In the scenario of one battleship againts four destroyers there is clearly an imbalance. I designed the battleship specifically as a destroyer killer. 4x11" main guns (to save weight for the smaller guns) + 14x7" + 14x4". Thefore my broadside was a total of 14 guns of 7" and 4" calibre. My battleship fired like a machine gun almost never hitting anything. At a combat distance of 2.5 km on average this is not reallistic. If both ships maintain a steady course as it was the case the battleship director system should find the mark not later than in the tenth salvo in the worst of cases (I am assuming the battle is taking place with 1905 to 1910 technology, this is not clear in the scenario). This was the first problem.
I was using HE ammunition. With this, even an 11" near miss shell creates an explosion that affects the superstructure, possibly the hull and certainly the exposed crew of a destroyer. Eventually there where hits, and many wrong things happened in my opinion. Those destroyers seem to be small units of 500 to 700 metric tonnes (again assuming 1905 to 1910 technology). However I needed more than ten impacts to really cripple one of such units. Remember some of those impacts correspond to 7" (175mm) HE rounds. The hull is penetrated, upper structures damaged, conducts of the chimneys broken (affecting efficiency of engines), fire started on several places, engines, boilers and pumps damaged, bulkheads bent of broken, pipes, electric and hydraulic circuits cut off, and a point is reached where fire cannot be contained (particullarly on those times where firefighting systems where primitive), flooding cannot be stopped and the destroyer either sinks, burns or at least stop being funcionall and retires from the battle (if it can do so). However there where destroyers with 75% damage on superstructure and 70% damage on the hull (flooding) that remained fully operative, running at full speed (totally impossible with such level of damage) and firing back.
And on the other side of the battle, the battleship was receiving an average of 1 to 5 impacts per second of 4" and smaller shells that cripled the battleship to a 50%. The battleship ended with severe flooding caused by 4" shells penetrating somehow an 11" of armoured belt, fire everywhere, the main towers, also with 11" frontal armour, broken down sometimes. Of course the fire director system of the destroyers, that should be far far more simply than that aboard a battleship and should have been seriously affected by the severe motion of the ships (rolling and heaving) was extremenly precise. My feeling is that 40 to 50% of their shots where actual hits.
The power of the destroyers was awesome. I have described the scenario where I won. On the first two tries the destroyers almost sunk me by gunfire alone.