Fletcher Pratt Pt 3 (what I think is wrong with the FP ship points)

In the previous post we saw the rather complicated looking formula for the ship points value. This is essentially the (standard) displacement in tons plus a term containing all the factors that I presume Fletcher Pratt thought contributed to ship staying power multiplied by the ship speed factor (10 plus half the speed in knots). My main complaint about this formula is that it has factors contributing to staying power that do not so contribute and other terms contributing which are accounted for elsewhere in the FP system.

Contribution of Speed to Staying Power
I will begin by considering the ship points value dependence on speed, I will conduct a sort of though experiment setting up a pair of hypothetical ships that differ only in maximum speed. These we would expect to have the same staying power since maximum speed contributes to a ships value in terms of its ability to choose the terms of engagement and possibly being more difficult to hit both of which are represented elsewhere in the FP system. Let us use LaArgentina as the subject of our thought experiment (since the ship data and calculations for its' points value can be found in both [1][2]. The points value for la Argentina may be written: \[{\rm{PV}}=668 \times \left( \frac{V}{2}+10\right)+6000\] where the \(668\) is the first bracketed term in the formula given in the earlier post [3],  \(V\) is the speed in knots and the \(6000\) is the standard displacement in tons. We suppose we have a pair of variants of this design which differ only in the efficiency of their main machinery which consumes the same fraction of displacement for both. We suppose that the first with the more efficient machinery can make a maximum speed of 32kts and the second with the less efficient machinery can only make a maximum speed of 29kts. This results in a difference in points values of \(668\times 1.5\) or about \(1000 \). Which is about 1/23rd of the actual points value of the 31kt La Argentina given in the references. The point is these ships are identical in all respects that effect the consequences of hits, but one is able to survive two more 6" gun hits than the other.

This speed dependence in points value may seem trivial but it is a matter of principle, we are making the ship points value formula more complicated to reflect a factor that should not be there in the first place. But you might say John Fisher said that speed is armour! Well he may have, and he may have had a point (though that is arguable when it is bought at the expense of other military features) but the contribution of high speed to survival is via the greater difficulty of hitting a fast ship (speed and so turn rate makes a ship a more difficult target for the opposition fire control systems). This difficulty is already represented in the range estimation in the gunnery system so is in effect being double counted.

Contribution of armour and armament to Staying Power
The first bracketed term in the points value formula contains a number of terms (all with positive coefficients) that depend on the number and size of the weapons that comprise the main and secondary batteries, and the numbers of other weapons and on the thickness of any protective armour in the belt, deck and on the main gun emplacements.

What is strange here is that the weapons if anything detract from a ships staying power, effectively adding extra vulnerabilities in the form of magazines and other ammunition storage and fueling systems. An argument could be made that the signs with which all the factors appear is wrong they should be negative factors rather than positive.

That armour contributes to staying power might be though a no-brainer, why provide it if it does not help a ship survive combat? However we again have a case of double counting the contribution of a feature. The armour thickness already modulates the effect of a hit, a hit does more damage if it penetrates the relevant armour than if it does not, and does yet more damage if the target is unarmoured. In rule design we should try to avoid this type of double accounting. the effects of a feature should if possible only appear at one place in a set of rules.

Summary
Every part of the FP points value formula other than the displacement term  is at best questionable if not obviously wrong. What the formula might represent is some form of cost or value of the ship, but not its' staying power.

References
1. Curry J., Fletcher Pratt's Naval Wargame, History of Wargaming Project, 2011
2. Featherstone D. Naval War Games, Stanley Paul, London, 1965, ISBN 0-09-076581-8
3. Larham R., Fletcher Pratt Wargame Pt 2, http://navalwargames.blogspot.com/2011/06/fletcher-pratt-wargame-pt-2.html