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Quality Rates with Quality Titles (the Magic Artisan/who is Known Far and Wide)

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I created several Celtic Tribolt Wands and recorded the Magic Attack bonus to see what effect the master title/amplified second title has on the distribution of rates. Since each stat is rolled independently, I could have gotten the rates of other stats, but I forgot to check those at the time. For this item, a roll may give 8-30 MA.

  • {Magic Attack|15,16,18,18,18,20,22,23,24,24,25,25,25,27,28,29,29,29}
  • {Percentile|31.8,36.4,45.5,45.5,45.5,54.5,63.6,68.2,72.7,72.7,77.3,77.3,77.3,86.4,90.9,95.5,95.5,95.5}
  • Mean Magic Attack = 23.1
  • Mean Percentile = 68.4

Based on the assumed rate for Dan 3 crafting without the title, you are expected to get a stat roll percentile of 20-100%; with a mean of 60%. Assuming the 'who is Known Far and Wide' second title amplifies the master title effect by 20% multiplicatively, then there are two models that might explain how the bonus is calculated; (1) multiplicatively or (2) additively.

  • (1) Multiplicatively, the base effect of the Magic Artisan title is calculated to be ~11.714% (60% * 1.11714 * 1.2 = 68.4%), or ~14.057% with the master and 2nd titles combined.
  • (2) Additively, the base effect of the Magic Artisan title is calculated to be ~7.029% (60% + 7.029% * 1.2 = 68.4%), or ~8.434% with the master and 2nd titles combined.

More testing would be required to determine the precise nature of this calculation, but overall there seems to be an even distribution of results within the range, meaning that the effect is probably added prior to the random number generation. For example, if the random stat was first rolled, then the bonus was flatly added onto that (eg. a bonus of +10% would shift the range of 20-100% to 30-110%) we would expect to see over-rolls (which has not been observed) or a higher proportion of capped-out rolls (rolls within the 100-110 being truncated to 100% quality). Since we do not see a disproportionate quantity of 100th percentile rolls, my hypothesis is that the title simply increases the minimum quality of the roll, which again can be applied either (3) multiplicatively or (4) additively.

  • (3) Multiplicatively, the minimum base effect of the Magic Artisan title is calculated to be ~53.620% (20% * 1.536195286195 * 1.2 though 100%), or ~84.343% with the master and 2nd titles combined (final range of 36.8686-100% quality).
  • (4) Additively, the minimum base effect of the Magic Artisan title is calculated to be ~14.057% (20% + 14.057% * 1.2 though 100%), or ~16.869% with the master and 2nd titles combined (final range of 26.869-100% quality).

Again, it more testing would be required but my guess is (since Nexon's developers tend to round percentages to multiples of 5) that it follows model (4), but with the master title increasing the minimum quality rate by +10% (+12% with the 2nd title). This would be in line with the minimum quality percentile seen of 31.8% (20% + 10% * 1.2 = 32%).

Hematin (talk)23:57, 10 October 2021