Analysis of Ship Combat Effectiveness

A long while ago we had a debate about the power of air units.  During the debate I performed an analysis of the power of air units used against some number of transports and destroyers.  Since all ships have an AA capability of 1, there was no need to consider whether the ships were destroyers or cruisers.  Battleships would change things a bit because of the “free hit.”  But the analysis gave us enough to draw a few conclusions.  Recently I played a game of Guadalcanal and I wondered about the true effectiveness of cruisers vs destroyers and/or battleships.  I decided to break out the pencil and paper and do an analysis.  I will post some answers when I have a few cases worked out.

BTW, when it comes to ships only, 2 cruisers (14 IPC) are better than 3 destroyers (15 IPC).  When you add air, that changes.  One Battleship is better than 3 destroyers too.

I’ve only computed a dozen or so including:

1 DD  vs  1 DD
1 DD  vs  1 CA
1 DD  vs  1 BB
1 DD & 1 Ftr  vs  1 DD
1 DD & 1 Ftr  vs  1 CA
1 DD & 1 Ftr  vs  1 BB
1 DD & 2 Ftr  vs  1 DD
1 DD & 2 Ftr  vs  1 CA
1 DD & 2 Ftr  vs  1 BB
2 DD  vs  1 DD
2 DD  vs  1 CA
2 DD  vs  1 BB
2 DD & 1 Ftr  vs  Something?
3 DD  vs  1 DD
3 DD  vs  1 CA
3 DD  vs  1 BB
3 DD  vs  1 CA & 1 DD
3 DD  vs  2 CA

Well, that’s 18 matchups so far.  Anyway, I expect to make a big post about it in about a week.  It started as a curiosity about whether 3 DDs (15 IPCs) were better than 2 CAs (14 IPCs).  It turns out that in a head to head matchup the 2 CAs are worth less than half an IPC more than the 3 DDs, but it is only because of the neglect of including air power.  While adding 1 Ftr to each side might still leave the CAs ahead, I suspect adding two or more Ftrs will give the DD force an edge.  One very surprising note is that while or course one DD vs one DD is even, if you add one Ftr to one DD, the other side gets the advantage in IPCs.  This is because the short sided team gets an opportunity to kill 8 IPCs but the heavy side only gets a chance to kill 5 IPCs and the short sided DD gets to shoot at the Ftr first.

Anyway, I am enjoying the exercise.

Yes, I am taking resilience into account.  Although can you ever really quantify the damage of having a cruiser sent back to the base card to take three turns to get back into the action?  On turn 4 in most games a damaged ship is as good as a kill.  When I award points for a damaged ship, I just give it the 2 IPCs it takes to repair it.  BTW, I am also taking into account the position on the battlebox for hits.  For example, when rolling four dice against three DDs there is a quirk in the damage chart.
1, 1, 2, 2 is a kill for all three ships, but
2, 1, 2, 1 is a kill for two ships and one damaged
Also, when the three DDs are rolling three dice at the CAs you can get the following possibilities:
2, 1, 2 is a kill for both cruisers, but
2, 2, 1 is one kill and one damaged cruiser
Things like this make it a very cumbersome calculation.

One more thing, before I said that when you add airpower to both sides of a 3-DD vs a-CA battle the DDs start to become strong.  I suspect it takes quite a bit of air power to make that happen.  The problem is that both sides start getting lots of AA dice when fighters are added to both sides.  Adding two fighters to both sides in a 3-DD vs 2-CA battle gives the DDs 7-AA dice and the CAs get 6-AA dice.  In most battles there wouldn’t be any air left to change the sea battle.

Here is a set of results.  I intend to edit this post a few times as I add more situations.  Check back every week or so.  Negative numbers are bad for the force shown in the second column.  D=destroyer, C=cruiser, B=battleship, f=fighter

0.00  D vs. D
0.61  D vs. C
2.85  D vs. B
0.94  D vs. DD
0.37  Df vs. D
0.76  Df vs. C
3.33  Df vs. B
2.09  Df vs. DD
-0.44 Dff vs. D
-0.36 Dff vs. C
-0.44 DD vs. C
2.65 DD vs. B
-1.69 DDD vs. D
-1.48 DDD vs. C
1.96 DDD vs. B
-0.40 DDD vs. CD
0.13 DDD vs.CC

Frimmel,

You make a good point about being able to rapid deploy a cruiser for the difference.  The difference of less than half an IPC can be misunderstood though.  The problem is that there is a good possibility that one side or the other will be wiped out (or effectively wiped out as happens when both DD get damaged, or one killed and one damaged, or of course, both killed).  There is a 4/36 chance both DD will “leave the board” against one CA, an 8/36 chance one DD is killed and an 8/36 chance one DD leaves the board.  There is a 12/36 chance the CA will be killed, and another 8/36 that the CA will leave the board.  So there is a (20/36 x 20/36 = 400/1296 = 31%) chance both sides will feel some loss of IPCs and have ships leave the board.  The more I look at the game, the more I conclude it is a series of big gambles.  That may capture the feel of the campaign for the real command decisions.  I still have a lot of matchups to work out.  The problem is that many of these won’t come up in a game.  It is the battle that includes a BB on each side, 3+ CA on each side and 4+ DD on each side, possibly with TRNs too, and lots of fighters that will be killed.