[@hosten2008; @zhou2012; @ben_dixon2009; @pfeifer2011; @howell2010_freq; @egan2012; @xu_guo2013] to reveal tiny changes of a variable of interest. In all those cases, a priori sensitivity limits were not due to the quantum nature of the light used ([*photon statistics*]{}), but instead to the insufficient resolution of the detection system, what might be termed generally as [*technical noise*]{}. WVA was a feasible choice to go beyond this limitation. In spite of this extensive evidence, “its interpretation has historically been a subject of confusion" [@dressel2014]. For instance, while some authors [@jordan2014] show that “weak-value-amplification techniques (which only use a small fraction of the photons) compare favorably with standard techniques (which use all of them)", others [@knee2014] claim that WVA “does not offer any fundamental metrological advantage" , or that WVA [@ferrie2014] “does not perform better than standard statistical techniques for the tasks of single parameter estimation and signal detection”. However, these conclusions are criticized by others based on the idea that “the assumptions in their statistical analysis are irrelevant for realistic experimental situations” [@vaidman2014]. The problem might reside in

Here we make use of some simple, but fundamental, results from quantum estimation theory [@helstrom1976] to show that there are two sides to consider when 