Weighing The Fog Of Battle, Part II

For the background to this post see the previous post "Weighing The Fog Of Battle, Part I" [1] where I discuss MacKay et al's paper  Weighing the fog of war:Illustrating the power of Bayesian methods for historical analysis through the Battle of the Dogger Bank [2].

What I want to discuss here is the part of their model (as I read it, to the best of my ability) that deals with gunfire exchange knocking out turrets. The relevant data, for HMS Invincible (Indomitable at Dogger Bank) and SMS Blucher, is shown in the table below. The number of turrets is the number able to fire on the beam, and no I do not count cross deck firing by the Invincibles. This may differ from that used in [2], but I think is more appropriate. I could also quibble about the rates of fire, possibly 1.5 and 4 rounds/min per gun might be more appropriate, but I will leave that for now.

		Prob of Hit	Resilience	Gun Effectivness	Gun RoF (rounds per min)	No Turrets	Ship RoF (rounds per min)
	Invincible	0.03	0.38	0.3	2	3	12
	Blucher	0.05	0.43	0.27	6	4	48

Given a hit, the probability of a turret being knocked out is Resilience of defender times the Gun Effectiveness of the attacker (I commented on the inappropriateness of this in the earlier post).

I have set up and run a simulation of a single ship engagement between Invincible and Blucher and after a maximum battle duration of 20 minutes at maximum rate of fire, in 86 of the 100 cases simulated Invincible is reduced to zero turrets on the engaged side with Blucher having an average of 3.8 turrets remaining on the engaged side. In the remaining cases at 20 minutes Invincible has an average of 1.2 and Blucher 3.3 turrets remaining. Which is decisively in Blucher's favour, and this result can almost solely be laid at the door of the different rates of fire and hit probabilities.

(even with reduced effectiveness and fewer guns, which for convenience I treat as 3 twin turrets rather than two twin and two singles, with a slightly lower rate of fire per gun Scharnhorst reduces Invincible to zero remaining turrets within 20 min in 46 of 100 cases simulated with average numbers of turrets remaining ~2 and ~3 in Scarnhorst's favour in the remaining cases).

If we factor in the small (but unspecified) chance of a hit being disabling a ship, Blucher also has an additional advantage due to its greater rate of fire.

References:
1. Larham R., Weighing The Fog Of Battle, Part I,  http://navalwargames.blogspot.co.uk/2017/08/weighing-fog-of-battle-part-i.html
2. MacKay N, Price C, Wood J, Weighing the fog of war:Illustrating the power of Bayesian methods for historical analysis through the Battle of the Dogger Bank, Historical Methods 2016 49 (2)  pp80-91