Other Combat Equations of Note
It's interesting to find out that a level 1 footman does (on average) the same amount of damage as a level 5 knight to any building. It may seem a little strange but it is easily explained. It works this way because a buildings defense is 20. Any footman/grunt or knight/ogre never even gets close to a basic damage of 20. This means when you use the combat equation, the basic damage is always taken right out of the picture. This means the piercing damage will be the only value that has any impact on the equation at all, when attacking a building. Now, remember that a footman has a piercing damage of 3, and a knight has a piercing damage of 4. Dividing these values by 2 (like the combat equation does) gives both units a minimum value of 4 (because of the round-up from a .5 decimal). Therefore, any level footman, grunt, knight, or ogre, will all do 2-4 damage on a structure per hit.
Bloodlust causes the basic and piercing damage to double. When an ogre with no weapon upgrades, or one weapon upgrades attacks a building, it will do double the damage it normally does (because the piercing damage gets doubled). The basic damage has no impact because the doubled amount from lust, is still less than the 20 armor rating of a structure. However, when you get both upgrades on an ogre, it changes. The doubled value of the lusted ogres basic damage is now 24. Four higher than that of the defense rating of a building. This means that the ogre will now do even more than just twice the amount of damage to a building. You can see why both sword upgrades in combination with bloodlust are so important.
The only 4 units, without bloodlust, to have over 20 points in basic damage are battleships/juggernauts (130), ballistas/catapults (80), subs/turtles (50), and destroyers (35). And I'm sure you are all aware of how fast these units can raze buildings.
I've heard many people say that you should go with the shield upgrades first if you are going to be fighting towers. But take a look at this. A guard tower has a basic damage of 4. A level 1 footman already has a defense of 4. The basic damage is already taken out of the equation. Upgrading shields won't cause less damage because the value of (basic damage - armor) in the equation, cannot go below 0. Combining this knowledge with the first part of this page, you will see that a level 1 footman does just as well against a tower as a level 5 footman.
I'm sure most of you know how important it is to upgrade your units, but this just serves as a reminder. A +2 to weapons or shields ends up being a huge amount in this game. If the enemy is 1 level ahead of you, you are going to lose a fight that involves the same number of units on both sides, every time. If the enemy is 2 levels ahead you, you are going to get wrecked. If you have grunts or ogres that will be attacking, make sure you are even, or ahead of your enemy in upgrades. Even if you are just a little bit ahead, you can time your attack, so that your upgrade finishes at the same moment that you attack. If the enemy's upgrade hasn't finished yet, then you will easily win the battle.
Upgrades - Example
Level 5 grunt attacks a level 3 grunt - ((10 - 4) + 3) = 9. That's 5-10 damage for each attack.
Level 3 grunt attacks a level 5 grunt - ((8 - 6) + 3) = 5. That's 3-6 damage per attack. The level 5 grunt does an average of 7.5 points of damage. The level 3 grunt does an average of 4.5 points of damage. Some simple calculations show that the level 5 grunt will win with 24 hit points remaining. That's alot. In battles with bigger numbers, the upgraded grunts will win with even more hit points. Don't be out-upgraded!
Level 2 Footman (shield) - Level 2 grunt (weapon)
Level 2 footman attacks the level 2 grunt - ((8 - 4) + 3) = 7. That's 4-8 damage for each attack.
Level 2 grunt attacks the level 2 footman - ((6 - 2) + 3) = 7. Exactly the same thing. So as you can see, the only difference between a sword and shield upgrade is the cost.
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