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Battle Performance

The Scharnhorst is very much a standard battlecruiser, against cruisers you are a battleship; against battleships you are a cruiser. Her nifty 20 second reload with her main battery ensures enough firepower and keeps enemy cruisers at bay. Her excellent dipersion and Sigma 2.0 makes BBs and CA rethink their strategies when they go against her, even if the 28cm main guns are a bit lackluster against ships facing you directly with their bow. However, most ships (save for Tirpitz and Yorck) do not come close to be able to perform close-quarters with Scharnhorst.

Dispersion at 18km (against stationary Izumo)

Here we are going to talk about another important factor: 80mm-95mm of deck armour. Firstly, the historical value should be 50mm (TN: thank WG later). Secondly, Scharnhorst has an astounding 105mm-150mm of horizontal armour thickness in game, this has been tested out in-game : Des Moines can only effectively dish out 50% of damage with AP at ranges greater than 22km (>79mm of horizontal penetration) on a Scharnhorst facing bow on; even North Carolina with 170mm of horiztonal penetration at 26km can only do 50% of AP damage on the Scharnhorst, not one of them reached citadel in fact.
In theory, the Scharnhorst cannot be reliably penetrated by all but Yamato’s 46cm when faced head on in normal combat situations.
In level, turning away (exposing the deck armour) or turning in (exposing the waterline armour) on incoming shells, the Scharnhorst’s citadel cannot be effectively penetrated by any gun but the 46cm

Screenshots of the tests at different angles and distance with Yamato, Des Moines and North Carolina

It is apparent that no matter what situaion, the penetrating hits mostly deal half the damage or less and with no citadel hits.
All in all, Scharnhorst will be a tricky opponent both in firepower and protection

Tactics & Summary

ᆞWhen compared to traditional battleships, the quick-firing 28cm guns will be more capable at suppressing enemy cruisers , hence your main targets should be cruisers, then battleships.
ᆞIts 30 knot top speed enables it to excel in quick repositioning, whether it should be flanking or defending a collapsed flank.
ᆞStrong armour, torpedoes for close-range brawling and good main battery makes you more than confident against battleships.