The Jahn-Teller (JT) distortion that can remove electronic degeneracies in partially occupied states and results in systematic atomic displacements is a common underlying feature to many of the intriguing phenomena observed in 3d perovskites, encompassing magnetism, superconductivity, orbital ordering and colossal magnetoresistance. Although the seminal Jahn and Teller theorem has been postulated almost a century ago, the origins of this effect in perovskite materials are still debated, including propositions such as super exchange, spin-phonon coupling, sterically induced lattice distortions, and strong dynamical correlation effects. Although the end-result of JT distortions often include a mix of such various contributions, due to coupling of various lattice, spin, and electronic modes with the distortions ("fingerprints", or "consequences" of JT), it is not clear what is the primary cause: Which cases are caused by a pure electronic instability associated with degeneracy removal, as implied in the Jahn-Teller theorem, and which cases originate from other causes, such as semiclassical size effects. Here, we inquire about the origin and predictability of different types of octahedral deformation by using a Landau-esque approach, where the orbital occupation pattern of a symmetric structure is perturbed, finding if it is prone to total-energy lowering electronic instability or not. This is done for a systematic series of ABX3 perovskite compounds having 3d orbital degeneracies, using the density functional approach. We identify (i) systems prone to an electronicinstability (a true JT effect), such as KCrF3, KCuF3, LaVO3, KFeF3 and KCoF3, where the instability is independent of magnetic order, and forces a specific orbital-arrangement that is accommodated by a BX6 octahedral deformation with a specific symmetry. On the other hand, (ii) compounds such as LaTiO3 and LaMnO3 with delocalized d states do not show any electronically driven instability. Here, their octahedral deformation mode results from coupling of lattice mode with semiclassical sizeeffects (sterically induced), such as BX6 octahedra rotations. (iii) Although RVO3 (R=Lu-La, Y) perovskites exhibit similar hybridizations as LaTiO3, their t2g 2 electronic structure is highly unstable and ABX3 (X=O, F) perovskites 1,2 show a number of systematic atomic distortions relative to the ideal cubic perovskite structure: the one made of corner-sharing, vertically positioned, all parallel BX6 octahedra with equal B-X bonds. The interpretation of much of the electronic and magnetic phenomenology surrounding such perovskites 1,2 , including superconductivity, colossal magnetoresistance, orbital ordering and metal-insulator transitions is intimately related to the understanding of the causes vs. consequences of the observed atomic distortions. Usually, distortion in ABX3 perovskites produce inequivalent B-X bonds length, such as the Q2 motion (cf. Figure 2 of Ref. 3 ) that differentiate bond length along the x and y directions. These exist either as in-phase motions ...