AFAIK, I cited a RATE or a likelihood of getting a symptomatic infection, not an endpoint as to what % of the total population might get infected. There is a slight correction to the likelihood (rate) of getting infected in the early stages of vaccination/pandemic infection saturation before herd immunity sets in. I did not allow for the % of asymptomatic cases in the unvaccinated population. So with that allowance, vaccination can be said to reduce your chances by 1/26 of those infected of getting a SYMPTOMATIC COVID-19 infection out of those that might be infected in the total population. Here’s the reasoning.
I think for the study statistics that we’re dealing with and for the study to be meaningful, one has to assume, as the researchers undoubtedly did, that both the experimental vaccinated arm and the control unvaccinated arm of the field tests were populations ~equally exposed to coronavirus.
The numbers that you cite are because in both the experimental and control arms the vast majority of participants were probably never exposed to COVID - so just to be clear, getting vaccinated did not reduce the chance of getting COVID to only 0.04% - the incidence of COVID in the vaccinated experimental arm. The estimate of how many people can be infected but never develop any symptoms is ~24% (and ~35% of cases transmitted by others BEFORE they develop symptoms). 59% of COVID Cases Stem from Asymptomatic Spread (webmd.com) So ~75% of all people exposed and infected develop symptoms eventually. Since given enough time, without a vaccination program, ~everyone will be exposed to COVID and presumably infected***. So out of 100 people infected, 76 would show symptoms. Vaccination reduces those infected showing symptoms by 1/20. So if everyone were vaccinated and then exposed to COVID-19, only 3.8 people out of 100 infected would be symptomatic. That’s ~1 chance in 26 of showing symptoms if vaccinated and then infected.
The two assumptions here are that ~everyone is susceptible to an infection, asymptomatic or symptomatic, without vaccination and the observation that vaccination reduces the rate of symptomatic cases by a factor of 20. Two things that would alter the calculation is if less than 100% of the population can be infected because some individuals don’t have the type of cell receptor that the virus spike protein can attach to, for instance, or the fact that as 70% to 90% infection/vaccination of the population is approached, even the infection of non-vaccinated individuals will slow and they’ll be protected by herd immunity and lack of viral transmissibility, not their own degree of immunity.
So perhaps it’s more correct to say during the early stages of vaccination before herd immunity is approached, being vaccinated would reduce your chances(rate of) symptomatic infection to 1 in 26 of out of all people infected. AFAIK, most modeling presumed that close to 100% of the naïve population is susceptible to coronavirus infection and the vaccination results show, unless you want to write them off as defective vaccine injections, that the vaccine reduces but does not eliminate your chances of getting a symptomatic COVID-19 infection. The best news is that vaccination reduces the chances of having a very serious infection requiring hospitalization or a lethal infection by 5x more (by a factor of 1/100).
I didn’t claim anything about what vaccination means to the relative number of asymptomatic cases. It would seem likely that the proportion of asymptomatic cases increases amongst those vaccinated relative to symptomatic cases and that would lessen the impact of vaccination if a larger proportion of people are now asymptomatic but still capable of transmitting virus to others and passing it forward.
***Since antibodies to the common cold wear off with time over a period of many months to years and the human population has never seen this coronavirus, it’s reasonable to assume that ~everyone is susceptible to infection, asymptomatic or not. In initial antibody surveys in California during early stages of the pandemic, less than 5% of the population had neutralizing antibodies against the virus.
EDIT: WITHOUT VACCINATION, only another 7% more of the U.S. population would be expected to be exposed to COVID-19 in the coming 2021 year - that’s assuming wearing masks and social distancing continues on, which offers protections to people, whether vaccinated or not. 0.07 x 330 million (U.S. population) = 23.1 million cases if ~all exposed get infected. When will COVID-19 vaccines start to make a difference? | Live Science