For each of the compounds MnTi2, FeTi2, CoTi2, NiTi2, PdTi2, PtTi2 and CuTi2, the differences between the total energies of the compounds in the MoPt2-, MoSi2- and NiTi2-type crystal structures are calculated. Trends of structural energy differences are analysed by performing 'frozen-potential' energy difference calculations and site-projected-energy analysis. Our analysis reveals that the Ti sites with icosahedral symmetry determine the structural stability in transition metal (TM)-Ti2 compounds. A connection with the stability of quasicrystal models is established.