Ehrayn's Crafting Quality - Rantings, Ravings and Reality

So you want to order or craft an MP set of armor, or weapon. Are you prepared to pay the price?

It seems from all the vnboards postings that most players just don't understand statistics. If you want an MP item crafted, you MAY pay an outrageous price, you may get lucky and pay little, or the crafter may absorb the pain of random numbers by charging you a flat price (by their choice, no matter if it pops up on their first or 200th try.) Whichever way, it's not your call as a customer, so be prepared to pay a deposit up front and dearly in the end.

It might seem cruel and unusual, so I'll share a quick primer on random numbers and statistics, and hope you appreciate your crafter's pain. Should all of this scare you (it should) you would best set a budget and communicate it with your crafter, so you can afford to pay for the finished product.

All LGMs items have a 2% chance of crafting a Masterpiece (100 % quality, called an MP in the lingo.) So do all younger crafters as long as the item cons 'Gray' to them (it's more than 50 points less than their current skill to craft.) That is one in fifty tries. So most customers (wrongly) assume they will get an MP in between 1 and 50 tries.

Rather than start with how many tries an MP will cost, let's start with how many tries it takes for a crafter to make you a 99% quality or better (MP). The chance of crafting a 99 is one in 4 tries, less the chance for an MP (1/4 * 49/50). The chance of getting a 99 or better is therefore (1/4 * 49/50) + 1/50. That is 26.5% chance on any one given try.

If it worked as people hoped, 26.5% + 26.5% would be 53% within the first two tries, and add 26.5% four times and it comes out to 106%, a sure thing within four tries. Wouldn't life be interesting if probability worked that way. Obviously, better than 100% is impossible, and so it doesn't work as those folks were hoping.

The odds on the second try is the remainder of the odds from the previous try, times the odds on this try, because if the previous try succeeded, we had finished. We multiply the remaining chance ((3/4 * 49/50) + 49/50) that we failed to get a 99/MP item, by the odds of getitng one on this try. ((1/4 * 49/50) + 1/50) * ((3/4 * 49/50) + 49/50), or a 14.97% chance ON THE SECOND TRY. For the odds of getting one within two tries, we can now sum the probabilities, 18.33% + 14.97%, and come up with a 33.31% chance within the first two tries.

The following try we do the same for all previous tries, so ((3/4 * 49/50) + 49/50) * ((3/4 * 49/50) + 49/50) * ((1/4 * 49/50) + 1/50). This is becoming illegible, so lets call p our probability;

p = (1/4 * 49/50) + 1/50

and let's call n our number of tries. The chances of success (s) on the n'th try can be written as

s = ((1 - p) ^ (n - 1)) * p

In a spreadsheet this is even easier. Take the first few columns...

  A B C
1 Tries Odds on THIS try Odds BY this try
2 1 =(1/4 * 49/50) + 1/50 =B2
3 =A2 + 1 =(1 - C2) * $B$2 =B3 + C2
4 =A3 + 1 =(1 - C3) * $B$2 =B4 + C3

If you copy this last row repeatedly down the page, excel will keep incrementing the references A3/C3 (pointing always at the previous row), but leave $B$2 unchanged in each copy, which is our chance of one success.

Lets look at the data from this table, shall we?

TriesOdds for EXACTLY
this many tries
Odds WITHIN
this many tries
126.50%26.50%
219.48%45.98%
314.32%60.29%
410.52%70.82%
57.73%78.55%
65.68%84.23%
74.18%88.41%
83.07%91.48%
92.26%93.74%
101.66%95.40%
111.22%96.62%
120.90%97.51%
130.66%98.17%
140.48%98.66%
150.36%99.01%
160.26%99.27%
170.19%99.47%
180.14%99.61%
190.10%99.71%
200.08%99.79%
210.06%99.84%
220.04%99.89%
230.03%99.92%
240.02%99.94%
250.02%99.95%

And let's see a graph...

Graph illustrating chances to craft a 99+ quality item

Now let's draw some conclusions from this data. First, warm fuzzie ones... over half the time your request a 99, it will arrive within the first three tries. Nine times out of ten it will take eight tries or less. And ninety nine times out of a hundred, it won't take more than 15 tries to have a 99 or better quality item crafted.

Feeling better now? You shouldn't. Although this chart shows only one in a thousand orders will take more than 23 tries, it can happen. And the odds within a certain number of tries will never, never, reach 100%. The odds gets progressively more improbable, but one in a million orders for a 99 quality item will take 45 tries or more!

Are you ready to return to the original question, how many tries will it take to get an MP item? If you followed along and created the spreadsheet, just change the cell B2 to =1/50 (or simply .02).

TriesOdds for EXACTLY
this many tries
Odds WITHIN
this many tries
12.00%2.00%
21.96%3.96%
31.92%5.88%
41.88%7.76%
51.84%9.61%
61.81%11.42%
71.77%13.19%
81.74%14.92%
91.70%16.63%
101.67%18.29%
111.63%19.93%
121.60%21.53%
131.57%23.10%
141.54%24.64%
151.51%26.14%
161.48%27.62%
171.45%29.07%
181.42%30.49%
191.39%31.88%
201.36%33.24%
211.34%34.57%
221.31%35.88%
231.28%37.17%
241.26%38.42%
251.23%39.65%
261.21%40.86%
271.18%42.04%
281.16%43.20%
291.14%44.34%
301.11%45.45%
311.09%46.54%
321.07%47.61%
331.05%48.66%
341.03%49.69%
351.01%50.69%
360.99%51.68%
370.97%52.65%
380.95%53.59%
390.93%54.52%
400.91%55.43%
410.89%56.32%
420.87%57.19%
430.86%58.05%
440.84%58.89%
450.82%59.71%
460.81%60.52%
470.79%61.31%
480.77%62.08%
490.76%62.84%
500.74%63.58%
510.73%64.31%
520.71%65.03%
530.70%65.72%
540.69%66.41%
550.67%67.08%
560.66%67.74%
570.65%68.39%
580.63%69.02%
590.62%69.64%
600.61%70.24%
610.60%70.84%
620.58%71.42%
630.57%71.99%
640.56%72.55%
650.55%73.10%
660.54%73.64%
670.53%74.17%
680.52%74.69%
690.51%75.19%
700.50%75.69%
710.49%76.17%
720.48%76.65%
730.47%77.12%
740.46%77.58%
750.45%78.02%
760.44%78.46%
770.43%78.89%
780.42%79.32%
790.41%79.73%
800.41%80.14%
810.40%80.53%
820.39%80.92%
830.38%81.30%
840.37%81.68%
850.37%82.04%
860.36%82.40%
870.35%82.75%
880.34%83.10%
890.34%83.44%
900.33%83.77%
910.32%84.09%
920.32%84.41%
930.31%84.72%
940.31%85.03%
950.30%85.33%
960.29%85.62%
970.29%85.91%
980.28%86.19%
990.28%86.47%
1000.27%86.74%
1010.27%87.00%
1020.26%87.26%
1030.25%87.52%
1040.25%87.77%
1050.24%88.01%
1060.24%88.25%
1070.23%88.49%
1080.23%88.72%
1090.23%88.94%
1100.22%89.16%
1110.22%89.38%
1120.21%89.59%
1130.21%89.80%
1140.20%90.01%
1150.20%90.21%
1160.20%90.40%
1170.19%90.59%
1180.19%90.78%
1190.18%90.97%
1200.18%91.15%
1210.18%91.32%
1220.17%91.50%
1230.17%91.67%
1240.17%91.83%
1250.16%92.00%
1260.16%92.16%
1270.16%92.31%
1280.15%92.47%
1290.15%92.62%
1300.15%92.77%
1310.14%92.91%
1320.14%93.05%
1330.14%93.19%
1340.14%93.33%
1350.13%93.46%
1360.13%93.59%
1370.13%93.72%
1380.13%93.85%
1390.12%93.97%
1400.12%94.09%
1410.12%94.21%
1420.12%94.32%
1430.11%94.44%
1440.11%94.55%
1450.11%94.66%
1460.11%94.76%
1470.10%94.87%
1480.10%94.97%
1490.10%95.07%
1500.10%95.17%
1510.10%95.27%
1520.09%95.36%
1530.09%95.45%
1540.09%95.55%
1550.09%95.63%
1560.09%95.72%
1570.09%95.81%
1580.08%95.89%
1590.08%95.97%
1600.08%96.05%
1610.08%96.13%
1620.08%96.21%
1630.08%96.29%
1640.07%96.36%
1650.07%96.43%
1660.07%96.50%
1670.07%96.57%
1680.07%96.64%
1690.07%96.71%
1700.07%96.78%
1710.06%96.84%
1720.06%96.90%
1730.06%96.97%
1740.06%97.03%
1750.06%97.09%
1760.06%97.14%
1770.06%97.20%
1780.06%97.26%
1790.05%97.31%
1800.05%97.37%
1810.05%97.42%
1820.05%97.47%
1830.05%97.52%
1840.05%97.57%
1850.05%97.62%
1860.05%97.67%
1870.05%97.71%
1880.05%97.76%
1890.04%97.80%
1900.04%97.85%
1910.04%97.89%
1920.04%97.93%
1930.04%97.97%
1940.04%98.01%
1950.04%98.05%
1960.04%98.09%
1970.04%98.13%
1980.04%98.17%
1990.04%98.21%
2000.04%98.24%
2010.04%98.28%
2020.03%98.31%
2030.03%98.34%
2040.03%98.38%
2050.03%98.41%
2060.03%98.44%
2070.03%98.47%
2080.03%98.50%
2090.03%98.53%
2100.03%98.56%
2110.03%98.59%
2120.03%98.62%
2130.03%98.65%
2140.03%98.67%
2150.03%98.70%
2160.03%98.73%
2170.03%98.75%
2180.02%98.78%
2190.02%98.80%
2200.02%98.83%
2210.02%98.85%
2220.02%98.87%
2230.02%98.89%
2240.02%98.92%
2250.02%98.94%
2260.02%98.96%
2270.02%98.98%
2280.02%99.00%

The first thing we discover, is that about half of the MPs you ever order will be crafted in less than 36 tries! That's wonderful news. About a third of the time, it will take 20 tries or less. And this table (you did copy more rows down, didn't you, to see all these numbers) also tells us that nine out of ten MPs you order will be delivered in 114 tries or less. Pricey, but that's why they are called MPs.

One out of every 20 will take more than 148 tries. One of of every 50 items or so takes more than 193 tries. 1% of the orders for an MP will take 228 tries or more.

One in 1000 orders would take 342 tries or more. One in 10,000 take 458 tries or more, one in 100,000 orders takes 570 tries or more, and one in a million orders for an MP item would take 685 tries or more!

Graph illustrating chances to craft a masterpiece item

Now for some possible reassurance.

Crafting your next item, the odds of an MP remain exactly 1 in 50. How can this be after everything we just covered? Because each attempt is a discrete event. The quality of your last item has no bearing on the odds of crafting your next item, unless Mythic's random number generator introduces some variance. Your odds of a 99/MP are slightly better than 1 in 4.

But before you ever again assume it will take 'just a few more tries', study the odds and remember this might be that rare item that refuses to turn out as an MP.

Before you keep going, remember that each craft is a discrete event, and right now you have a 50/50 chance of getting an MP in the next 35 tries.

And perhaps the best advise, save the best make thus far, and only craft, or have crafted, what you can afford to spend. Learn about the sunk-cost fallacy before you continue.

Is ón cheann a thagann an cheird.

Ehrayn