One of the central questions of materials science is which crystallographic structure a certain alloy or compound will adopt as a function of elemental composition, pressure and temperature. This question can be traced back all the way from the Bronze Age via the first steel makers of the Middle Ages and the metallurgists of the 19th century to the present day. Experiences drawn from centuries of alloy making have given rise to well-established rules of thumb for alloy development and detailed phase diagrams for equilibrium conditions. However, a rigorous theory for single-phase alloys out of equilibrium is less well established. This study employs state-of-the-art electronic structure calculations based on density functional theory to tackle this problem. This method employs a reformulation of quantum mechanics to solve the many-body Schrodinger equation that describes the system. In our case, the system is a titanium alloy, where titanium is substitutionally alloyed with elements such as aluminium, chromium, vanadium and molybdenum. We find that chromium and vanadium stabilise the β phase, while scandium destabilises it. The strength of this effect is directly proportional to the additional d-electrons present in the alloying element. The effect appears to be additive, and the positional effects of the alloying atoms appear to be small. Using the results from the calculations we can construct new phase diagrams and equations of state for these alloys. This gives us a theoretical confirmation for established rules of thumb and provides us with new insights when constructing new alloys.