I think I’ve come up with an explanation clear enough to help everybody understand what exactly will happen in regards to tanking after the changes.
Each resistance component Rn, regardless of the origin, reduces damage taken by a (1 - Rn × Pn) multiplicative factor applied to the incoming damage, where Rn is the value of the resistance attribute of the component normalised to 1 and Pn is the stacking penalty applied to that component, if any.
For example, a non stacking penalised (P1 = 1) component with resistance attribute R1 = 30% = 0.3 reduces incoming damage by a (1 - 1 × 0.3) = 0.7 multiplicative factor.
The general formula is as follows:
dmg_taken = dmg_incoming × (1 - R0) (1 - R1×P1) (1 - R2×P2) …
where the first component R0 is the base resistance value provided by the ship, which may depend on ship bonuses and skills, but is not affected by the change.
Now, the effect of the change will be the multiplication of the Rn values in that formula by a 0.8 factor for the resists that are provided by mods affected by the change, e.g. if component 1 is affected by the change, but component 2 isn’t, the damage taken after the change will become:
dmg_taken = dmg_incoming × (1 - R0) (1 - 0.8×R1×P1) (1 - R2×P2) …
To see the relative effect of the changes on tanking, we need to divide (not subtract) the damage taken after the changes by the damage taken before the changes.
Since the effect of each component is multiplicative, the factors associated to components not affected by the changes cancel each other when doing the division, and only factors provided by components affected by the change remain, leaving the relative change in damage taken as follows, where now only terms corresponding to mods affected by the change are taken into consideration:
relative_change = (1 - 0.8×R1×P1) (1 - 0.8×R2×P2)… / (1 - R1×P1) (1 - R2×P2) …
which can be rearranged and written as follows:
relative_change = ((1 - 0.8×R1×P1) / (1 - R1×P1)) × ((1 - 0.8×R2×P2) / (1 - R2×P2)) …
This shows several things:
(1) the relative increase in the damage taken does not depend on the value of the resists provided by components that are not affected by the change
(2) the total relative increase in the damage taken is the product of the relative increase caused by each of the resist components affected by the change, which is given by the formula:
(1 - 0.8×Rn×Pn) / (1 - Rn×Pn)
where Rn is the resistance attribute before the changes, and Pn the stacking penalty, if any.
(3) the greater the number of resist mods affected by the change that are used for a given damage type, the greater the relative increase in the damage taken will be for that damage type
Also, the value of (1 - 0.8×Rn×Pn) / (1 - Rn×Pn) increases as the value of Rn increases, which leads to:
(4) the higher the resist, the higher the relative increase in the damage taken becomes
Let’s see some examples.
A non stack penalised mod with a 60% resist attribute affected by the change will cause the damage taken to be increased by a factor:
(1 - 0.8 × 0.6) / (1 - 0.6) = 1.3
which is a 30% increase in the damage taken caused by that mod alone.
If the resist attribute is 30% instead, the damage taken will increase by a factor
(1 - 0.8 × 0.3) / (1 - 0.3) = 1.086
which is a much lower 8.6% increase in the damage taken.
If we have the two mods above fitted and a stack penalty of 0.869 applies to the second, its effect on the damage taken would be modified to be:
(1 - 0.8 × 0.3 × 0.869) / (1 - 0.3 × 0.869) = 1.07
and the combined effect would be an increase in the damage taken by a factor of 1.3 × 1.07 = 1.391, i.e. a 39.1% increase.
So does this mean you won’t be able to do PvE content you could do before? Depends.
Fits that relied on high resist mods for tanking will take significantly more damage after the change, but it may not matter much if they were overtanked, as is often the case for battleships running L4 missions with good skills, for example.
You may have or want to change your fit, ship and/or tactics, so you don’t rely so heavily on resist mods for tanking, but in most cases you’ll still be able to run the same PvE content as before, just maybe not the same way you could do it before.
The problem will be high end PvE content for which no alternative to high resist fits exist or has been figured yet. CCP may need to make some adjustments to those in order for them to be doable again.