Talk:Type 91 Armor Piercing Shell/@comment-3213090-20151203040927/@comment-26486243-20151218165935

If we assume your battleship is at firepower cap so that the additional FP from this isn't a factor:

Main Gun + Main Gun + Radar + Seaplane 120% dmg * 2 Otherwise 100% dmg * 1

Main Gun + Main Gun + AP Shell + Seaplane: 162% dmg * 1 Otherwise 130% dmg * 2 Otherwise 108% dmg * 1

The case where AP Shell becomes a liability relative to not having it at all applies only when comparing 162% dmg vs 120% dmg * 2. When enemy armor roll = 243, AP shell cut-in does 1 damage. When enemy armor roll = 180, Double attack does 1 damage. 243-x > 2(180-x) 243-x > 360 - 2x x > 117

Therefore, it is a benefit in the highest-frequency trigger when the enemy rolls an armor value greater than 117. It is a liability in the highest-frequency trigger when the enemy rolls an armor value of 116 or low. However, at armor value 117, the damage dealt through both attack types is 126. Therefore, for it to ever be a better idea to carry a radar instead of an AP shell in pure damage numbers, you need to hit something that rolls an armor value significantly lower than 117 and yet has much more than 126 health.

The list of targets fulfilling this requirement are as follows: Wa-Class Flagship Transport, Anchorage Princess/Demon, Armored Carrier Princess/Demon, Southern Demon, Southern War Demon. Against all other boss-class targets the AP shell is superior, and against fodder it doesn't matter whichever you use since you'll sink it anyway.

We are, however, ignoring completely the fact that AP shells also trigger a higher damage double attack at a lower rate, and that even single attacks hit harder when AP shells are equipped.