Eco-efficiency is generally defined as the ratio of an economic and an environmental variable. This interpretation is also cited in connection to its most popular implementation, known as the "BASF eco-efficiency portfolio analysis". There is, however, something strange about this. A ratio is easily visualized as a slope, but BASF's method is working with a distance, which can be formulated as a weighted sum, not as a ratio. Upon closer analysis, it further shows that the two variables receive equal weight. These findings are contradicting the ISO 14045 standard and the perception in mainstream literature. We discuss the relevance of this shift of viewpoint. We also discuss some of the extensions, namely, the socio-efficiency analysis and the SEEbalance. We finally investigate the recent changes that were introduced in the eco-efficiency method, including an eco-efficiency index, and conclude that these changes have been reported in an incomplete way, or in documents that are difficult to trace. Effectively, this means that the most popular way to calculate and visualize eco-efficiency is unverifiable, impeding its status as a science-based method for sustainable industry support. We end by sketching the path forward.