Modern orthopaedic implants use lattice structures that act as 3D scaffolds to enhance bone growth into and around implants. Stochastic scaffolds are of particular interest as they mimic the architecture of trabecular bone and can combine isotropic properties and adjustable structure. The existing research mainly concentrates on controlling the mechanical and biological performance of periodic lattices by adjusting pore size and shape. Still, less is known on how we can control the performance of stochastic lattices through their design parameters: nodal connectivity, strut density and strut thickness. To elucidate this, four lattice structures were evaluated with varied strut densities and connectivity, hence different local geometry and mechanical properties: low apparent modulus, high apparent modulus, and two with near-identical modulus. Pre-osteoblast murine cells were seeded on scaffolds and cultured in vitro for 28 days. Cell adhesion, proliferation and differentiation were evaluated. Additionally, the expression levels of key osteogenic biomarkers were used to assess the effect of each design parameter on the quality of newly formed tissue. The main finding was that increasing connectivity increased the rate of osteoblast maturation, tissue formation and mineralisation. In detail, doubling the connectivity, over fixed strut density, increased collagen type-I by 140%, increased osteopontin by 130% and osteocalcin by 110%. This was attributed to the increased number of acute angles formed by the numerous connected struts, which facilitated the organization of cells and accelerated the cell cycle. Overall, increasing connectivity and adjusting strut density is a novel technique to design stochastic structures which combine a broad range of biomimetic properties and rapid ossification.