Despite the strong support for exergy in thermodynamics, the industry still relies on energy based power plant efficiencies. The paper exposes errors with energy based efficiencies and improves the graphical representation of plants efficiencies. Among others, energy efficiencies cannot recognised that Combined Heat and Power (CHP) plant may be less efficient than condensing plants or that fossil fuel based plants should always be more efficient than any biomass plants because irreversibilities from biomass spontaneous thermo-chemical reactions are much higher than with coal or natural gas. Profitability equations fail to distinguish the true technical efficiency so exergy must be used, if only to enhance power plants understanding. Two novel graphs are introduced. Graph #1 combines all in a single graph; total, electrical and thermal exergy efficiencies. Graph #2 splits thermal exergy efficiency into two components related to; plant thermal losses and useful heat output quality. Data from 24 existing and design plants is used to support the graphs. Graph #1 shows different rankings of efficiencies than what is typically understood by the industry. Graph #2 shows that achieving further higher thermal energy efficiency barely increases the total exergy efficiency. If possible, it is better to increase the useful heat output quality. (C) 2015 Elsevier Ltd. All rights reserved.