This paper introduces and indicates how to deploy a novel energy metric, to be adopted for advanced monitoring and diagnosis of telecommunication central offices and data centers. Such an activity is motivated by the worldwide increasing telecommunication players awareness of the need to substantially reduce their energy demand, both to increase their market competitiveness and meet the stringent greenhouse gas emission regulations. The proposed metric, named utilization factor, was thus defined according to the peculiar energy breakdown of central offices. The aim was to conceive an index that focuses more on telecommunication energy adsorption and, in turn, enables climatic independent efficiency evaluation of the central offices under investigation. Then, suitable data-processing techniques were applied to develop a reliable utilization factor predictive model, whose identification and validation tasks were carried-out over an extended central offices database. The availability of a large amount of data was suitably exploited through data analytics approaches, particularly enabling diagnosis-oriented model development. Upon successful testing of its accuracy, the model was finally proven to be a strategic tool to perform model-based fault detection and isolation of relevant faults that may arise during central office monitoring tasks, such as abnormal data acquisition and non-optimal energy management. The suitability of the proposed metric, to be deployed as an innovative and synthetic energy index, was evaluated over an extended fleet of central offices and data-centers. It was found that the majority (about 70%) of tested central offices exhibits either adequate energy and thermal management or sensor-related only faults.