This is extremely unlikely. Yes, there were 4 cases of Bell’s Palsy amongst vaccine people who received the Pfizer/BioNTech vaccine in their Phase 3 trial. This falls well within the normal incidence of Bell’s Palsy in the general population (calculations below if you want to keep reading). As it happens, there were none in the control group. This is likely a statistical anomaly, which you see when your sample size is too small to collect sufficient data points for the signal you are trying to detect—Bell’s Palsy is not common and the number of participants in the Phase 3 trial was too small to accurately measure its occurrence. Statistical anomalies appear real when you look too closely at small data sets. For instance, if you flip a coin you will inevitably get runs of either heads or tails, but the numbers of heads vs. tails will even out if you flip the coin enough times. If a run of heads or tails occurs early in your experiment and you stop the experiment immediately after the run, it will appear to favor either heads or tails over the other. This is why something called “statistical power” is important when designing trials. An underpowered trial may not detect truly rare events. The incidence of Bell’s Palsy is somewhere around 15-30 cases per 100,000 people per year. Let’s use the middle of that range (22.5) and run the numbers. The Pfizer trial followed 65,000 people for three months so 22.5/100,000 x 65,000 = 15 cases expected per year in that population; over three months (1/4 of the year) one would expect to see 3.6 (or 4) cases of Bell’s Palsy. Q.E.D.