Let’s assume that all PC backgrounds and traits are assigned randomly (there are 13 backgrounds so about 7.5% of PCs have each background).
Out of every 1000 Player Characters:
15 are fire eaters. (d10 entertainer routines, of which you get 1d3) Makes sense that this number is so high, since every bad fantasy movie has at least one fire eater per crowd scene. Fire eating is apparently riveting entertainment in Fantasy Europe.
10 are librarians. (d8 sage specialty)
10 are blackmailers. (d8 criminal specialty) Blackmailers are not the most dashing of outlaws, and it’s hard to reconcile them with heroic fantasy. Nevertheless, I’m looking forward to many D&D adventures inspired by the life of Charles Augustus Howell..
A whopping 19 are raised by wolves. (d8 outlander personality trait, of which you get two)
4 are guild blacksmiths. (d20 guild business) This might sound naiive, but I absurdly thought that a smith background would be MORE common among adventurers than a raised-by-wolves background. Obviously I was off by a factor of 5. That’s why “Smith” is such a rare last name and “Wolfson” is so common.
It makes sense to me that people with terrible jobs and no prospects for the future are more likely to become murderhobos than people with, for example, trade skills and guild membership. In my experience, when players are asked about their PC’s family, they tend to have no parents, siblings, spouses, children, or friends (which the players insightfully recognize are just ways the DM can adventure-hook them without some noble paying a reward to do it). This is possibly a peek into the player’s internal needs that he’s trying to fulfill at the gaming table; as citizens of a civilized society we have few opportunities to experience romantic danger, travel to exotic locations, wealth, power over others, or prestige and fame. Similarly, how many players come to the first game session of a campaign to roll up a character after just having helped a cousin move into a new house? Being able to choose your friends and family can be wonderfully empowering. The obvious place to start is at “none” because you didn’t think this through yet and everyone else is ready at the entrance to the Yeti Concubine’s Treasure Palace tapping their feet.
You’re right, Wolfson IS probably more common than Smith among PCs.
The backgrounds are not evenly distributed, as noted in the PHB. Guild artisans are stated to be the most common background in its very description. Cute statistics though.