© 2015, The Author(s). In collider physics, jet algorithms are a ubiquitous tool for clustering particles into discrete jet objects. Event shapes offer an alternative way to characterize jets, and one can define a jet multiplicity event shape, which can take on fractional values, using the framework of “jets without jets”. In this paper, we perform the first analytic studies of fractional jet multiplicity Ñjet in the context of e+e− collisions. We use fixed-order QCD to understand the Ñjet cross section at order αs2, and we introduce a candidate factorization theorem to capture certain higher-order effects. The resulting distributions have a hybrid jet algorithm/event shape behavior which agrees with parton shower Monte Carlo generators. The Ñjet observable does not satisfy ordinary soft-collinear factorization, and the Ñjet cross section exhibits a number of unique features, including the absence of collinear logarithms and the presence of soft logarithms that are purely non-global. Additionally, we find novel divergences connected to the energy sharing between emissions, which are reminiscent of rapidity divergences encountered in other applications. Given these interesting properties of fractional jet multiplicity, we advocate for future measurements and calculations of Ñjet at hadron colliders like the LHC.