[en] Up to now, the Standard Model of elementary particle physics is in very good agreement with most data. However, it has various shortcomings which motivate the presence of new physics at the TeV scale. The first major step following a potential discovery of new particles at the Large Hadron Collider (LHC) is the determination of their intrinsic properties, foremost masses and spins. Event topologies of new physics signals with a conserved parity motivated by precision data and the dark matter paradigm require for sophisticated measurement procedures, which have been developed in recent years. These techniques often rely on simplifying assumptions, albeit they need not necessarily be fulfilled. In this thesis we investigate the impact of combinatorial and off-shell effects on new physics cascades in three different contexts. A detailed understanding of these effects is essential for the topic of model parameter determination of new physics signatures at the LHC. First, we study the non-resonant contributions of a broad gluino on mass and spin measurements as a prime example for the importance of off-shell effects. A phenomenological scan over the gluino's width-to-mass ratio yields a severe smearing of invariant mass distributions and as a consequence thereof drastically shifted endpoint positions. Spin determinations, on the other hand, are barely affected and a model discrimination of the two prime candidates SUSY and UED is not at risk. In the second part, we assess the feasibility of the gluino dijet endpoint measurement in three fully inclusive scenarios at the LHC to investigate the impact of combinatorial and SUSY backgrounds on its precise determination. We develop a method to disentangle two major signal contributions and extract their associated edges with good accuracy. For this we use existent kinematic variables and propose new ones to overcome the former's deficiencies. The last part governs the issue of so-called 'fake combinatorics', where distorted mass edges originate from additional particles with non-standard quantum numbers'' instead of false assignments of decay configurations. We study the contributions of exotic fermions within standard SUSY cascades, highlight their impact on affected invariant mass variables and discuss how their presence may be distinguished from ordinary, plain SUSY signals. (orig.)