If you have any questions on how I did the math, or my methods for testing, feel free to ask and I will do my best to answer them.
How magic find(MF) works:
When a piece of loot drops, the game does a single roll which determines the quality of the item (NOTE: I am almost positive there is a second roll done to determine the ilevel)
For a boss, the baseline drop chances for items are:
Orange/green: not a damn clue
when you increase your MF, the above drop rates are multiplied by 1+MF. This is done to all non blue and above items,so for example, if you had 75% MF, your chance for a given boss drop to be a yellow would be 0.02 x (1+0.75) = 0.035, or 3.5%
the implications of this is that MF will start to be devalued after 173%, as after that point every boss drop should be guaranteed to be a blue or better(though I don't have enough MF gear currently to prove this empirically), and therefore any additional MF would only affect your chance to get yellows.
all that was horribly wrong, I was pretending blizzard would make the system linear, of course they wouldn't.
as it stands, I sadly don't have enough MF gear to get an accurate equation, If anyone has 250+ MF, and would like to help out with the data collection PM your email and I will give you editing access to the spreadsheet.
How Nephalem valor(NV) works:
There are two components, to NV. the first is the standard magic find increase
the second component affects the quantity of loot that drops
the base line number of drops a boss has is 6, and for each stack of NV you will get an additional drop, and with the 5th stack that additional item is guaranteed to be a rare. Tomes:
Tomes drop on their own loot table, meaning that you cannot get a tome instead of getting an item.
the baseline drop rate for tomes is 50%.
Now NV/MF does affect tome drops, though I don't have a sample size nearly large enough to be fully confident in determining exactly how it affects the drop rate.
at this point all I know is that it certainly increases the chance of tomes dropping, and also appears to increase the number of possible tome drops; as I have seen 0-2 tomes drop with NVx5/108% MF, versus only 0-1 tomes dropping when I had NVx0/0% MF
Other thoughts,not substantiated by testing:
Rares/elites drop 4 items, plus tomes, and while I don't have any data to back it up, it certainly feels like the drop rates (%chance) are about the same as bosses.
For tomes it also feels like even with NVx5/108%MF the drop rate was about 50%, and I never got more than one tome from a single elite.
I hope to get some more free time in the near future so I can further test how tome drops work, as well as test other acts to see if the drop rates are consistent. If anyone would like to help with this sort of thing, especially people who have the ability to easily farm act 3/4 bosses, I would greatly appreciate any and all help. The only thing that I ask is that you be as accurate as possible with your data collection, as tainted data makes for bad science (for example I forgot to put on my 0% MF gear a few times during testing, though I luckily caught my self mid fight most of the time, the 28% MF area in my spreadsheet was when I messed up)
btw., at 350% mf (5x NV included) i still see whites from bosses, and after recent patch i hardly see rares on inferno whimsyshire (mostly crap blues/whites).
apparently it didn't get set to public the first time I tried to do that... should be fixed now.
also if you're still getting whites that would mean that that MF's effect is nonlinear, and that I'm going to need to do some more thinking to try and figure out that equation, I'll see what I can do about getting a better model working. I could be talking out of my ass here but if the effect is nonlinear that would suggest a two roll system.
So, after a long night of testing, this is what I've got:
MF's effect is nonlinear and has diminishing returns, more specifically it's logrithmic:
Note that MF% is the Y axis, and drop rate is the X axis.
again my sample sizes are limited (especially with the 113%MF data point) and I don't have the MF gear to get data points for the 200-250 region, but I think I'm getting closer to the right answer (or at least to a less wrong one)
after I can get a more accurate R^2 value, I intend to go about seeing if I can figure out if the increase in blue drop chance occurs at the same rate as yellow drop chances
No, it means that as you increase your MF, each additional % will be worth less than the previous.
That's not what I read from your graph.
Have a look at it. Try seeing yourself with 10% dropchance for a rare; that means you have approximately 115% MF. If you want to get to 20% dropchance that equals ~180% MF. If you want 30% dropchance that equals ~215% MF. 40% -> ~235% MF and 50% -> ~ 250% MF. Increasing MF from 250 to 300 gives a boost from 50% dropchance to almost 100%, while an increase in MF from 50 to 100 pushes you from approximately 6% dropchance to 9%...
To me that looks very much like each % MF gets better the more you're currently sitting at...
- - -
Allow me to demonstrate: if I assume that your graph displays the right data, then
y = 78.004 * ln(x) + 302.66
in which y = MF and x = dropchance.
Rearranging stuff a bit you get
y - 302.66 = 78.004 * ln(x)
(y - 302.66)/78.004 = ln(x)
exp[(y - 302.66)/78.004] = x
In other words: your dropchance is exponentially proportional to MF and therefore it will seem as if MF gets better the more you already have.
- - -
Are you sure that you have plotted correctly? 'cause in the graph you give the formula y = 78.004*ln(x) + 302.66 and for the graph, y = % MF and x = droprate, while you state in the original post that x = %MF and y = droprate...
As you stated, sample size is way too small to give any conclusive data. There's too much randomness that can go around to give a reasonably good confidence interval.
Anyway, my real questions are about the formula you use. The formula is to find rare (yellow) items right? ln(MF) seems as it should be ok, with MF being (100+MF%)/100, but the +302? Is the value the formula yields supposed to be divided by 100 to give a percentage number?
Just to make it clear. ln(MF) with 0% mf would have the value 0? and with 100% mf it should have the value ln(2)? Is this how this is supposed to be interpreted?
you both are right, I got the axis' screwed up and it is currently an exponentially increasing function. I figure this is due to inaccurate data points, namely the 113% MF point, as I had like 3 or 4 runs at that value. I'm currently doing more runs at 113%MF to get a more accurate point there, which should hopefully help out.
Ah that name always makes me laugh, reminds me of the gold old days in wow listening to bad techno and Digo's bad stories about woman. was it beepz or zest that would tell you to Tclap all the time? had a lot of fun. just wanted to say hi when i saw the name, if you're not TGM then disregard.