# Math:Dragon Platebodies

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

[math] R_{gp} = \frac {P}{T_{tot}} [/math]

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

[math] T_{tot} = T_{smith} + T_{smelt} + T_{mine} + T_{luck} [/math]

## Contents

#### Smithing Time

The smithing time is simply the time it takes to complete one smithing action. [math] T_{smith} = 2s [/math].

#### Bonuses

[math] B_s = \begin{cases} 1 & \text {if signet is not equipped} \\ 1.1 & \text {if signet is equipped} \end{cases} [/math]

[math] B_m = \begin{cases} 1 & \text {if mining gloves are not equipped} \\ 2 & \text {if mining gloves is equipped} \end{cases} [/math]

[math] B_g = \begin{cases} 0.01 & \text {if gem gloves are not equipped} \\ 1 & \text {if gem gloves are equipped} \end{cases} [/math]

#### Smelting Time

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

[math] N_{smelt} = \frac {5I_{smith}} {Q_{smelt}} [/math]

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

[math] T_{smelt} = \frac {10I_{smith}}{Q_{smelt}} \text{s} [/math]

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

[math] I_{smith} = 1 - 0.1 \left \lfloor \frac {M_{smith}}{20} \right \rfloor [/math]

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

[math] Q_{smelt} = B_s \left ( 1 + 0.1 \left \lfloor \frac {M_{smelt}+10}{20} \right \rfloor \right ) [/math]

#### Mining Time

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

[math] O_{do} = N_{smelt}I_{smelt} [/math]

[math] O_{ro} = 2N_{smelt}I_{smelt} [/math]

[math] O_{co} = 6N_{smelt}I_{smelt} [/math]

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

[math] I_{smelt} = 1 - 0.1 \left \lfloor \frac {M_{smelt}}{20} \right \rfloor [/math]

Next, the number of mining actions for each ore is calculated. For dragonite, [math]N_{do}[/math] ,and runite, [math]N_{ro}[/math] ,this is calculated as:

[math] N_{do} = \frac {O_{do}}{Q_{do}} [/math]

[math] N_{ro} = \frac {O_{ro}}{Q_{ro}} [/math]

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

[math] Q_{do} = B_mB_s \left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{do}}{10} \right \rfloor \right) [/math]

[math] Q_{ro} = B_mB_s\left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{ro}}{10} \right \rfloor \right) [/math]

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

[math] N_{co} = \frac {O_{co} - N_{do} - N_{ro}}{Q_{co}} [/math]

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

[math] Q_{co} = B_mB_s \left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{co}}{10} \right \rfloor \right) + 1 [/math]

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, [math]H_o[/math], and the pickaxe bonus speed (0.5 for dragon), [math] P_{bs} [/math].

[math] T_o = \frac {3(1-P_{bs})H_o+R_o}{H_o} [/math]

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, [math] M_o [/math] and the probability to not consume health provided by perfect swing potions, [math] P_{ps} [/math].

[math] H_o = \frac {\left \lfloor M_o+5 \right \rfloor}{1-P_{ps}} [/math]

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

[math] T_{mine} = T_{do}N_{do} + T_{ro}N_{ro} + T_{co}N_{co} [/math]

#### Diamond Luck Time

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

[math] T_{luck} = \frac {2Q_{diam}}{I_{luck}} \text{s}[/math]

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:

[math] Q_{gem} = B_g \left ( N_{do} + N_{ro} + N_{co} \right ) [/math]

Then the average number of diamonds follows as:

[math] Q_{diam} = 0.05Q_{gem}[/math]

The average number of diamonds to craft a potion depends on the mastery, [math] M_{luck} [/math] and is given by:

[math] I_{luck} = 1 - 0.0025M_{luck}+0.002 [/math]

#### Calculating Profit

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

[math] V_{gem} = \sum S_iP_i [/math]

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, [math] S_{luck} [/math], multiplied by the quantity made:

[math] S_{diam} = B_s \frac {2S_{luck}}{I_{luck}} [/math]

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

[math] P = 3450Q_{smith}+V_{gem}Q_{gem} - (N_{do} + N_{ro} + N_{co})C_g [/math]

Where [math] C_g [/math] is the cost per glove charge. Gem gloves are 250 gp per charge, while mining gloves are 150 gp per charge.

[math] Q_{smith} [/math] is the average number of platebodies made per smithing action and is dependent on platebody mastery, [math] M_{smith} [/math], as per:

[math] Q_{smith} = B_s \left ( 1 + 0.1 \left \lfloor \frac {M_{smith}+10}{20} \right \rfloor \right ) [/math]