Fretting Fatigue (FF) has been considered as fatigue in a region of stress concentration due to the contact accelerated by mechanical erosion (possibly enhanced by metal transformations and/or chemical reactions in an aggressive environment). Whether the effect of erosion is significant or not is not clear. However, recently a more precise quantification of the effect of stress concentration has been attempted (some authors have used the terminology “crack analogue” and “notch analogue”). Most practical cases are concerned with finite stress concentration, so that a “notch analogue” criterion seems more appropriate, like for example in the Hertzian FF set of experiments like those on Aluminium alloy (Al/4%Cu, HE15-TF) by Nowell in the late '80s, and (A12024) by Farris in late 90s. Application of the “notch analogue” with a simple stress concentration criterion is usually overconservative for a notch (and indeed it is for the experiments considered, although it may not in general because of mechanical erosion effect in the FF case), so that “averaging” methodologies have been proposed where unfortunately the best-fitting averaging constant turns to be not just a material constant. In fact, in the present paper the “best fitting distance” is shown to be much smaller than what expected from existing Kf criteria.