Efficiency

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Efficiency is a term that is used to talk about how well time on RuneScape is used to gain experience, money, or both.

Efficiency is often used in the context of evaluating, based on how valuable you perceive your time to be, two different methods to train a skill for which their experience per hour and profit per hour rates are known or calculated. If one method gives more experience per hour than the other and also costs less or gives more profit, then there is no question which method is more efficient. However, if one method gives faster experience than the other but costs more or gives less profit, then which is the more efficient method depends on what the player perceives his/her value of time to be. It is possible to calculate which method is more efficient for a player with a known value of time, or at what value of time the two methods are equally efficient.

Efficiency cannot take into account enjoyment of the game and therefore a method considered "most efficient" may not necessarily be the preferred method. However, for many players, it would be.

Comparing two methods

Finding the better method for a known value of time

One way to compare two methods for training a skill is by using the equation:

$E={\frac {V-P}{X}}$

where:

• E is efficiency rating, with a lower value indicating a more efficient method.
• V is your value of time per hour (often this is the profit per hour you could be making if you were using your time making money instead, but also may include the value of experience- for example, if Graahk runecrafting at 91+ runecrafting is 900k profit per hour, someone with 91+ runecrafting should value their time at least 900k per hour, but also may wish to add on some additional amount to take into consideration runecrafting experience gained.)
• P is the profit per hour of the method being considered.
• X is the experience per hour of the method being considered.

When using this equation, only methods that give experience in one skill can be used. Methods that give experience in multiple skills can only be used if only one type of experience is being considered- but then the extra experience in other skills would give the method an edge over methods that only give experience in one skill, so the equation would not be as effective.

The equation also cannot be used to compare methods to train different skills; it can only be used to compare methods to train one skill.

Values used in the equation should either be used in full, or all multiplied or divided by some constant. In practice the easiest way to use the equation is to express experience, profit, and value of time in terms of "k's" (thousands) of coins or experience per hour. Essentially the k can be ignored then.

A method that costs money has a negative profit per hour.

For example, suppose that you are considering burning maple logs to train firemaking, and can burn 1200 per hour at 135 firemaking experience each. Maples cost 36 coins each. Based on these numbers, burning maples would give 162k firemaking experience and cost 43k cash per hour. To calculate the efficiency of this method you also need a value of time per hour. For now suppose that your value of time per hour is 400k. Therefore, the efficiency rating of the method is

$E={\frac {400k--43k}{162k}}={\frac {443k}{162k}}=2.736$

Now suppose that you are also considering burning yew logs. Let's assume you can also burn 1200 per hour, and that yew logs give 202.5 firemaking experience each and cost 440 coins each. Then, burning yews would give 243k firemaking experience and would cost 528k cash per hour. For burning yews based on these numbers and also based on a 400k per hour value of time:

$E={\frac {400k--528k}{243k}}={\frac {928k}{243k}}=3.819$

Based on these calculations, burning maples would be significantly more efficient than burning yews. As one may expect, the higher time is valued, the more worth it more expensive methods become.

Finding a value of time at which two methods are equally efficient

Now suppose that you're not sure what to value your time at, as many people don't have any specific idea. It is possible to compare two methods and get a value of time per hour at which one method becomes better than the other. This could help you choose which method to use.

The value of time at which two methods for training the same skill become equally efficient is given by the equation

$V={\frac {P_{1}X_{2}-P_{2}X_{1}}{X_{2}-X_{1}}}$

where:

• V is the value of time per hour at which the two methods are equally efficient.
• P₁ is the profit per hour of method 1.
• P₂ is the profit per hour of method 2.
• X₁ is the experience per hour of method 1.
• X₂ is the experience per hour of method 2.

Typically the faster and more expensive method is used for method 2.

Going back to the maple and yew logs example, taking maples as method 1 and yews as method 2, the two methods would be equally efficient at a value of time per hour of

$V={\frac {(-43k)(243k)-(-528k)(162k)}{243k-162k}}={\frac {75087k*k}{81k}}=927k$

Therefore, based on these calculations, burning maple logs would be more efficient for a player who values time at under 927k per hour, and burning yew logs would be more efficient for a player who values time at over 927k per hour.

 template = :Efficiency/Calc
 form = efficiencyCalcForm
 result = efficiencyCalcResult
 param = experience1|Experience per Hour (Method 1)||integer|
 param = drop1|Choose||select|Profit per Hour,Coins per XP
 param = profit1|Profit (Method 1)||number|
 param = experience2|Experience per Hour (Method 2)||integer|
 param = drop2|Choose||select|Profit per Hour,Coins per XP
 param = profit2|Profit (Method 2)||number|

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Why the equations work

Consider the first equation

$E={\frac {V-P}{X}}$

The units in the numerator are coins per hour. The units in the denominator are experience per hour. The units for E are therefore coins per experience. E is a measure of how much one experience costs, but also valuing time. Suppose that you can gain 250k crafting experience per hour at a loss of 1M coins per hour, and value time at 1M coins per hour. The number that most people would consider the "cost per experience" would be 1000k/250k = 4 coins per experience. However, this value does not take into account the time spent training. Instead of training, you could be making money! Essentially, by training, you are losing the opportunity cost of your value of time. In this example, to gain that 250k crafting experience, you actually would be losing 1M worth of time in addition to the 1M of coins lost. Therefore, you actually are paying 8 coins per crafting experience if both time and money are considered. This is equal to the efficiency rating for the method.

This idea is where the equation for the efficiency rating comes from. V / X is equal to the cost per experience in time. P / X is equal to the profit per experience in money, or -P /X is equal to the cost per experience in money. Therefore, the total cost per one experience, considering both money and the opportunity cost of time, is equal to

$E={\frac {V}{X}}-{\frac {P}{X}}={\frac {V-P}{X}}$

Now consider the second equation

$V={\frac {P_{1}X_{2}-P_{2}X_{1}}{X_{2}-X_{1}}}$

This is simply a solution for value of time when setting the efficiency ratings for two methods equal to each other:

$E_{1}=E_{2}={\frac {V-P_{1}}{X_{1}}}={\frac {V-P_{2}}{X_{2}}}$

Cross-multiplying gives $X_{2}(V-P_{1})=X_{1}(V-P_{2})$

Expanding gives $X_{2}V-P_{1}X_{2}=X_{1}V-P_{2}X_{1}$

Getting V on one side gives $X_{2}V-X_{1}V=P_{1}X_{2}-P_{2}X_{1}$

Factoring V out gives $V(X_{2}-X_{1})=P_{1}X_{2}-P_{2}X_{1}$

Dividing gives $V={\frac {P_{1}X_{2}-P_{2}X_{1}}{X_{2}-X_{1}}}$