The energy conversion in solar cells has conventionally been limited by the Shockley-Queisser limit. Singlet fission (SF), a decay mechanism where a single excited singlet state is converted into two triplet states, can drastically improve this efficiency. For the most part, observation of SF has been limited to crystalline structures in solids and films, where strong ordering was present. Here we report on singlet fission in a disordered system where organic chromophores are distributed on the surface of a rare gas cluster. In this case, the intermolecular distances and degree of excitation can be varied to obtain their effects on the rate of singlet fission. We introduce a kinematic model that takes into account the details of the geometrical arrangement of the system as well as the time-dependent populations of the relevant states of each molecule and evaluate the trends obtained by SF on the experimental observables.