now maintain. Luck was the most important piece of the equation for me as I think it is for many athletes.