# A Math Tour to Tribe

Here I will talk about some of the Mathematics behind Tribe. Tribe is easy to quantify because armor/shield can realistically be assume as 0.

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1. Efficiency (the simplified model)
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First, assume that everything has the same range. Both side start firing at each other at the exact same time. To further simplify, assume that ship does not lose damage output until every ship on one side is destroyed. In such a scenario, 2 fleet is consider equal when

Enemy HP/(XYour DPS) = (XYour HP)/Enemy DPS

Where X is the ratio of your ship to enemy ship.

Taking that equation and cross multiply, we get

X = [(Enemy DPS * Enemy HP)^0.5]/[(Your DPS* Your HP)^0.5]

Since the only factor you can influence is your ships, Enemy Stats are ignored, therefore

Ship Rating = (DPS*HP)^0.5

Now, adding cost into the equation

Efficiency = [(DPS*HP)^0.5]/Cost

# ========================================= 2. Hit Chance

In regard to Hit Chance

Because the smallest hull (ex. Utopia) is always preferred, ship size can be ignored in the equation because the multiplier is constant.

Speed vs Tracking

Hit Chance = 1-(speed/tracking)

Efficiency Against Weapon A = [(DPS*(HP/(1-(speed/tracking))))^0.5]/Cost

This equation can be simplified to

Efficiency Against Weapon A = [(tracking/(tracking-speed))^0.5 * (DPS*HP)^0.5]/Cost

# ========================================= 3. Range

Throwing range into the equation, and we get the whole picture.

If enemy has superior range, then you will lose ships before you gets to fire. Conversely if you have superior range, then enemy will lose ship before he/she gets to fire.

We can combine this into 1 variable, Engagement Death, or ED

ED = % ships remain before entering firing range * (1/(% enemy remain before entering firing range))

Efficiency = [(ED) * (tracking/(tracking-speed))^0.5 * (DPS*HP)^0.5]/Cost

# ========================================= 4. Conclusion

I am sure you figure out what you need to do by now. If not, sorry no hot tips here.