Ejection fraction (EF) is considered to provide clinically useful information. Despite its enormous popularity, with more than 75,000 citations in PubMed, only few studies have traced the origin(s) of its foundation. This fact is surprising, as there are perhaps more papers published that criticize EF, than the number of publications that actually provide a solid (mathematical) basis for its alleged applicability. EF depends on two volume determinations, namely end-systolic volume (ESV) and end-diastolic volume (EDV). EF is defined as 1-ESV/EDV, yielding a metric without physical units. Previously we formulated a robust analytical expression for the nonlinear connection between EF and ESV. Here we extend that approach by providing a formula to illustrate that EF is strongly associated with half the sum (HS) of ESV and EDV. HS is not new, but forms a major component in the recently introduced Global Function Index. For 420 heart failure (HF) patients we found for left ventricular angio data: R(ESV, eDv) = 0.92, R(EF, ESV) = -0.90, and R(EF, HS) = -0.65. For echo (33 HF patients stages A, B, C and D): R(EF, HS) = -0.82. For the right atrium (CMRI in 21 acute myocardial infarction patients): R(EF, HS)=-0.65. For the left atrium (N=86) R (EF, hS)=-0.46. ESV indicates the level to which the ventricle is able to squeeze blood out of the cavity via pressure build-up. In contrast, EF refers to relative volume changes, not to the mechanism of pumping action. We conclude that for each cardiac compartment EF borrows its acclaimed attractiveness from the fact that for a wide patient spectrum the ESVand EDV correlate in a fairly linear manner. Attractiveness of EF features a straightforward mathematical derivation, rather than reflecting underlying physiology. Clinical Relevance - Ejection fraction (EF) is found to reflect (mean) ventricular / atrial size, and is primarily associated with end-systolic volume, which variable in turn highly correlates with diastolic volume. As a mathematical construct, EF has little affinity with 'function', which is a central concept in physiology.