Math:Dragon Platebodies

From Melvor Idle
This page is out of date (v0.14).

This page is very outdated.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

Overview

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]

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]