  We present a method to calculate the soft function in Soft-Collinear
Effective Theory to NLO for N-jet events, defined with respect to arbitrarily
complicated observables and algorithms, using a subtraction-based method. We
show that at one loop the singularity structure of all observable/algorithm
combinations can be classified as one of two types. Type I jets include jets
defined with inclusive algorithms for which a jet shape is measured. Type II
jets include jets found with exclusive algorithms, as well as jets for which
only the direction and energy are measured. Cross sections that are inclusive
over a certain region of phase space, such as the forward region at a hadron
collider, are examples of Type II jets. We show that for a large class of
measurements the required subtractions are already known analytically,
including traditional jet shape measurements at hadron colliders. We
demonstrate our method by calculating the soft functions for the case of jets
defined in eta-phi space with an out-of-jet pT cut and a rapidity cut on the
jets, as well as for the case of 1-jettiness.
