# Math:Dragon Platebodies

This page is very outdated. The current GP rates are likely to be drastically different.

#### Overview

The gp rate, $\displaystyle{ R_{gp} }$ was calculated by finding the profit, $\displaystyle{ P }$ from performing 1 platebody smithing action, and dividing by the total time, $\displaystyle{ T_{tot} }$, required to perform that action. Note that this is the per second rate, and must be multiplied by 3600 to obtain the hourly rate.

$\displaystyle{ R_{gp} = \frac {P}{T_{tot}} }$

The total time can be found by combining the time from mining ores($\displaystyle{ T_{mine} }$), smelting bars ($\displaystyle{ T_{smelt} }$), smithing the bars into platebodies ($\displaystyle{ T_{smith} }$), and making diamond luck potions ($\displaystyle{ T_{luck} }$).

$\displaystyle{ T_{tot} = T_{smith} + T_{smelt} + T_{mine} + T_{luck} }$

#### Smithing Time

The smithing time is simply the time it takes to complete one smithing action. $\displaystyle{ T_{smith} = 2s }$.

#### Bonuses

$\displaystyle{ B_s = \begin{cases} 1 & \text {if signet is not equipped} \\ 1.1 & \text {if signet is equipped} \end{cases} }$

$\displaystyle{ B_m = \begin{cases} 1 & \text {if mining gloves are not equipped} \\ 2 & \text {if mining gloves is equipped} \end{cases} }$

$\displaystyle{ B_g = \begin{cases} 0.01 & \text {if gem gloves are not equipped} \\ 1 & \text {if gem gloves are equipped} \end{cases} }$

#### Smelting Time

First, the number of smelting actions required, $\displaystyle{ N_{smelt} }$ is calculated by dividing the average number of ingredients to perform one platebody action, $\displaystyle{ I_{smith} }$, by the average quantity of bars produced by one smelting action, $\displaystyle{ Q_{smelt} }$.

$\displaystyle{ N_{smelt} = \frac {5I_{smith}} {Q_{smelt}} }$

This is then multiplied by the time it takes to smelt an item, which gives:

$\displaystyle{ T_{smelt} = \frac {10I_{smith}}{Q_{smelt}} \text{s} }$

The average ingredient cost is dependent on the Mastery level of dragon platebodies,$\displaystyle{ M_{smith} }$ ,and is reduced by 0.1 for every 20 mastery levels.

$\displaystyle{ I_{smith} = 1 - 0.1 \left \lfloor \frac {M_{smith}}{20} \right \rfloor }$

The average quantity of bars is dependent on the Mastery level of dragon bars, $\displaystyle{ M_{smelt} }$, and is increased by 0.1 for every 20 mastery levels above -10. The signet ring multiplies this amount by 1.1.

$\displaystyle{ Q_{smelt} = B_s \left ( 1 + 0.1 \left \lfloor \frac {M_{smelt}+10}{20} \right \rfloor \right ) }$

#### Mining Time

First, the amount of dragonite ore ($\displaystyle{ O_{do} }$), runite ore ($\displaystyle{ O_{ro} }$), and coal ore ($\displaystyle{ O_{co} }$), are calculated by multiplying the number of smelting actions, $\displaystyle{ N_{smelt} }$ by the ingredient cost to perform one smelting action, $\displaystyle{ I_{smelt} }$ and the number quantity of the ore in the recipe.

$\displaystyle{ O_{do} = N_{smelt}I_{smelt} }$

$\displaystyle{ O_{ro} = 2N_{smelt}I_{smelt} }$

$\displaystyle{ O_{co} = 6N_{smelt}I_{smelt} }$

The average ingredient cost to perform one smelting action depends on the Mastery level of dragon bars, $\displaystyle{ M_{smelt} }$, and is reduced by 0.1 for every 20 mastery levels.

$\displaystyle{ I_{smelt} = 1 - 0.1 \left \lfloor \frac {M_{smelt}}{20} \right \rfloor }$

Next, the number of mining actions for each ore is calculated. For dragonite, $\displaystyle{ N_{do} }$ ,and runite, $\displaystyle{ N_{ro} }$ ,this is calculated as:

$\displaystyle{ N_{do} = \frac {O_{do}}{Q_{do}} }$

$\displaystyle{ N_{ro} = \frac {O_{ro}}{Q_{ro}} }$

Where $\displaystyle{ Q_{do} }$ and $\displaystyle{ Q_{ro} }$ are the average quantity of ore produced per mining action for dragonite and runite respectively. These are dependent on the mastery of the ores,$\displaystyle{ M_{do}, M_{ro} }$ ,which gives a 0.01 increase in the average quantity per 10 mastery levels, the ore bonus from the pickaxe used,$\displaystyle{ P_{ob} }$, (0.07 for dragon), and if the signet ring is worn or not.

$\displaystyle{ Q_{do} = B_mB_s \left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{do}}{10} \right \rfloor \right) }$

$\displaystyle{ Q_{ro} = B_mB_s\left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{ro}}{10} \right \rfloor \right) }$

For coal ore the number of mining actions, $\displaystyle{ N_{co} }$ , is reduced due to the coal generated from the mining skillcape while mining dragonite and runite ores. It is given by:

$\displaystyle{ N_{co} = \frac {O_{co} - N_{do} - N_{ro}}{Q_{co}} }$

Additionally, the quantity of ore per mining action is increased by one:

$\displaystyle{ Q_{co} = B_mB_s \left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{co}}{10} \right \rfloor \right) + 1 }$

Finally the average time to perform a mining action is calculated. This is dependent on the respawn time of the ore, R_{o}, the effective ore health, $\displaystyle{ H_o }$, and the pickaxe bonus speed (0.5 for dragon), $\displaystyle{ P_{bs} }$.

$\displaystyle{ T_o = \frac {3(1-P_{bs})H_o+R_o}{H_o} }$

The respawn times for dragonite, runite and coal ore are 120s, 60s and 10s respectively.

The effective ore health is dependent on the mastery of the ore, $\displaystyle{ M_o }$ and the probability to not consume health provided by perfect swing potions, $\displaystyle{ P_{ps} }$.

$\displaystyle{ H_o = \frac {\left \lfloor M_o+5 \right \rfloor}{1-P_{ps}} }$

Finally, to obtain the total time spent mining the sum of mining actions multiplied by time per mining actions is calculated:

$\displaystyle{ T_{mine} = T_{do}N_{do} + T_{ro}N_{ro} + T_{co}N_{co} }$

#### Diamond Luck Time

The time to make diamond luck potions, $\displaystyle{ T_{luck} }$ is dependent the number of diamonds mined, $\displaystyle{ Q_{diam} }$, and the average number of diamonds required to craft a potion $\displaystyle{ I_{luck} }$ as follows:

$\displaystyle{ T_{luck} = \frac {2Q_{diam}}{I_{luck}} \text{s} }$

The quantity of diamonds mined depends on the number of mining actions performed and if gem gloves are worn. First we define the average number of gems mined as:

$\displaystyle{ Q_{gem} = B_g \left ( N_{do} + N_{ro} + N_{co} \right ) }$

Then the average number of diamonds follows as:

$\displaystyle{ Q_{diam} = 0.05Q_{gem} }$

The average number of diamonds to craft a potion depends on the mastery, $\displaystyle{ M_{luck} }$ and is given by:

$\displaystyle{ I_{luck} = 1 - 0.0025M_{luck}+0.002 }$

#### Calculating Profit

To calculate the profit per platebody the average value of a gem, $\displaystyle{ V_{gem} }$ must first be calculated. Without making diamond luck potions, this is simply the sum of the gems sell price, $\displaystyle{ S_i }$ multiplied by their probabilities, $\displaystyle{ P_i }$ (these can be found on the Mining page).

$\displaystyle{ V_{gem} = \sum S_iP_i }$

This results in a value of 381.25 gp per gem.

When making diamond luck potions the sell price of a diamond is replaced by the sale price of the potions, $\displaystyle{ S_{luck} }$, multiplied by the quantity made:

$\displaystyle{ S_{diam} = B_s \frac {2S_{luck}}{I_{luck}} }$

The profit is then calculated by adding the value of items made and subtracting the cost of gem/mining gloves:

$\displaystyle{ P = 3450Q_{smith}+V_{gem}Q_{gem} - (N_{do} + N_{ro} + N_{co})C_g }$

Where $\displaystyle{ C_g }$ is the cost per glove charge. Gem gloves are 250 gp per charge, while mining gloves are 150 gp per charge.

$\displaystyle{ Q_{smith} }$ is the average number of platebodies made per smithing action and is dependent on platebody mastery, $\displaystyle{ M_{smith} }$, as per:

$\displaystyle{ Q_{smith} = B_s \left ( 1 + 0.1 \left \lfloor \frac {M_{smith}+10}{20} \right \rfloor \right ) }$