ORIGINAL: Local Yokel
I wouldn't want to place much reliance on an analysis based on the data presented in stuman's link. It's interesting, but there seem to be some errors that may well skew your results.
To begin with, I can see no mention of Hyuga, sunk by air attack at Kure in July 1945.
Furthermore, there are some inconsistencies in the data presented. In particular, HM Ships Valiant and Queen Elizabeth are included amongst the sinkings by virtue of de la Pene's brilliant attack, notwithstanding that they were raised and returned to service (of course, they were never really sunk because ABC had the band playing on the quarter deck the day after the attack [;)]). Paradoxically, neither Caio Duilio nor Littorio appear in the list of ships sunk in port, notwithstanding that after the Taranto attack a bandsman could only have blown bubbles through any wind instrument on Caio Duilio's deck.
I reckon the Germans got about the best value they could from their 'fleet in being' stratagem, given the land-centric nature of their war. When you look at the extent of the Allied assets tied down by their modest outfit of heavy units, the mode in which these were employed looks like good value for money. The same goes for the U-boat campaign.
The problem with a 'fleet in being' strategy is that the point is reached when the preponderance of the opposing forces becomes such that it is treated as the paper tiger it has become. Had they the logistical means to do so, it appears that in 1942-43 the Japanese still had the potential to impose a serious setback upon the American advance across the Pacific by means of a mass commitment of their battleships. Probably you can argue that such potential evaporated with the growth of the US fast carrier force, but whilst the Japanese still retained some air strength, even in attenuated form, it complemented and gave validity to their gun ships. This suggests to me that if the US invasion of the Marianas was the critical battle on the perimeter that the Japanese could not afford to lose, it was here at the latest that they could and should have committed their battle line - to do so on any occasion subsequent to defeat in the Marianas would be merely to reinforce failure.
Oh dear . . . well if there are some sinkings not included, then yeah that analysis is all messed up.
On the issue of the band playing on . . . the fellow who did the post noted in several cases that the vessels were raised--actually I was intrigued to learn that in some cases they were turned into immobile gun platforms! Heh! Learn something on this forum everyday.
In those instances where the ship was simply 'underwater' and not 'sunk,' or even where it was sunk but in shallow enough water to resurrect (Pearl) I suppose the argument you could make is for "Major Incapacitation/Sinking" instead of just plain old and finalistic SUNK.
I hear you what you are saying about their value being synergistic with airpower, etc., and it is a reasonable point that I'll go along with (I'd "agree" but I don't know WHAT I'm talking about! so I'll just go along! [:D] ). It certainly does seem salient to distinguish between them being (1) the ultimate and virtually indestrutible weapon system: (2) vulnerable but useful when properly deployed in concert with other weapons systems; and (3) totally obsolescent and useless. If I understand you Local Yokel you are arguing for (2), and I'd go along with that (again, indulge me! I have no idea what I'm talking about here!).
But, consider what the first one was named "I Ain't Skeered Uh Nuthin'!!" (aka "Dreadnought"). While that may in large part be nationalistic hyperbole, it does lend itself more to an initial interpretation of the weapon system as being (1) ultimate and virtually indestructible.
On the other hand, I seem to recall hearing about some of the intra-national wrangles among commanders with different philosophies, meaning plane-club versus gun-club disputes. Seems like there was one Japanese high-level commander who swore by the CV as the future and nearly went so far as to argue for BBs as (3) totally obsolescent and useless.
ORIGINAL: Tiornu
Air Only Sinkings (n = 20 74.07%)
Keep in mind that this posits only a battleship versus aircraft juxtaposition. How many battleships were sunk when defended by aircraft?
Good question. I'd guess much lower eh?
The other analyses that would be interesting to know: (a) for every instance were a BB was attacked by aircraft, how many resulted in: (i) no damage; (ii) nominal damage; (iii) serious damage; (iv) sinking/incapacitation;
(b) what about other surface vessels? and as Local Yokel points out, what about CVs too?