I suspect luck plays little or no role. Probably just unpredictable how people turn out. Genetics is a I think huge, and diet and medical care are important as well.

If you take the height of my mothers brothers and father, add in the height of my father and his brothers and father and average it all together....you come up with 5'10"

I'm 5'11" and had much better medical care, a balanced diet and grew up in the country where I was fairly active running and climbing.

If I hadn't been born with a heart defect and spent much of my first 7 years in hospitals I'd probably be taller yet.