The Open Access Citation Advantage (OACA) has been a major topic of discussion in the literature over the past twenty years. In this paper, we propose a method to constitute a control group to isolate the OACA effect. Thus, we compared citation impact (MNCS) of 2,458,378 publications in fully OA journals to that (weighted MNCS) of a control group of non-OA publications (#10,310,842). Similarly, we did the same exercise for OA publications in hybrid journals (#1,024,430) and their control group (#11,533,001), over the period 2010-2020. The results showed that there is no OACA for publications in fully OA journals, and that there is rather a disadvantage. Conversely, the OACA seems to be a reality in hybrid journals, suggesting that a better accessibility tends to improve the impact of publications. The lack of OACA for publications in fully OA journals is to be expected, as a great proportion of OA journals are newly created and less attractive to high-impact senior researchers. Another striking result of this paper is the fall of the OACA from 2016. The citation advantage fell from 70% to 9% between 2016 and 2020 (for publications in hybrid journals). We wonder if this fall is linked to the increase in the notoriety of pirate sites (eg Sci-Hub) from 2016. In other words, the democratization of pirate sites instantly cancels the positive effect of OA publication insofar as the question of access to scientific content no longer arises.