In their important and innovative study, Dagan et al. (2021) were the first to provide evidence on the effectiveness of BNT162b2 mRNA Covid-19 vaccine on a large scale population. The authors used a matched pair Israeli sample of 596,618 individuals belonging to the vaccinated group and 596,618 individuals with similar characteristics belonging to the unvaccinated group. Based on the information obtained in Figure 2 of Dagan et al. (2021) on cumulative events 14, 21 and 28 days after the first dose, the authors of this Note found inconsistencies between the calculated effectiveness of the dose from Figure 2, and the reported effectiveness rates in Table 2. Compared to the effectiveness rate reported by Dagan et al. (2021), and referring to the criteria of: documented SARS-CoV-2 infection, symptomatic Covid-19 and severe Covid-19, 14-20 days after the first dose, according to the CDC formula, our calculations suggest an elevated effectiveness of the vaccine ranging between 1.75%-4.67%. Referring to the criteria of Covid-19 hospitalization and death, 14-20 days after the first dose, our calculations suggest a reduced effectiveness of the vaccine ranging between minus 2.77% and minus 2%. Given the widespread public vaccination resistance, transparency and accuracy in vaccination effectiveness might prove to be especially important. As of October 31, 2021, the official accumulated Covid-19 cases are 247,376,970 and deaths worldwide are approx. 5 million persons. Consequently, the implication of a 2% gap after 21 days is 4.947 million cases and 100,000 deaths.