The Stack formula coming from Kreuzfeld, Ozymandiac and Vann has been modified to take accounts of 2 hits units.
@Baron:
@Kreuzfeld:
@Ozymandiac:
@Kreuzfeld:
Ususally, subs is the most costeffective unit to buy for defence.
I’m not following this. Suppose I have 48 IPCs and want to buy a defensive fleet.
-I buy 8 subs, receive metapower=881=64.
-I buy 6 destroyers, receive metapower=662=72.
Aren’t destroyers the units with a higher metapower and as such better as defensive units?
I think I also said that it was dependent on what other ships you had available. Subs isn’t best if you only have subs. I would expect the optimal ratio for subs vs other ships would be between 40 and 60 % of your fleet.
if you have no fleet, then you would be correct.
lets ssume you have 2 CV + 4 ftr, + 2 DDs + 2 subs. I will count the CV as 2 units. For your fleet so far, you have 26 pips and 12 hp. if you buy 6 subs, you will have 38 pips and 18 hp. if you buy 10 subs, you will have 34 pips hand 20 hp.
with sub
342020 = 13600
with DD
381818 = 12312
So, as you can see, the sub will be better for your metapower. It will also give you a better lossdistribution.
But, I think your point is interessting. I think this formula can be used to figure out what you want to buy. Just calculate your metapower and hp, and figure out what units you should add. This can be extremely nice russia, germany, japan and USA.
This need a few Edits to be correct:
lets assume you have 2 CV + 4 ftr, + 2 DDs + 2 subs. I will count the CV as 2 units.
For your fleet so far, you have 26 pips and 12 hp.
If you buy 6 Destroyers (D2= +12Def pips), you will have 38 pips and 18 hp.
If you buy 8 subs (D1= +8Def pips), you will have 34 pips hand 20 hp.
with Submarines:
342020 = 13600
with Destroyers:
381818 = 12312
But applying avg pips of stack to follow the formula almost to the letter, this give:
with Submarines:
(34/20)2020 = 34*20 = 680
with Destroyers:
(38/18)1818 = 38*18 = 684
And, considering Carrier being 1 unit for 2 hits, to apply this stack formula to the letter:
with Submarines:
(34/18)2020 = 755.6
with Destroyers:
(38/16)1818 = 769.5
So, in lasts 2 cases, you get a better defense with Destroyers compared to Subs purchase.
This contradict your initial thesis.
This rise a question: how consider the number of units compared to hits in this formula?
75 Cruisers Attack 3 vs 40 Battleships D4, 2 hits
Cruisers 225 pips, 75 hits vs BBs 160 pips and 80 hits
Cruisers
3* 75^2= 16875
Battleships
4* 80^2 = 25600, too high!!!
Or
4* 40^2 = 6400, too low!!!
But AACalc gives a pretty even match still win by Cruisers:
Overall %*: A. survives: 53.4% D. survives: 46.2% No one survives: 0.4%
Maybe the formula need this addition (1.618034) on hits or rolls for all 2 hits units
Battleships
*4 [(401.618034)^2] = 16755**
So, this seems to work.
However, IDK the derivative formula…
So, the complete Stack formula would be :
**Metapower = units^2 * power
N1 is nb of 1 hit units
N2 is nb of 2 hits units
(N1+ N2*1.618034)^2 * avg power [total power/(N1+N2 units)] = Metapower**
For instance, comparing these 2 fleets on defense:
2 CV + 4 ftr, + 2 DDs + 10 subs
(16 hits + 2*1.618034)^2 * 34 pips/18 units = 698.9
2 CV + 4 ftr, + 8 DDs + 2 subs
(14 hits + 2*1.618034)^2 * 38 pips/16 units = 705.6
And this confirmed that adding DDs brings more defense metapower.
But not that much.
And this returns to the tricky Subs, DDs and planes triangle.
If attacker brings a lot of planes, Subs but no DDs, defending Subs will not protect the fleet core from air attack.
ENIGMA_Vann formula_Cost vs Odds_Roster charts_D6_D8_D12_D10.xls