"Kill Ratios for Bombs" by Thomas Pfister 1997 v2.6/7

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Kill Ratios for Bombing

by: Thomas Pfister

I´ll try to explain how bombs/defenses exact work.


1) Defense coverage.

Each Defense type has a specific base defense coverage, that is the value of Defense coverage _ONE_ Defense gives:


SDI d=0.99%

Missile d=1.99%

Laser d=2.39%

Planet d=2.99%

Neutron d=3.79%


The coverage of more then one Defense is calculated


Def(base)=1-((1-d)^n), while n is the number of Defenses.


e.g. 100 Neutron-Defs:


=1-((1-3.79%)^100)

=1-((1-0.0379)^100)

=1-(0.9621^100)

=1-0.0208)

=0.9792

= 97.92%


This is the coverage versus normal Bombs like cherrys and versus packets and meant killing Pop.


Versus buildings the Defense coverage is halfed:


Def(build)=Def(base)*.5


e.g. versus 100 Neutron Defs:


= 97.92% *.5

= 48.96%


Versus invasions the coverage is 75%


Def(inv)=Def(base)*.75


e.g. versus 100 Neutron Defs:


= 97.92 * .75

= 73.44


Versus smart bombs the coverage is calculated the following


Def(smart)=1-((1-(d/2))^n)


e.g. versus 100 Neutron defs:


= 1-((1-(3.79%/2))^100)

= 1-((1-(1.895%))^100)

= 1-((1-0.01895)^100)

= 1-((0.98105)^100)

= 1-(14.76)

= 0.8524

= 85.24%


2) Normal Bombs

Normal Bombs works linear, that means


Pop_Kills(normal)=sum (kill_bomb_type(n)*#(n)) * (1-Def(base))


e.g. 10 Cherry(2.5%) + 5 M70(1.2%) vs 100 Neutron Defs (97.92%)


= Sum (2.5% * 10; 1.2% *5) * (1-97.92%)

= SUM (25% ; 6%) * 2.08%

= 31% * 2.08 %

= 0.31 * 0.0208

= 0.00868

= 0.868% of planetary Pop will be killed


Destroy_Build = sum (destroy_build_type(n)*#(n)) *(1-Def(build))


e.g. 10 Cherry(10 buildings) + 5 M 70(6 buildings) vs 100 Neutron Defs


= sum (10*10; 5*6) * (1-(97.92%/2))

= sum (100;30) * (1-(48.96%))

= 130 * (1-0.4896)

= 130 * 0.5104

= ~66 Buildings will be destroyed.


If you increase the number of bombs the bombing result will increase linear.


3) Smart Bombs

Doesnt work linear, the kills will be:


Pop_kill(smart)= (1-Def(smart))-(1-Def(smart)* ((1-smart_type_1)^n1) * 1-smart_type_2)^n2)....)


e.g. 10 Annihilators(7%) + 5 neutron (2.2%) vs. 100 Neutron-Defs(Def(smart(=85,24%)))


= (1-85.24%)- (1-85.24%) * ((1-7%)^10) * ((1-2.2%)^5))

= (1-0.8524) -(1-0.8524) * ((1-0.07)^10) * ((1-0.022)^5))

= 0.1476 - (0.1476 * (0.93^10) * (0.978^5))

= 0.1476 - (0.1476 * 0.484 * 0.895)

= 0.1476 - 0.0543

= 0.0933

= 9.33% of planetary Pop will be killed.


As the second term (which gives at least 0.0543) goes versus zero if the number of bombs increase, the maximum kills will be the first term (14.76%) with high Bomb numbers, but with 100 Annihiltaors it will be already very near this value. So with planetary Pop say around 350.000 and a high growth rate say >16% it is impossible to bomb a planet out with smart bombs, as the pop growth is anyway higher then the kills from Bombing.


Hope this is helpful and explains how Bombs/Defs works.


Thomas


Shane Kearns wrote:

I've spun up a spreadsheet with Thomas' formulae - Data for all bombs and defences are already in it (except MCM which I can't remember off hand).


Just put in the number and type of defences, number and type of bombs (up to 8 different bombs supported) and it gives you expected kills, minimum kill (for standard bombs) and installations destroyed.