There's more going on in a subway map than just tracing lines through stops. The most important quality of a transit map is that it be easily legible, even when glanced across a crowded rush-hour car. Looking at it, you should be able to figure out how this network of colored lines and pips translates to the real city outside, but geographic fidelity is often a secondary consideration.
Still, you might be surprised by just how inaccurate your local subway map is compared to the topographic truth of the city. Created by Benjamin Schmidt, an assistant professor of history at Boston's Northeastern University who we've written about before, this visualization warps the maps of three subway systems to overlay their actual city grids.
Not so surprisingly, Schmidt's visualization of New York City's subway reveals that the MTA has one of the more geographically accurate subway maps around: it's essentially accurate except for the orientation of its cardinal directions. Boston's MBTA also doesn't look too bad, only becoming truly mutated along the Orange and Green lines where the designers of the original map tried to make stops look closer together than they actually are.
The real freak show, though, is Washington, D.C.'s metro, which looks like a piece of Silly Putty stretched across a few miles. This almost certainly reflects the design of a subway map for a city where the majority of stations are outlying stops: as a rule, subway maps tend to distort more the farther away from the city center that you get. I'd imagine that you might even be able to tell how much a city's subway map was designed with urban dwellers versus suburb commuters in mind, just by seeing how much it distorts.
You can interact with Schmidt's geographically accurate subway maps on his official website here.
[Image: Washington D.C.'s Metro. Courtesy of Ben Schmidt]