How unsafe is this city exactly?

If you follow the U.S. news, you must know that a crane on East 51st Street in New York collapsed yesterday killing at least four people. My mother has been saying, as long as I can remember:" don't walk below those things, you never know when they can fall..."
She is a wise woman. But I already knew that. M. thinks she's overprotective. I sometimes do too. But when she's right, she's right.
I don't know how many times I've passed beside or below a construction site, with an option of crossing the street and totally avoiding it. It's a bit harder in N.Y.C. since there's always construction, everywhere, but it's doable. If one is not too lazy.