Caped crusaders

I was adding it up the other day, and if I'd given my life over to being ready to explode in crusading violence every time the occasion arose I would have got into fights twice, some forty-five years ago. Unless I actually went around starting fights myself, which is hardly the done thing.
Riffing off that, Batman can apparently run into thugs mugging someone in an alleyway about what? Once, twice a week? I mean, he's looking for them, but even so, if a mugging takes (let's be generous) ten minutes, and if it takes him ten minutes to cover a single (multi-alley) block...
Let's say he's patrolling after dark five nights a week...say 50 hours, or 300 ten-minute periods... and has two hits. One in 150.
Let's say that Gotham City has 500 downtown blocks (he doesn't seem to do the suburbs much - nowhere to swing from). That means that in any given ten night minutes there are three and a bit muggings, or a total of a thousand muggings (or break-ins, bank robberies, or gang hits, or arson cases) a week.
That seems about right; if Batman's strike rate was much more than 2 in a thousand it might reduce crime below the level where there's enough of it to keep him busy . An ecological balance.
Though... a thousand crimes, given recidivism, probably implies between three hundred and five hundred actual criminals. And he takes out two a week - that's a hundred a year. Or a one chance in five of going down. You'd think that odds like that would have to reduce the attractions of crime.
Except that, to be fair, a number of Batvillains aren't homo economicus; in the latest movie the Joker, for example, makes rather a point of it.
The same, of course, applies to Spiderman, though his spider-sense may mean he has a wider search area at any given moment. On the other hand, he doesn't have a car, so it probably evens out.