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In Game of Thrones: Winter is coming, everything is about the math. Building your city, Gathering, Attacking, Defending, Researching, Expeditions, Attacking the Rebel Camps, Endurance and Motivation Recovery, Hospital and Healing and all other actions you can think of have a mathematical formula in background.
So what? All other games work with math as well too. How is that related you ask? The answer is in one word: “Optimum”. What is the optimum play style? How to grow better? How to attack better? How to be a more efficient player for your alliance in different events? These are the important questions which you need to ask yourself to become a better player in this or any other games.
GoT:WiC offers a very simple formula for every concept in the game, and offers a system of Buffs which will adjust these formulas for different players, based on their previous researches and other achievements. In this guide, we will have a deep review on the basic mathematics behind the buffs and bonuses and the ways to obtain them. In the next guide(s) I will introduce the different buffs and bonuses which are introduced in this game and then I will talk about each one of them individually.
Disclaimer: All formulas in this guide are based on a player model and are written to give you a better understanding about the way buffs and bonuses effect and may not be the exact actual formulas implemented in game.
The Math behind Buffs and Bonuses
GoT:WiC is using a linear formula for every concept in the game. This means the following formula is effecting for every buff in this game:
This means if you have 100% buff, then the result is twice more than the base value. If you have 200% buff, the result is three times more than the base value. In other words, Buffs mean, how much more of that base value you get.
Let’s review some examples:
- 100% Total attack buff means that your troops attack value is twice more than the base value
- 100% Research speed buff means that your researches will happen twice faster
- 100% Motivation recovery buff means that you will earn twice the motivation in same amount of time
As you can see in the examples, the buffs are all linear but the final effect might not be. For example, for research speed buff, the speed is twice more, which means the total time of researches are half the value. The time of researches follow a 1/x function.
This has a direct consequence for buffs like this: increasing the buff for the same percentages has more effect when you have less of the buff. For example, from 0% to 100% this buff reduces the time from 1 to 1/2 which is 1/2 of the value reduced and from 100% to 200% this buff reduces the time from 1/2 to 1/3 which is just 1/6 value reduced.
These buffs are basically effecting with non-linearity using the following formula:
You can see how this decay for effectiveness happen in the following plot:
As a result, increasing these buffs have more value when you don’t have much of them, and when you got a lot of those, you’re better off investing on other buffs that might be more beneficial to you. These all prove that it’s very important to know all of the buffs and how they effect.
Sources and types
Before talking about the buffs individually, I have to review the sources from which you can obtain these buffs. Buffs can come from many places, like researches, lord equipment, talents etc… Some of these sources are permanent, which means when you obtain the buff you can never lose it. We call these the owned bonuses or the passive bonuses. Some other sources, for example lord equipment, or great city buffs, will only give you the buff if you currently have the source activated. We call these the active bonuses.
For example, for each Castle exterior, there is Owned bonuses and Active bonuses. For High Keep, owning this castle exterior will give 5000 hospital capacity no matter which castle exterior is now equipped for you, but only equipping it will give the research speed, gold dragon production and motivation recovery buffs.
Passive bonuses can be majorly obtained at: Buildings and Glory, Researches, Troop Skins, Commanders, Tavern, Refinement, Equipment collection bonuses, Castle exteriors and Marching animations
Active bonuses can be majorly obtained at: Sept of Seven, Dungeon and Hall of faces, Great city buffs, Lord equipment, The badges, Dragon passive skills, Castle exteriors and Marching animations
There might be other temporarily or permanent sources for different buffs, Like the “We stand together to fight this pandemic” event which is a special event for Covid days.
From this point of this guide forward I’ll be reviewing different types of buffs individually.
a) Creation speed buffs
These buffs are mainly the ones which will increase the speed of growing by reducing the time for different tasks. These buffs are all with 1/x effect, so they will have less value as they are increased higher.
- Building Speed reduces the time for upgrading buildings (Normal level and Glory levels). This is a very important bonus for players who recently started the game so they can reach level 25 castle faster.
- Research Speed reduces the time for researching in Maester’s Tower. Researches are very important for increasing all other bonuses and your main objective for growing in game will be the researches.
- Forging Speed reduces the time for Creating and upgrading lord equipment. It’s not a very important bonus as usually the equipment doesn’t take a lot of time to be created or upgraded.
b) Gathering speed buffs
These buffs will help you to gather better. These buffs are all with 1/x effect, so they will have less value as they are increased higher.
- Resource Gathering Speed reduces the time your soldiers take to gather same amount of resources from a resource node. By resources I mean Grain, Wood, Stone, Iron and Gold. Note that all troop types have same base gathering speed. Only dragon skills offer single resource gathering speed bonuses as well.
These individual bonuses will be summed up with the main bonus to determine the bonus for that gathering march (which also must have your dragon with them)
In summary, the total bonus for each gathering node is calculated like this:
- Diamond Gathering Speed reduces the time your soldiers take to gather same amount of diamonds from a diamond mine. Diamond mines appear in winner and looser kingdoms after each KvK (kingdom vs Kingdom) event.
c) Resource Productions
These bonuses will increase the base production of resources from your outer city buildings (Farmland, Lumberyard, Quarry, Mine and Mint) and have linear effect.
d) Resource Capacity
Resources capacity determine how much your outer city can produce at max. When your capacity is full, then the resource production will stop. Increasing these buffs, increase your capacity and as a result, your castle will be able to produce more resources. These buffs have linear effect.
e) Resource Protection
Resources protection determines the amount of “protected” resources you can keep in your castle. Anything above this limit will be open for taking when enemy attacks you and win. Warehouses which are under level 25 will only protect Non gold resources. Warehouses level 25 can protect gold dragons too. Also diamonds and black diamonds are safe from pillages.
- Resource Protected Limit This is a scalar value – not a multiplier. Basically this will be added to your warehouse capacity and will increase the limit directly that way.
- Resource Protection Bonus This is a linear buff on Protected limit value.
f) Resource Transport
Transportation of resources to your allies, happen from your market. These buffs will help with that.
- Transport Capacity This is a scalar value – not a multiplier. This value will be directly added to your transport capacity and will increase the limit of resources you can transport in one march.
- Transport Tax Rate The amount of resources you send to your ally is never equal to the amount they receive. The lost resources in the process is called tax. This bonus will reduce the tax rate, so as a result you can transport resources to your allies more efficiently. This buff has linear effect.
It’s noteworthy that all other types of transferring resources between players are taxed. For example, pillaging other player’s castles won’t give you the same amount of resources they lose.
- Investment Amount This scalar bonus (not a multiplier) will increase the amount of investment you can do in Iron bank.
- Lord EXP Bonus This buff with linear effect will increase the experience your lord receives. Lord receives experience when you finish quests, you attack others, you train or heal troops etc …
Battle Preparation Bonuses
a) Creation speed buffs
These buffs are mainly the ones which will increase the speed of growing by reducing the time for creating troops and fortifications. These buffs are all with 1/x effect, so they will have less value as they are increased higher.
- Training Speed: This buff will increase your troop training speed in barracks. Increasing this bonus means, you will be creating more troops in same time frame. As increasing army gives you battle rating, increasing this bonus helps you to get more overall power in shorter time. Having too many army – more than the amount that you can hide in other castles or gathering nodes – is not recommended though.
- Fortifications Construction Speed: This buff will increase your speed in creating the fortifications in your wall. Fortifications will defend your city as long as your wall is not fallen. In current game meta focusing more on troops buffs are more recommended.
b) Hospital buffs
These buffs and bonuses are about healing your troops in your hospital when they are wounded. As attacker a percentage of your troops will always die and only a percentage will be hospitalized. As defender, all your damaged troops will be hospitalized unless if you don’t have hospital capacity.
- Hospital Healing Speed: This buff will increase your healing speed in hospital. Healing is faster than training normally and can consume normal speed ups and a special speed ups which is specified for healings. This buff has a 1/x effect and has lesser increase in outcome when its increased from a higher value.
- Hospital Capacity: This scalar (not multiplier) buff will increase your capacity and size of hospital. Your troops can only get wounded till your hospitals have free capacity. When hospital capacity is filled, any new wounded troops will instantly die.
- Hospital Capacity Increased: This multiplier buff will increase your capacity and size of hospital with a multiplier after the scalar value is calculated.
- Mortality Rate: This buff that can only be modified because of the Ancient (Red) passive dragon skills which are available on Winter Raffle event, will modify the rate the troops get wounded or die. By default, 40% of the damaged troops from attackers die and rest can be hospitalized and 100% of the damaged troops from defenders can be hospitalized (as long as there is hospital capacity)
- Mothers Mercy: This buff that can only be modified because of the Ancient (Red) passive dragon skills which are available on Winter Raffle event, will automatically heal all your wounded troops after battle for free with a chance.
c) Training Quantity Buffs
- Single Training Quantity: This scalar (not multiplier) buff will increase the amount of your troops you can train at the same time from your barracks. The higher your training quantity is; the more troops you can queue in barracks but this has no effect on the training speed of the troops.
- Single Training Quantity Bonus: This multiplier buff will be multiplied in your training quantity value and will show the total quantity you can train in one go in barracks.
d) Training Cost Reduction
These buffs will reduce the training cost of troops. The higher these buffs are; you need less resources to train same amount of troops. They’re especially important for training tier 4 troops that need a lot of grain and gold. These buffs have a 1/x outcome on the resource costs too, meaning increasing these buffs when they have a higher value has less effect.
e) Fortifications Recovery
Fortifications Recovery is the bonus for the recovery of your damaged fortifications. Just like hospitals for troops and how they get wounded, some of your fortifications won’t be lost and you’ll be able to recover them. These buffs will increase the recovery rate of them. These buffs have linear effect.
f) Wall buffs
These buffs will enhance your wall.
- Durability: Durability is the total health of your wall. When enemy attacks your castle, before they can attack your troops the wall durability must be zeroed. Increasing this scalar value will increase your wall durability.
- War Durability Increased: This multiplier buff will increase your durability after its scalar value is calculated linearly.
- Durability Recovery Rate: When your wall is damaged, it will take few days to recover and be ready again. In this time the durability of your wall will be recovered bit by bit. The higher this scalar value is the more durability will be recovered in same amount of time passed.
- Durability Recovery Rate Increased: This is the multiplier bonus which will increase the Durability recovery rate linearly.
g) Lord execution and Hall of Faces Blessing Enhancement
These buffs will enhance your dungeon and Hall of faces execution.
- Execution Shorten Rate: Depending on the level of the captured lord, the execution time will be more. When this buff (with 1/x effect) increases, the time needed before you can execute the enemy lords decreases.
- Hall of Faces Blessing Duration: For each executed lord, hall of faces will be active for 24 hours. With this linear bonus, this time period increases.
- Upkeep Consumption Reduction: All troops will use grain as upkeep. This bonus will reduced the troop upkeep with 1/x effect.
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