Streetcar Mystery

Copyright ©2006 by Paul Niquette. All rights reserved.
Inspired by a riddle of unknown origin submitted by Kirk Rummel.

It ought to be plain how little you gain 
by getting excited and vexed.
You'll always be late for the previous train, 
and always in time for the next.
-- Piet Hein , poet and scientist (1905-1996)
Back in 1890, a certain courier made pick-ups and deliveries in a certain section of Brooklyn.  Every day, he would ride the streetcars that ran four times per hour along DeKalb Avenue between Flatbush and Broadway. 
In those days, two overlapping trolley services operated on the DeKalb tracks, which branched both north and south onto the Flatbush Line.  Every other car heading either south to Prospect Park or north to the newly opened Brooklyn Bridge. 
The courier always disembarked before Flatbush.  Over a period of many weeks, he noticed something strange: Though he boarded the streetcars completely at random, he would find himself riding on a Brooklyn Bridge car twice as often as one running to Prospect Park.
What is your explanation?