Costumed Crimefighters!!

If I understand the concept right, Batman and other costumed crime fighters only protect the world against villains who also wear costumes, like The Joker and Catwoman. Apparently the hundreds of plain clothed thieves that roam cities just aren't worth the bother to him, or maybe they just don't present the challenge that the costumed thieves do. Consider the villain's need to leave tailor-made clues like the Riddler (Batman loves those), or their similarly clad henchmen, and their hideouts completely outfitted with furniture and knickknacks that fit their persona. Only someone like Batman with his one-of-a-kind "batwear" and "batproducts" living in a "batcave" with a "batmobile" would fully appreciate them. Even the police just throw up their hands and turn on the Batspotlight. Which leads me to wonder, if I see someone dressed like a penguin reeking havoc on my city, who exactly is my city's costumed crimefighter? I mean, I want to make sure the "little tuxedoed psycho" is caught, but I sure don't want to approach someone dressed like a spider thinking he's our costumed hero only to find out he's some guy on his way to a costume party or, my luck, one of The Black Widow's henchmen...