From Wikipedia:

As of 2010, all forms of violence resulted in about 1.34 million deaths up from about 1 million in 1990. Suicide accounts for about 883,000, interpersonal violence for 456,000 and collective violence for 18,000.

Note: (https://en.wikipedia.org/wiki/Violence#cite_ref-Loz2012_107-1\)

So, not that noncentral.

(Although, deaths aren't the only outcome of violence, I haven't read the cited study and there may be a huge availability bias here.)

Also, how often are analogies backed up by statistics?

Self-harm counts as violence too, doesn't it? And it's not always accidental. The analogy stands.