¶ Detailed analysis of the mathematics of Bombing using examples
¶ Shield Generator (SG) Parameters
You can view them on your Planet:
A special feature of the SG is that its overall strength (Structure of all levels) is increased at the expense of other buildings on the Planet. The more other buildings there are and the higher their level, the stronger the Shield Generator will be, which means the time to capture the Planet will increase. And this in turn increases the chances of protecting it. Let's note that if the level of the building is greater than the level of the SG, then its structure will be taken into account only up to the level of the SG.
¶ Buildings defense (structure) parameter:
Command Center (CC) - defense 700
Mine - defense 500
Warehouse - defense 250
Power Plant (PP) - defense 300
Detection Station (DS) - defense 350
Trade Office (TO) - protection 400
Cosmodrome - defense 450
Spacecraft Plant (SP) - defense 550
Missile Tower (MT) - defense 650
Shield Generator (SG) - defense 750
¶ How to calculate?
Total total durability of the SG = the sum of all durabilities of the SG at each of its levels.
The durability of SG of the level N = the sum of all structures of all buildings at level N, including SG, divided by 2.
Let us denote the sum of all buildings structures of level 1, 2, ..., N as S1, S2, ... Sn.
The durability of SG of the level 1, 2, ..., N as Sup1, Sup2, ..., SupN.
And the required total durability of the Shield Generator as SumSG.
The sum of all buildings structures of level N takes into account only those buildings whose level is equal to or greater than N.
We start counting from "below".
For the first level you need to add up the structure of all buildings of the first level:
Sup1 = S1
For the second level you need to add up the structure of all buildings of the first level and second level:
Sup2 = S1 + S2
Or add S2 to the previous result:
Sup2 = Sup1 + S2
And for the third:
Sup3 = S1 + S2 + S3 = Sup2 + S3
That is, in general terms:
SupN = S1 + S2 + ... + Sn = Sup(N-1) + Sn
Moreover, if the level of the SG is 3, and the level, for example, of the warehouse is 2, then S3 will not take into account the warehouse.
Then
SumSG = Sup1/2 + Sup2/2 + ... + SupN/2 = (Sup1 + Sup2 + ... + SupN) / 2
Looks complicated. If the buildings are of different levels, then calculating this manually is quite problematic. Here it is better to make a table in Excel or in Google documents.
You can notice that the higher the level, the “fatter” the durability of the SG at this level, since it includes S1 N times, S2 (N-1) times, and so on.
If all buildings have the same level, then the formula becomes simpler, since all S are equal:
Sup1 = S1 * 1
Sup2 = S1 * 2
SupN = S1 * N
SumSG = (S1 + S1 * 2 + ... + S1 * N) / 2 = ( 1 + 2 + ... + N ) * S1 / 2 = (N * (N + 1) / 2) * S1 / 2
SumSG = (N * (N + 1) / 2) * S1 / 2
Where N * (N + 1) / 2 - is the sum of the arithmetic progression from 1 to N.
Let's try to understand it with an example.
¶ Example 1
The Planet has, building and it's level:
- Command Center 12 lvl
- Three Mines 12 lvl
- Nine Cosmodromes 12 lvl
- Warehouse 4 lvl
- Detection Station 4 lvl
- Trade Office 4 lvl
- Power Plant 4 lvl
- Spacecraft Plant 8 lvl
- Four Missile Towers 8 lvl
- Shield Generator 8 lvl
Then, the sums of all buildings structures of specific level will be:
From the first to the fourth levels of the building do not change, so
S1 = S2 = S3 = S4 = CC 700 + Mines 500 * 3 + Cosmodromes 450 * 9 + Warehouse 250 + DS 350 + TO 400 + PP 300 + SP 550 + MT 650 * 4 + SG 750 = 11,450
Buildings Warehouse, DS, TO and PP are of level 4. Therefore, after it they are not taken into account. From the fifth to the eighth level we have:
S5 = S6 = S7 = S8 = CC 700 + Mines 500 * 3 + Cosmodromes 450 * 9 + SP 550 + MT 650 * 4 + SG 750 = 10,150
The remaining building levels do not count because the Shield Generator itself is level 8.
The sums of all buildings structures up to level will be:
Sup1 = S1 = 11,450
Sup2 = Sup1 + S2 = 11,450 + 11,450 = 22,900
Sup3 = Sup2 + S3 = 22,900 + 11,450 = 34,350
Sup4 = Sup3 + S4 = 34,350 + 11,450 = 45,800
Sup5 = Sup4 + S5 = 45,800 + 10,150 = 55,950
Sup6 = Sup5 + S6 = 55,950 + 10,150 = 66,100
Sup7 = Sup6 + S7 = 66,100 + 10,150 = 76,250
Sup8 = Sup7 + S8 = 76,250 + 10,150 = 86,400
Then
SumSG = (Sup1 + Sup2 + ... + Sup8 ) / 2 = (11,450 + 22,900 + 34,350 + 45,800 + 55,950 + 66,100 + 76,250 + 86,400) / 2 = 399,200 / 2 = 199,600
¶ Example 2
The Planet has, building and it's level:
- Command Center 30 lvl
- Five Mines 30 lvl
- Nine Cosmodromes 30 lvl
- Warehouse 30 lvl
- Detection Station 30 lvl
- Trade Office 30 lvl
- Power Plant 30 lvl
- Spacecraft Plant 30 lvl
- Four Missile Towers 30 lvl
- Shield Generator 30 lvl
All buildings are of the same level, so the formula is simpler.
S1 = CC 700 + Mines 500 * 5 + Cosmodromes 450 * 9 + Warehouse 250 + DS 350 + TO 400 + PP 300 + SP 550 + MT 650 * 4 + SG 750 = 12,450
Sup30 = S1 * 30 = 12,450 * 30 = 373,500
SumSG = (N * (N + 1) / 2) * S1 / 2 = (30 * (30 + 1) / 2) * 12,450 / 2 = 2,894,625
It would seem that in both examples Sup8 and Sup30 do not match the pictures, although SumSG does. But the fact is that the game is still in Beta, so there are bugs. The bug is in displaying the current level. The total durability is correct. This can be checked during Bombardment, the total durability of the Shield Generator will be indicated there.
And more about bugs. For some reason, for a free planet, the total durability of the SG is also different from the calculations. Also, the general Bombing report may also contain inaccuracies, but if you open it in Detail, then each individual report will contain correct information.
Conclusion.
The higher the level of the Shield Generator and the higher the levels of the other buildings, the greater the “upper” durability of the SG. It will be the first to receive damage.
¶ Bombing Example 1
To begin with, let's take an afk Player as an example, the planet Torium has 3 mines, it has enough energy, so the Dome will work.
The Planet has, building and it's level:
- Command Center 20 lvl
- Three Mines 20 lvl
- Eight Warehouses 20 lvl
- Cosmodrome 20 lvl
- Detection Station 1 lvl
- Trade Office 20 lvl
- Power Plant 20 lvl
- Five Spacecraft Plants 20 lvl
- Missile Tower 1 lvl
- Shield Generator 20 lvl
Let's calculate the total durability of the Shield Generator:
First, let's calculate the defense, since all the buildings here are of the same level with the exception of the Detection Station and the Missile Tower, then we'll calculate without them:
S = CC 700 + Mines 500 * 3 + Warehouses 250 * 8 + Cosmodromes 450 + TO 400 + PP 300 + SP 550 * 5 + SG 750 = 8 850
S1 = S + DS 350 + MT 650 = 8,850 + 1,000 = 9,850
Sup1 = S1;
Sup2 = Sup1 + S;
Sup3 = Sup2 + S;
and so on
Sup20 = Sup19 + S
SumSG = (Sup1 + Sup2 + Sup3 + ... + Sup20) / 2 = (S1 + (S1 + S) + (S1 + S + S) + ... + (S1 + S * 19) ) / 2 = (S1 * 20 + S * (1 + 2 + ... + 19)) / 2 = (S1 * 20 + S * (19 * (19 + 1) / 2 ) ) / 2 = (S1 * 20 + S * 190 ) / 2 = (9,850 * 20 + 8,850 * 190) / 2 = 1,878,500 / 2 = 939,250
Dome.
The screenshot shows that instead of 100,000 damage, 50,000 was dealt. This is the Dome working. At the same time, the energy consumption of Valkyries is 100,000 units.
Let's conclude that 939,250 strength will be demolished in 939,250 / 50,000 = 18.785 = 19 ticks.
Excess damage will go to the Shield Generator.
The screenshot shows that there were 20 reports (four pages with five reports per page), the last one was damage to the Missile Tower. That is, the Shield Generator actually accounted for 19 ticks.
Here you can see from the energy consumption that the excess damage went into SG.
Missile Towers.
The strength of all Missile Towers is = number of all MT levels * 650 = 1 * 650 = 650
The screenshot shows that the damage done was half as much as the energy spent. This demonstrates the operation of the Dome even without the Shield Generator building if there is energy on the Planet.
Conclusions.
If we added another 650 units of energy to the fleet, the Missile Tower would be destroyed, and the remaining buildings would remain untouched. After this, the Bombing was automatically cancelled. In this case, a Titan must be sent separately to capture the planet.
It is the amount of energy that regulates the accuracy of the Bombing of the Planet, if your goal is to keep “civilian” buildings intact.
Note also that every tick one Valkyrie was destroyed by the Missile Tower. We needed to make sure that 10,000 Valkyries were active at each tick, so we had to send them with a reserve.
¶ Mini Example 2
Let's take the already familiar case of the Shield Generator and Planet in T30 (all buildings are level 30).
Without a dome, Bombing of such planet (Shield Generator only) will take:
2,894,625 / 100,000 = 28.94 = 29 ticks or 5 hours.
And with the Dome it’s twice as long: 10 hours.
During this time, it is quite possible to protect it, even if it is located far from the OS.
