> If the vaccine was 90% efficient, you would expect the vaxed death to be 40%, not 84% (84% implies a 15% vaccine efficiency).

I'm not too sure how you arrived at your figures, but here's my back of the envelope calculation for the percentage of either expected deaths or expected cases coming from the vaccinated part of an age group:

  V * (1 - E) / ((1 - V) + (V * (1 - E))

where V is the percentage of the age group that's vaccinated (~95% for >70yo) and E is the effectiveness against either death or symptomatic disease (which isn't exactly the same as a case, I know), i.e. only (1 - E) of the vaccinated population will face death or symptomatic disease.

Playing around with the effectiveness values, 87% of cases and 84% of deaths from the vaccinated in the >70yo group doesn't look impossible.

If you have a population of 100 positive cases, 87 vaxed, 13 unvaxed. Let's assume the unvaxed death rate is 100% (it doesn't mater).

If the vaccine is 90% efficient, then 10% of the 87 vaxed will die, 100% of the 13 unvaxed will die, therefore the % of vaxed in the deaths will be (we are using the same formula) 10% * 87 / (10% * 87 + 13) = 40%

If the vaccine is 15% efficient, then 85% of the 87 will die, and the % of vaxed in the deaths will be 85% * 87 / (85% * 87 + 13) = 85%

You're using "efficient" to mean effectiveness against death given infection, but the vaccines aren't close to 90% effective against that. [1] says they're 54% effective against death given infection, which actually predicts 78% of deaths being in the vaccinated if you plug it in to the formula.

[1] https://assets.publishing.service.gov.uk/government/uploads/...