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Out of curiosity, what is the source for this information? - Andy talk 14:15, 7 September 2007 (EDT)

The research I performed. Some of it is still available on the official forums (redux folder), most of the initial discovery part has been scrolled away though. :( Crit damage ratio and spell penalty information should still be on there, though.

So uh, how do I do the little signature thingie? :S Like this? HOFMANNM1 12:40, 8 September 2007 (EDT)

Heh. Four tildes. IE: ~~~~. That's all. All of the information you've posted seems like it'd be difficult to research is all, though I don't doubt the possibility. I was curious if it was a specific post or not, and it is helpful to cite sources of information such that the information can be verified as accurate. - Andy talk 22:54, 9 September 2007 (EDT)

Unfortunately, the discovery phase *just* got scrolled off. (Incidentally, this is before I got a better read on spell penalty.)

That's as far back as the boards go, but I do have a copy of the posts prior to that where I first started figuring it out:

  1. 1583

So we all know redux factors are a little blurry. Mark was the first to notice the connection between the ratio of crit damage to raw damage and redux factor. Now, when I was eliminating some other possibilities, I took my warrior and smacked him around 263 times with everything relevant kept constant (skills, DF, etc.). Using a weighted average protocol that I think I went into before, I obtained a redux factor. Super. It did not take much effort to establish what the average crit damage to raw damage ratio was (nor to obtain standard deviations for both numbers).

So I figured, why not make arbitrary groups of 15 out of this data by sorting it by Excel's random function and compare the values of RF and CRR (crit/raw ratio) to the "baseline" value? And further, why don't I repeatedly sort by random? The chances of getting the same group of 15 are pretty dang low, after all, and I can't go back and get more data for this set.

So that's what I did. The results are awfully appealing. First, of the 272 sets of data I took, only 2 fell outside a +/- .09 CRR range (both were higher). They won't be included in the following graphs because I like the symmetry. In each category (-.09 = -.094999 to -.085) I did a straight average of the deviations of the RF from the baseline value in hopes that I'd be able to establish numerically what Mark's been talking about. (I also kept track of how often a group fell in each particular category). Here's a graph of the first thing, because it's really dang impressive if you ask me:

(Please not that the drop to 0 at -.1 and .1 is the graph's way of expressing DIV/0 errors (which seems like a redundant way of writing it, but anyway): that is, there were no samples.)

So like I said, that's pretty doggone cool. I'm going to keep going for awhile with this to because I want a good 10-15 samples in each bin. Speaking of samples per bin, I decided to graph that too:

(The green line is a Poisson distribution which approaches the binomial distribution. I used Poisson because of the aforementioned ultra-high results.)

I'm hoping Mark will be able to explain that ginormo spike at -.04 with his RF1/RF2 thing, because I have no idea how that happened. There should be +/- 15 bars on each number, but I felt that would make the graph too busy. It's tantalizingly close to being able to resolve the spike, but I'm pretty sure that's a real feature there.

and #1613

I believe I've come across a very powerful tool to aid in redux analysis. To briefly reiterate the history, Mark noticed awhile back that the crit damage ratio seemed to have an inverse relation to the redux factor on any given shot; that is to say, a lower crit damage ratio would result in a higher redux factor. I had 263 samples from previous redux testing that kept redux points and attacker constant. I took 100 arbitrary random samplings of 15 hits apiece, took a weighted average of the redux factor, a pure average of the ratio of reduced crit damage to total reduced damage (Crit Damage Ratio or CDR), and compared them to the same values for the entire set of 263 samples. I then used Excel to pluck out the data into 15 bins ranging from -.07499 to .07499 deviation from the sum CDR. I ended up using those numbers because none of the groupings fell outside the range. Finally, I took averages of these bins, and graphed them like so: (with trendline provided by Excel)

No doubt you can see that this graph only ranges from -.05 to +.05. The reason for this can be seen from the following graph which shows the population of each bin (blue line) compared to a binomial distribution (green line):

Numerically, I got less than 12 hits for each of the bins outside the .05 range, and it doesn't make sense to try and find a reliable average with that few datapoints.

Now, I looked at that first graph and realized the slope was awful close to 2.5, so I decided to see what would happen if I just made a line with slope of 2.5 and compared the predictions to my results.

Note that the y-axis is in thousandths of RF (for instance, the 1 in 56.1% redux). The model predicts the deviations accurately to within less than one thousandth, which is good enough for me. I constricted this graph to .04 because only at the .04 mark do I get 50 or more samples.

It would take a really long time to get up to 50 samples for the outlier bins, so I'm ok with saying that this is how CDR impacts RF. For each hundredth away from the average CDR, the observed RF goes in the opposite direction from its baseline by 2.5 thousandths.

HOFMANNM1 22:49, 14 September 2007 (EDT)

Proposed Revision to equation

In Order of Operations, Part 1:

Total damage taken = (reduced raw damage + crit damage) - trunc((redux factor *(reduced raw dmg + crit dmg))

Proposed Changing to: Total damage taken = Ceiling( (1 - Redux Factor) * (Reduced Raw Damage + Crit Damage))

Easier to follow

I'll bring it to Mark. I have more revisions from him to do when I haven't been playing since 8 am. VANKRASN39 (talk) 23:57, 17 September 2016 (CDT)
Sounds good, thanks Allereli. I may just whip up a quick spreadsheet or something to Calc Redux based on the latest Mark Calculations. I made a couple spreadsheets to evaluate redux on the threads that I'm sure you're reading. --HJELTE (talk) 10:11, 18 September 2016 (CDT)
Mark says: "Both formulas are correct but Whirlin's is a simplified version and it's the one that I would normally use. The reason I opted for an expanded format was to give the reader, IMO, an easier conceptualization of how the redux factor is applied to damage reduction but I have no objection to replacing it."
I'll leave it up to consensus if others want to chime in. VANKRASN39 (talk) 11:38, 18 September 2016 (CDT)

Could someone please fix the math?

The equations are all broken. "Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle \mathrm{1060 + \frac{2000}{level}}}" is rather hard ot understand. GEHAYI (talk) 22:58, 9 July 2020 (CDT)

The wiki manager is aware that equations are not displaying properly. I have passed along your comment in case someone would like to respond; I do not have information to do so. MOD-GSMOTTE (talk) 11:48, 11 July 2020 (CDT)