Guide [updated] Analysis On T1/t2/t3 Material Refinement Rates

Update: Profession bombs, type of material, and level of material do not play a role in refinement rates.

Edit: Salted had posted the rates a few months ago here without my knowledge. This thread independently verifies with his posted rates.

tl;dr: After a successful refinement, there is a 88.15% chance of obtaining a T1 material, 10.65% chance for T2, and 1.20% chance for T3. Profession bombs, type of material, and level of material do not play a role in refinement rates.

Introduction
T3 materials, especially higher level materials, are greatly sought after in the marketplace. However, there is high demand for these materials, but not enough players to gather the materials to meet the demand. There are also anecdotal evidence from various players that profession bombs, mainly speed, and lower level materials play a role in increasing the rates of T2/T3 refinement rates. In this thread, I will discuss the chances of obtaining a T1/T2/T3 material after a successful refinement in order to help players plan out their time in obtaining said materials.

Methods
109 data points over a span of 6 days were collected, totaling 9917 materials. Of these materials, 5999 were successfully refined. Each data point is determined by the usage of a refinery without leaving the GUI window. Once the GUI window is exited, the data point is considered finished, and a new data point is generated when the window is opened again. Each data point records the level, time and day, player refining the material, type and what said material is refined into, listed success rate of refinement, number of refined materials, number of successful refinements divided into T1/T2/T3 subcategories, and whether said material was processed during a profession bomb (xp, speed, or both).

Many strict, sub-data sets were also made to test for influencing factors: level of material, type of material, and profession bombs. These consist of data very similar to each other based on level, material, and whether it was refined during a profession bomb or not.

Results
The data set can be found at this Google spreadsheet here. Aggregating all data together, the chances of obtaining a T1 after a successful refinement is 88.15% ± 1.08%, T2 is 10.65% ± 1.03%, and T3 is 1.20% ± 0.37% at the 99% confidence interval. The data is summarized below in Table 1.

Table 1. Ratio of T1/T2/T3 of successful refinements with 99% and 95% confidence interval. Also shown is the P-value after normalizing the data.
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In each of the sub-data sets, the differences between their respective factors obtained a P-value greater than 0.05. This signifies that level of material, type of material, and profession bombs do not play a role in influencing T1/T2/T3 refinement rates. For more info, look into the spreadsheet.

Conclusion
Aggregating all data together, the chances of obtaining a T1 after a successful refinement is 88.15% ± 1.08%, T2 is 10.65% ± 1.03%, and T3 is 1.20% ± 0.37% at the 99% confidence interval. The level of material, type of material, and profession bombs do not play a role in influencing these rates. It is unclear whether XP only or speed only bombs play a role in influencing refinement rates, but it is assumed to not play a role because profession parties do not influence these rates. In light of the official rate as mentioned from Salted, the actual rates may be slightly off from his rates. When looking at the 95% confidence interval for T1 rates, the official rate of 89% is not included, indicating that the rate for T1 may be lower than officially announced. In light of this low rate of T3 materials, players need to plan accordingly on their schedules whether it is worth their time to gather these materials.

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Discussion and Comments
In laymen terms, what does all of this mean? 88% of your successful refinements will become T1, 11% will become T2, and 1% will become T3. This, however, does not include the losses obtained after a failed refinement, which many of you hate.

Lets make a hypothetical example that you need 1 T3 Sky Paper. Your successful refinement rate is 50%, and it takes on average 2 minutes to collect and refine 10 Sky Wood. In order to have a 50% chance of getting at least 1 T3, you need to successfully refine 69 Sky Wood. This then calculates to 138 Sky Wood or 28 minutes since half of your Sky Wood will fail to refine. It may seem short, but remember that this is a 50% chance to obtain at least 1 T3 after 69 successful refinements. In order to have a 99% chance to obtain at least 1 T3, you will need 459 successful refinements, or 918 Sky Wood, or 3 hours of your time. DO NOT CONFUSE THIS AS INCREASING YOUR CHANCES AFTER EVERY SUCCESSFUL REFINEMENT! The chances of obtaining said T3 are always the same after each refinement! This example is a cumulative probability of obtaining 1 T3 after x successful refinements, otherwise known as the Bernoulli process.

Take that example into consideration when obtaining T3 materials.

As for the slight difference in the official rate and the rates obtained from this data set, I find it interesting that they slightly differ even despite the 95% confidence interval. Perhaps Salted put out an estimate of the rates and not the actual rate down to the decimal places.

Some strategies for gathering:

• If you only want XP, do not bother refining. Throw away materials as you get them or let the server spam you on not being able to hold more unprocessed materials. Look out for prof parties.
• If you only want materials, refine either as soon as you can't hold anymore unprocessed resources, or better, store in your bank and wait until you reach your maximum success rate of refinement (usually 70%). Look out for prof parties/speed bombs.
• If you want the best of both worlds, well lots of time will have to be sacrificed. It's a balancing act between both points stated above.

If you have any questions or comments, leave your message below. Many thanks to Ehbyn for contributing data and providing moral support and Lilithia_ for providing data.

 

Salted confirmed the rates on the following post: https://forums.wynncraft.com/threads/chance-of-refining-tier-3-material.246076/#post-3026028
Seems like you were on point though, nice job!

 

Oh wow, I guess this proves that Salted is right then (if you ever doubted his numbers). Now I wonder whether the factors I mentioned also influence these rates as well, though my gut feeling (and also evidence) says that they do not.

 

An update to the thread has been posted. More data points have been collected to conclude the following things:

• Profession bombs, type of material, and level of material do not play a role in refinement rates.
  • It is unclear whether XP only or speed only bombs play a role in influencing refinement rates, but it is assumed to not play a role because profession parties do not influence these rates.
• In light of the official rate as mentioned from Salted, the actual rates may be slightly off from his rates. When looking at the 95% confidence interval for T1 rates, the official rate of 89% is not included, indicating that the rate for T1 may be lower than officially announced.
  
• Strategies for gathering included.