QUOTE(Tenboro @ Jun 21 2013, 18:11)
You can generalize that to apply to rolling stats in the 95th percentile of the range, assuming your total loot quality adds up to capping the floor at 25. As LotD is a factor applied to the quality bonus, you can't calculate it that easily, but the floor cap does go all the way up to 75.
QUOTE(Tenboro @ Mar 12 2013, 22:08)
If it simply guaranteed a minimum value, it would still increase "average" quality, but it would not increase the chance of getting a keeper. So to be specific: the system does indeed work in a way that increases the odds of getting high quality equipment, because it increases the lower bound of the stat rolls, it doesn't simply guarantee a roll above a certain value.
It was changed some time back, but the way the system currently determines a stat is to roll a value between x and 200, then put that through an exponential function that results in a value q between 0 and 1. This is multiplied by the stat variance and finally added to the base minimum stat, giving a final stat somewhere between the minimum and maximum allowed stat, before it goes on to the other parts of the equipment generator.
The various quality modifiers are all combined into one value between 0 and 0.75, which is multiplied by 200 to give the lower bound of that initial roll, which is x above. So if you have a maxed combined quality bonus of 0.75, it will roll a value between 150 and 200.
(And the base quality score, for all intents and purposes, is the weighted average for q.)
Problem is we are not rolling against a fair linear system. The curve that determines q is exponential.
Let's assume a roll equal to or greater then 197 puts you in the 95th percentile, not a bad guess since the curve is exponential.
(I'm not going to drop 0 out of the possible rolls, so instead of rolling between 0 and 200 using 200 as the denominator, I will be using 201 because there are that many possible values, if this needs to be changed I will do so.)
Below is the chance of a single stat being high enough that if all other rolls are the same or better will put the gear into mag/legendary category.
Single Stat Roll:
0.00 quality mod: 1.99% (000-200)
0.25 quality mod: 2.65% (050-200)
0.50 quality mod: 3.96% (100-200)
0.75 quality mod: 7.84% (150-200)
Five Stat Roll (just single roll to the fifth power)
0.00 quality mod: 2.90*10^-7% (000-200) (1 in 345025251)
0.25 quality mod: 1.30*10^-6% (050-200) (1 in 076662818)
0.50 quality mod: 9.74*10^-6% (100-200) (1 in 010263770)
0.75 quality mod: 2.97*10^-4% (150-200) (1 in 000336939)
Ten Stat Roll (just single roll to the tenth power)
0.00 quality mod: 8.40*10^-16% (000-200) (1 in 1.19*10^17)
0.25 quality mod: 5.88*10^-14% (050-200) (1 in 5.87*10^15)
0.50 quality mod: 9.49*10^-13% (100-200) (1 in 1.05*10^14)
0.75 quality mod: 8.81*10^-12% (150-200) (1 in 1.14*10^11)