Connections are most important, down to a baseline of skill, which we can call "competence."

As long as your skill level is "competent" or higher, connections will win the day.

But once your skill level falls below competent, connections become less and less powerful - such that the further down you go in terms of skill, the more bad ass your connections need to be in order to meet with success.

Best example I can think of this - Roseanne singing the National Anthem on live television: Total lack of musical skill + being Roseanne = one live, nationally televised performance of the national anthem.

Ancillary Modifiers:

Likability can sometimes fill in gaps otherwise left by skill, if all connections are otherwise even.

Incredible skill can sometimes overpower the need for connections entirely.

Pure crapshoot luck sometimes makes everything said in this comment meaningless :)