The wording isn't correct though.
It's correct to say that 'more sober people are killed in accidents than drunk people', but that's not the same as saying 'sober people are more likely to be killed in accidents'. The first one tells you about the incidence, the second one says that being sober increases your risk.
If you want to judge the risk, you have to put the delta cases in relation to the vaccinated/unvaccinated population, because the vast majority of people in that age group is vaccinated.
Here's what it looks like for the 50+ age group in England (
source):
Population: 21,297,965 (100%)
2 doses: 19,611,831 (92.1%)
1 dose: 20,329,682 (95.5%)
0 doses: 968,283 (4.5%)
So, for every unvaccinated person in that age group there are 20 people that have received 2 doses of the vaccine. Now, if both the vaccinated and unvaccinated group had the same delta infection risk, you would expect to see the same 1:20 ratio among delta cases.
I
f you have 976 unvaccinated delta cases, you would expect to see 19,768 vaccinated delta cases if the infection risk was the same in both groups. But you actually only have 3,546 vaccinated delta cases.
These numbers suggest that the vaccine is 82.1% effective in preventing serious delta infections after 2 doses.