Comments on Chapter 10 of The Fletcher Pratt Book, Pt I

Preamble
There are many points in Chapter 10 "The Fletcher Pratt Rules and Reality" of [1] where questionable claims are made. Before I start dissecting the chapter I should say that I am in general agreement with the thesis of the chapter that the Fletcher Pratt wargame Rules (FPWGR) are not a valid model of naval warfare for the 1914-1945 period, not even when restricted to surface actions. Some of my reasons for claiming this are reported in other posts in this blog, and other will be reported in future. However I also believe that there are ideas in the FPWGRs that are intrinsically interesting and potentially educational, these are reported (or will be) elsewhere. I should also state that Michael Vlahos's book Blue Sword [2] might clear up most of the questions about the influence of the FPWGRs on US Naval doctrine as it covers the history of wagaming at the Naval War College over the relevant period, however I have not yet located a copy at an affordable price so its analysis must wait for another occasion (if the History of Wargames Project could re-publish it I would be the first in the queue to buy a copy).

Phil Barker's Remarks and John Curry's Comments on Them
I wish to start in this post by discussing the very opening paragraphs. We start with a quote from an article by Phil Barker published in The Nugget in 2006:

This is one of thoe legendary systems that everyone has heard of but very few played with. Since the author is long dead, there is no chance of hurting his feelings and I can mention his rule set is credited in some USN circles with being responsible for many of the initial defeats in the Pacific in WW2. It would not have been a bad set for refighting Jutland (though in fine weather and unrestricted visibility), but its concentration on gunnery of the fighting line at extreme range and downplaying of the surface ship torpedo led to tactical mistakes made fatal by the Long Lance torpedo.

John Curry then observers that Phil is not a Naval expert but claims his anecdotal report carries weight because he is an older guy who has been involved in wargaming for a long time. This is an argument from authority (by proxy), that is hearsay carries weight because of the indirect authority of the reported. We can therefore discard this as evidence without further consideration. However I am not going to do that because John in the next paragraph points out the apparent value place on the game just before and during WW2 by the Naval War College and this is a documented report (Time Magazine 1939, but I think I would like to see the item myself).

Analysis of Removal of TT from US Heavy Cruisers
The doctrinal problem that we are discussing is the belief that cruisers (other than those intended to work with destroyers) would not engage in surface combat at ranges where torpedoes could be used, and therefore were more a liability than an asset on heavy (and large light) cruisers. The story told at [3] is that this belief was a result of wargaming studies conducted at the Naval War College. This may also have been because due to the low rate of fire of the 8" gun these cruisers were vulnerable at night and poor visibility to fast moving targets such as destroyers [4] (and also to the high rate of fire of 6" gun cruisers). Also, as [4] also claims, that during construction (of the Pensacola and Salt Lake City) it became evident that they would be able to accommodate director fire control. This presumably pushed the expected effective range up from ca 10000m to possibly in excess of 20000m (the range of their guns was in excess of 28000m). Looking at the photo of Pensacola as complete in[4] it is evident that she was completed with spotting tops but no DCT.

We can establish an indicative timescale for the wargaming that lead to these decisions by looking at the completion dates of the first four groups of US treaty cruisers. The Pensacolas were designed and completed with torpedo tubes, as was the succeeding Northampton class. The next class (Portland) had the torpedo tubes deleted in the course of design (I find this an ambiguous term, what we can say with certainty is that they completed without tubes), so presumably this is some time between the freezing of the design of the previous class and the completion of Indianapolis, the first of the Portlands to complete. This puts the date of the decision somewhere between 1929 and early 1932. Thus we can probably date the wargames to no later than 1931 and possibly as early as 1929.

Comparison of the Time Line of Removal of Cruise TT and that of the FPWRG
As we have seen NWC studies had concluded that US treaty cruisers would be vulnerable at night and in poor visibility to light forces and so as they would outrage them in better conditions they would not be used under these circumstances and so did not need torpedo tubes (may be a bit of interpretation on my part here, and it still sounds ludicrous to me but I have seen similar behaviour in modern times so.. ). These conclusions were drawn before 1933.

In [1] we discover that Fletcher Pratt claims to have written the first version of his rules in 1928, but not shared them with his friends until 1933. If this is accurate then I rest my case the FPWGR could not have been the rules used in the NWC games supporting the removal of TT from US heavy cruisers, and so the doctrinal errors were probably in place before the NWC ever saw the FPWGRs.

(The reader will note that unlike Phil Barker I have no qualms about possibly hurting peoples feelings, though will be upset when mine are hurt be someone pointing out the faults in my arguments, but that is war(gaming) for you :).

References
1. Curry, J., Fletcher Pratt Naval Wargame, the history of wargames project 2011
2. Vlahos, M., Blue Sword, Naval War College 1980.
3. CA-32 New Orleans, http://globalsecurity.org/military/systems/ship/ca-32.htm
4. Conway's, All the World's Fighting Ships 1922-1946, Conway Maritime Press 1980.

Test page for using MathJax for LaTeX on Blogger

There is a javascriptb block containing:

<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript">
</script>

in the HTML source on this page which causes the rendering of LaTeX using MathJax the delimiters are slash( and slash) for inline maths and slash[ and slash] for display maths. (the slash is the \ character which if I used it would lead to confusion)

This is inline with tex \tex in square brackets delimiters [tex] 4\times \sin(x^2) [/tex] these are set up as alternate delimiters using the guidance on the MathJax site.

Some continuous text with inline maths \( \sin(x)^2 \) some more text. Now a display equation (in a bigger font!):

\[ \int_0^3 f(x)\; dx=7 \]

Now display maths between Tex \Tex delimiters:

[Tex]\int_1^2 g(x)\; dx =17 [/Tex]

The JavaScript block can be placed in the template html rather than at the top of each post.

(Looks like the Tex delimiters only display correctly on chrome! Better switch any posts over to delimiters that will work on any browser. Other sources indicate that the problem may well be with Internet Exploder rather than anything else)

Fletcher Pratt Pt 4 (what I think is wrong with the FP Gunnery/Damage models)

The basic model of damage from gunfire is attritional. Each hit contributes a number of points of damage (which is modulated by armour penetration ..) and the loss of fire power and speed of the ship is proportional to the fractional damage (the points damage received divided by the ships points value). This is a perfectly acceptable model if that is how you want to represent accumulated damage in the game (in my opinion it is not the most suitable model for gaming but that is another story)

In addition to the attritional damage if in the measuring up in the gunnery round a shell is deemed to have fallen on a gun position (assuming the ability to penetrate the local armour) that gun position is deemed knocked out. There are at least two problems with this, the first is that this means that the conditional probability of a gun position hit is the ratio of gun house plan area to deck area of the ship which may be OK-ish at long range but will be wrong at shorter ranges. Secondly it is inconsistent with the attritional model of ship damage effectivly double counting the guns when it comes to taking damage. In addition we could ask why we do not apply the same method to machinery spaces.

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