More than 44% of building energy consumption in the USA is used for space heating and cooling, and this accounts for 20% of national CO2emissions. This prompts the need to identify among the 130 million households in the USA those with the greatest energy-saving potential and the associated costs of the path to reach that goal. Whereas current solutions address this problem by analysing each building in detail, we herein reduce the dimensionality of the problem by simplifying the calculations of energy losses in buildings. We present a novel inference method that can be used via a ranking algorithm that allows us to estimate the potential energy saving for heating purposes. To that end, we only need consumption from records of gas bills integrated with a building's footprint. The method entails a statistical screening of the intricate interplay between weather, infrastructural and residents' choice variables to determine building gas consumption and potential savings at a city scale. We derive a general statistical pattern of consumption in an urban settlement, reducing it to a set of the most influential buildings' parameters that operate locally. By way of example, the implications are explored using records of a set of (N= 6200) buildings in Cambridge, MA, USA, which indicate that retrofitting only 16% of buildings entails a 40% reduction in gas consumption of the whole building stock. We find that the inferred heat loss rate of buildings exhibits a power-law data distribution akin to Zipf's law, which provides a means to map an optimum path for gas savings per retrofit at a city scale. These findings have implications for improving the thermal efficiency of cities' building stock, as outlined by current policy efforts seeking to reduce home heating and cooling energy consumption and lower associated greenhouse gas emissions.