User blog:DecuGamer/Math in Knights and Dragons: Part 3: Balance

Hi guys!

Many of you for sure thought what armors are better: with high defense, attack or balanced? Answer for this question is more important than you think. Today I'm gonna present you what kind of armors is better: unbalanced, pretty balanced, or perfectly balanced. For unbalanced armors im gonna make which is better, too: attack or defense.

Introduction
Okay, but how to check it? Well, the best method is to simulate battles versus armors which have the same sumarized stats and the same elemental advanatage. I will say all of them counters one element of enemy, so we will have simplier math (* 1 Advantage Factor). Let's get started!

To make this math even simplier, I choosed one numer for sumarized stats: 2500. Why? Because it will be very easy to calculate stats. Let's compare 5 armors then. Armor wins when enemy died first, or it dealt more damage to enemy and died both. Armors will have the same attack moment to prevent advantages. Just will be easier to comparise, again.

These 5 armors are:
 * 1500 attack 1000 defence - Unbalanced: attack = U:A
 * 1375 attack 1125 defence - Pretty balanced: attack = PB:A
 * 1250 attack 1250 defence - Perfectly balanced = PB
 * 1125 attack 1375 defence - Pretty balanced: defence = PB:D
 * 1000 attack 1500 defence - Unbalanced: defence = U:D

Who'll get more wins? Let's check it by simulating all armors vs each other (Let's say all armors doesn't have guild, and their knights are level 100). '''We know then attack of knight = 240 * (A/ED). A = Our attack, ED = Enemy defence, as always.''' I'll make buttons which can show the battle, and post all results below.

Fights
 U:A attack: 240 * (1500/1125) = 320 

PB:A attack: 240 * (1375/1000) = 330

Pretty balanced: attack would win.  U:A attack: 240 * (1500/1250) = 288

PB attack: 240 * (1250/1000) = 300

Perfectly balanced would win.  U:A attack: 240 * (1500/1375) = 261 or 262

PB:D attack: 240 * (1125/1000) = 270

Pretty balanced: defence would win.  U:A attack: 240 * (1500/1500) = 240

U:D attack: 240* (1000/1000) = 240

No one would win, both armors would lose.  PB:A attack: 240 * (1375/1250) = 264

PB attack: 240 * (1250/1125) = 267

Perfectly balanced would win.  PB:A attack: 240 * (1375/1375) = 240

PB:D attack: 240 * (1125/1125) = 240

No one would win, all armors would lose.  PB:A attack: 240 * (1375/1500) = 220

U:D attack: 240 * (1000/1125) = 213

Pretty balanced: attack would win.  PB attack: 240 * (1250/1375) = 218

PB:D attack: 240 * (1125/1250) = 216

Perfectly balanced would win.  PB attack: 240 * (1250/1500) = 200

U:D attack: 240 * (1000/1250) = 192

Perfectly balanced would win.  PB:D attack: 240 * (1125/1500) = 180

U:D attack: 240 * (1000/1375) = 174/175

Pretty balanced: defence would win.

Results

 * U:A vs PB:A = Winner: PB:A
 * U:A vs PB = Winner: PB
 * U:A vs PB:D = Winner: PB:D
 * U:A vs U:D = Winner: -
 * PB:A vs PB = Winner: PB
 * PB:A vs PB:D = Winner: - 
 * PB:A vs U:D = Winner: PB:A
 * PB vs PB:D = Winner: PB
 * PB vs U:D = Winner: PB
 * PB:D vs U:D = Winner: PB:D

So, who won most battles? Let's check final results!


 * U:A = 0 wins, 4 losses
 * PB:A = 2 wins, 2 losses
 * PB = 4 wins, 0 losses
 * PB:D = 2 wins, 2 losses
 * U:D = 0 wins, 4 losses

What is the best? Of course perfectly balanced!

Ending and final thoughts
Thanks for reading this blog post! Hope it will help you! Stay tuned and wait for newer math in K&D posts! Do you want to know something about game which is covered by numbers? Write propositions for next posts! Next parts will be propably about friends, next about Arena, even next about calculating unknown stats even more (like all boss armors stats or new GW epics), and even even next about serious Magic Numbers theorycrafting (thanks Lux, gonna think about it!). Stay tuned and goodbye!