Conclusion

The very recent announcements by Moderna and Pfizer give some hope of coping effectively with the pandemic. Their performances in terms of efficacy do not differ much, with the Pfizer's one performing somehow better, definitely more that the bare numbers spread around by the media (“94.5% vs 95%”) would suggest.

Obviously, our results and our distributions depend on the very few data publicly available and on very simplifying assumptions, since there are many other variables that play important roles in considering which of the two is `better' or `more promising' in order to fight the pandemic, and on which we do not even try to enter, because they go far beyond our field of expertise. In fact, we wish to stress that our contribution is mainly methodological, even considering that further announcements will follow, as we strongly believe that a correct communication of a scientific result must clearly state its uncertainties, both in the official publication and (especially) in the press releases, avoiding to add excessive decimal figures that can be misinterpreted by lay people (and not only) as a very sharp result. Moreover, as far as questions of practical interest are concerned, the uncertainty on the efficiency, possibly reported in detail by a probability distribution of its possible values, is without doubt important to develop realistic quantitative models and what-if scenarios of the development of the pandemic, once a part of the population has been vaccinated.