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| === Calculating the GP Rate === | | === Calculating the GP Rate === |
| 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. | | The gp rate can be calculated by finding the profit of completing a single platebody action and dividing by the time to complete the action and gather/craft all sub components. |
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| <math> R_{gp} = \frac {P}{T_{tot}} </math>
| | {{Main|Reference=Math:Dragon_Platebodies}} |
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| 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>).
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| <math> T_{tot} = T_{smith} + T_{smelt} + T_{mine} + T_{luck} </math>
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| ==== Smithing Time ====
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| The smithing time is simply the time it takes to complete one smithing action. <math> T_{smith} = 2s </math>.
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| ==== Smelting Time ====
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| 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>.
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| <math> N_{smelt} = \frac {5I_{smith}} {Q_{smelt}} </math>
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| This is then multiplied by the time it takes to smelt an item, which gives:
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| <math> T_{smelt} = \frac {10I_{smith}}{Q_{smelt}} \text{s} </math>
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| 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.
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| <math> I_{smith} = 1 - 0.1 \left \lfloor \frac {M_{smith}}{20} \right \rfloor </math>
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| 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.
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| <math>
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| Q_{smelt} =
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| \begin{cases}
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| 1 + 0.1 \left \lfloor \frac {M_{smelt}+10}{20} \right \rfloor & \text {if signet is not equipped} \\
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| 1.1 \left ( 1 + 0.1 \left \lfloor \frac {M_{smelt}+10}{20} \right \rfloor \right ) & \text {if signet is equipped}
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| \end{cases}
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| </math>
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| ==== Mining Time ====
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| 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.
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| <math> O_{do} = N_{smelt}I_{smelt} </math>
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| <math> O_{ro} = 2N_{smelt}I_{smelt} </math>
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| <math> O_{co} = 6N_{smelt}I_{smelt} </math>
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| 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.
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| <math> I_{smelt} = 1 - 0.1 \left \lfloor \frac {M_{smelt}}{20} \right \rfloor </math>
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| 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:
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| <math> N_{do} = \frac {O_{do}}{Q_{do}} </math>
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| <math> N_{ro} = \frac {O_{ro}}{Q_{ro}} </math>
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| 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.
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| <math>
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| Q_{do} =
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| \begin{cases}
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| 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{do}}{10} \right \rfloor & \text {if signet is not equipped} \\
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| 2\left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{do}}{10} \right \rfloor \right ) & \text {if signet is not equipped and mining gloves equipped} \\
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| 1.1 \left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{do}}{10} \right \rfloor \right ) & \text {if signet is equipped} \\
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| 2.2 \left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{do}}{10} \right \rfloor \right ) & \text {if signet and mining gloves are equipped}
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| \end{cases}
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| </math>
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| <math>
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| Q_{ro} =
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| \begin{cases}
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| 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{ro}}{10} \right \rfloor & \text {if signet is not equipped} \\
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| 2\left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{ro}}{10} \right \rfloor \right ) & \text {if signet is not equipped and mining gloves equipped} \\
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| 1.1 \left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{ro}}{10} \right \rfloor \right ) & \text {if signet is equipped} \\
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| 2.2 \left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{ro}}{10} \right \rfloor \right ) & \text {if signet and mining gloves are equipped}
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| \end{cases}
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| </math>
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| 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:
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| <math> N_{co} = \frac {O_{co} - N_{do} - N_{ro}}{Q_{co}} </math>
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| Additionally, the quantity of ore per mining action is increased by one:
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| <math>
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| Q_{co} =
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| \begin{cases}
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| 2 + P_{ob} + 0.01 \left \lfloor \frac {M_{co}}{10} \right \rfloor & \text {if signet is not equipped} \\
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| 1 + 2 \left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{co}}{10} \right \rfloor \right ) & \text {if signet is not equipped and mining gloves equipped} \\
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| 1 + 1.1 \left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{co}}{10} \right \rfloor \right ) & \text {if signet is equipped} \\
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| 1 + 2.2 \left ( 1 + P_{ob} + 0.01 \left \lfloor \frac {M_{co}}{10} \right \rfloor \right ) & \text {if signet and mining gloves are equipped}
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| \end{cases}
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| </math>
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| 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, H_o, and the pickaxe bonus speed (0.5 for dragon), <math> P_{bs} </math>.
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| <math> T_o = \frac {3(1-P_{bs})H_o+R_o}{H_o} </math>
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| The respawn times for dragonite, runite and coal ore are 120s, 60s and 10s respectively.
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| 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>.
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| <math> H_o = \frac {\left \lfloor M_o+5 \right \rfloor}{1-P_{ps}} </math>
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| Finally, to obtain the total time spent mining the sum of mining actions multiplied by time per mining actions is calculated:
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| <math> T_{mine} = T_{do}N_{do} + T_{ro}N_{ro} + T_{co}N_{co} </math>
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| ==== Diamond Luck Time ====
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| 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:
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| <math> T_{luck} = \frac {2Q_{diam}}{I_{luck}} \text{s}</math>
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| 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:
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| <math> Q_{gem} =
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| \begin{cases}
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| 0.01 \left ( N_{do} + N_{ro} + N_{co} \right ) & \text {gem gloves are not equipped} \\
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| N_{do} + N_{ro} + N_{co} & \text {gem gloves are equipped}
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| \end{cases}
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| </math>
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| Then the average number of diamonds follows as:
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| <math> Q_{diam} = 0.05Q_{gem}</math>
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| The average number of diamonds to craft a potion depends on the mastery, <math> M_{luck} </math> and is given by:
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| <math> I_{luck} = 1 - 0.0025M_{luck}+0.002 </math>
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| ==== Calculating Profit ====
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| 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#Gems|Mining]] page).
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| <math> V_{gem} = \sum S_iP_i </math>
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| This results in a value of 381.25 gp per gem.
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| 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:
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| <math>
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| S_{diam} =
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| \begin{cases}
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| \frac {2S_{luck}}{I_{luck}} & \text {if signet is not equipped} \\
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| \frac {2.2S_{luck}}{I_{luck}} & \text {if signet is equipped}
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| \end{cases}
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| </math>
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| The profit is then calculated by adding the value of items made and subtracting the cost of gem/mining gloves:
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| <math> P = 3450Q_{smith}+V_{gem}Q_{gem} - (N_{do} + N_{ro} + N_{co})C_g </math>
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| 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.
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| <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:
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| <math>
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| Q_{smith} =
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| \begin{cases}
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| 1 + 0.1 \left \lfloor \frac {M_{smith}+10}{20} \right \rfloor & \text {if signet is not equipped} \\
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| 1.1 \left ( 1 + 0.1 \left \lfloor \frac {M_{smith}+10}{20} \right \rfloor \right ) & \text {if signet is equipped}
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| \end{cases}
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| </math>
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| == Fishing for Whales (Max 1140k/hr) == | | == Fishing for Whales (Max 1140k/hr) == |
