Upgrades

In Arcadius, tools can have their lifespan and overall power upgraded at the blacksmith for a fee.

The current upgrades are

* **Durability** for the lifespan
* **Impact** for the power or damages

## Durability

### Description

Durability is equivalent to the hitpoints of a tool. Every succesful use of a tool sees its durability reduced by a finite amount of points.

The durability cannot be negative, so any use that would give a negative durability has it rounded to 0.

### Formulas

Almost every formula relies on the **tier** of a tool. The tier value is not an official number but has been used by players.

#### Base durability

The durability that any tool starts with can be calculated :

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{\displaystyle base\\_durability = 10 \times tier^{2}}

#### Durability increment

The durability gained for each upgrade is :

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{\displaystyle durability\\_increment = 5 \times tier}

#### Cost per durability level

Each level is more expensive than the previous one. The cost increments by a value that is:

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{\displaystyle cost\\_increment = 200 \times \left( tier -1 \right)}

The cost of the n-th level is therefore :

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{\displaystyle cost\_n = n \times 200 \times \left( tier -1 \right)}

And the total cost from the n-th level is :

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{\displaystyle total\\_cost\_n = cost\\_increment \times n \times \left( n + 1 \right) \times \frac{1}{2} }

## Impact

### Description

Impact is equivalent to the damages or power of a tool. Every succesful use of a tool sees its target hitpoints reduced by a finite amount of points.

The impact is doubled when the hit value is equal to 100%, without any penalty for the tool or the user.

### Formulas

Almost every formula relies on the **tier** of a tool. The tier value is not an official number but has been used by players.

#### Base impact

The impact that any tool starts with can be calculated :

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{\displaystyle base\\_impact = 2 \times tier^{2}}

#### Impact increment

The impact gained for each upgrade is :

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{\displaystyle impact\\_increment = tier}

#### Cost per impact level

Each level is more expensive than the previous one. The cost increments by a value that is:

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{\displaystyle cost\\_increment = 200 \times \left( tier -1 \right)}

The cost of the n-th level is therefore :

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{\displaystyle cost\_n = n \times 200 \times \left( tier -1 \right)}

And the total cost from the n-th level is :

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{\displaystyle total\\_cost\_n = cost\\_increment \times n \times \left( n + 1 \right) \times \frac{1}{2} }

### Special discount

There is an undocumented feature that is directly linked to the impact value. this feature redcues the cost to repair a tool by a constant amount.

* For impact levels that are between 0 and 80 (included) : no discount (0%).
* For impact levels that are between 81 and 120 (included) : 30% discount.
* For impact levels that are between 121 and

∞

{\displaystyle \infty}

 (included) : 50% discount.

## Repair

Both type of upgrades have a direct consequences on the repair price. It increases with each upgrade bought and increases even more if the upgrades are varied.

### Description

When repaired at the blacksmith, a tool regains all its durability. The cost is proportionnal to the missing durability.

### Formulas

Almost every formula relies on the **tier** of a tool. The tier value is not an official number but has been used by players.

#### Maximum repair cost

The cost to repair a tool that has 0 durability left is :

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{\displaystyle maximum\\_repair\\_cost = \frac{tier^{4}}{5} + \frac{tier^{3}}{10} \times \left(impact\\_level + durability\\_level\right) + \frac{tier^{2}}{20} \times \left(impact\\_level \times durability\\_level\right) }

This formula shows that if one type of upgrade is left to level 0, then the 3rd part of the above equation is 0 and minimizes the cost.

This formula shows that if both type of upgrade are used, then the 3rd part of the above equation grows fast and makes the cost increase fast.

#### Proportionnal repair cost

Since the repair cost is proportionnal to the missing durability, repairing any tool costs :

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{\displaystyle repair\\_cost = maximum\\_repair\\_cost \times \frac{current\\_durability}{maximum\\_durability}}

#### Discount

If the tool is eligible then a discount can be applied to the repair cost :

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{\displaystyle final\\_repair\\_cost = repair\\_cost \* \left(1 - discount\right)}