Math Behind the Defense

[Anarchos]

First off there are a few things you need to know about your cities wall. It affects your cities basic defense, your troops defense, and your attackers attack force.

A level 25 wall makes your city defense 1270.
1270 x 125% = 158,750. Your city defense is added to your troops defense. So troops defense +158,750=defense

A level 25 wall makes your attacks hit at 75% attack.

A wall at level 25 increase your troops defense by 25% after your cities basic defense has been added to your troops count.

The formulas I'll be using are done with a wall at level 25 and no rams being used to attack. obviously you'll want to use rams, but the math I'll use is calculated to show the effectiveness of the wall and different troop types so rams were not factored.

Also I used 20,000 Population count for offense and defense. I split the population when using sentries and lancers. So 10,000 of each.

The formula is troop count x troop defense + city defense x defense bonus(wall)

Infantry Defense
Guardian: 140x5,000=700,000+158,750=858,750x1.25= 1,073,437.5
Sentry: 65x10,000=650,000+158,750=808,750
Lancer:
25x10,000=250,000+158,750=408,750
408,750+808,750=1,217,500x1.25=1,521,875

Infantry attack
Berserker: 50x20,000=1,000,000x.75=750,000

Sentry/Lancer VS. Beserker
1,521,875-750,000=
771,875 remaining defense

Guardian VS. Beserker
1,073,437.5-750,000=
323,437.5 remaining defense

Mounted Defense
Guardian:
115x5,000=575,000+158,750=733,750x1.25=917,187.5
Sentry:
25x10,000=250,000+158,750=408,750
Lancer:
50x10,000=500,000+158,750=658,750
658,750+408,750=1,067,500x1.24=1,334,375

Mounted Attack
Guardian:
115x5,000=575,000x.75=431,250
Knight:
110x6,666=733,260x.75=549,945

Lancer/Sentry VS. Knight
1,334,375-549,945=
784,430 remaining defense

Lancer/Sentry VS. Guardian
1,334,375-431,250=
903,125 remaining defense

Guardian VS. Knight
917,187.5-549,945=
367,242.5 remaining defense

Guardian VS. guardian
917,187.5-423,250=
485,937.5 remaining defense



Obviously when attacking you want to fully deplete the targets defense, so when looking at these formulas it shows you the type of troop you want to use to attack and defend against other troop types. The lower the remaining defense number, the less troops left.

[Anarchos]

Let me know what you think about the post and if it helps you decide what to attack or defend with. Maybe we can get a sticky!

[Anarchos]

If you want to figure out the number of troops reaming just do the formulae in reverse starting with the remaining defense number.

Remaining defense x .75 = troop total defense - city defense = troop defense. Divide that by the defense score for a single one of the troops and you'll have a number. That number is the amount of troops still alive.

[natale7]

1'270x125% gives 1'587.5,
not 158'750
Thats hunderd time less then what you say above

[Anarchos]

How right you are. However if your run the numbers in the simulator 20,000 berserkers would kill 4,964 lancers and sentries with a 25 wall which is 49.64% of the defense killed. The wall says it gives 125% defense. But if you multiply the cities defense of 1270 against 1.25 the final number of lancers an sentries killed is much higher than 49%. When multiplying the city defense against 125 it produces the correct number. I may not have communicated as well as I should have but the cities defense is multiplied by 125%, not just an additional 25%.

[Michael2]

say there is 1000 berserkers in the city defending for example. ie defense of 5. with a wall lvl of 25

city defense = 100%+wall defensive bonus(troop defense+wall basic defense)
= 100%+125%(5x1000+1270)
=2.25x6270
=14107.5

thats how its done