What is the point of armor piecing shells fired from destroyers?

AP shells do a lot of damage if they penetrate (but not over-penetrate), but if they don't, then it's better to use high-explosive shells because they reliably do mediocre damage and can set the enemy on fire.

So, in case of destroyers, if you use AP shells:

• against battleships or heavy cruisers, your shells will just bounce off their armor, causing zero damage.
• against destroyers or light cruisers, your shells will over-penetrate, doing less damage than HE shells.

Maybe there are a few light cruisers where AP shells could be effective, I didn't yet find any.

So, are there situations when it makes sense to fire AP shells from destroyers?

Solution 1:

There's a few criteria to consider when thinking about switching to AP in a destroyer:

1. Enemy angle. You need a nearly perfect broadside to get effective hits on anything that has more than the thinnest armor.
2. Shot location. Don't shoot a battleship's belt armor with your destroyer AP. Hit the superstructure instead.
3. Ship line. Soviet and German destroyers both have AP with high enough penetration to do significant damage.
4. Range. You likely shouldn't bother with AP in a destroyer unless you're within about 6-8km of the target, depending on the ship. The shells don't retain penetration power over long distances very well.

Remember that when gun-boating in a destroyer, you're always going to be aiming for giving your enemy a 'death of a thousand cuts'. You'll never see huge numbers with destroyer AP, but firing salvos that do 2-3k damage every 5 seconds or so really adds up.