Sorry this was not meant to match the measured data, but as an example that basis functions do not have to be linear in nature to have linear behavior as a whole.

see http://en.wikipedia.org/wiki/Bernstein_polynomial

This looks correct. What software did you use to plot this, by the way?

How do you explain the enormous difference in the peak heights of the 25% and 50% curves?

Looks like Mathematica.

I just downloaded his spreadsheet, here are the equations:

0% resist rate chance: 150*x^2 - 250*x + 100 (pretty sure this is exact)
25% resist rate chance: 275x3 - 545x2 + 275x - 0 (not optimized)
50% resist rate chance: -338.42x3 + 369.8x2 - 19.56x + 0 (not optimized)
75% resist rate chance: 120x2 - 45x + 0 (relatively well optimized)

Cubics are a nightmare to fit. Someone else can figure those out, but these are raw data trendlines.

Again, Kenco's is close, but not quite, as he shows 100% hits past 68%.

There is no functional reason they need to be equivalent in any form. The way it works now is good since it rapidly diminishes the 25% column before max resist, which would be bad to have too many hits around of those numbers (see: Hydross). The offset are the outlying quadratic functions.

Finally.

Back before the expansion, I got into a somewhat heated debate with my guild about whether resistance scores had a linear (every point matters) or a tiered (74 out of every 75 points are useless ho ho) effect. I tried to graph out approximate values and run tests, but some of them didn't really buy it because of some of the values--namely, that my felhunter at 220FR wasn't taking any 0% resists. That seems like it might now have an explanation.

I'd love to see the exact formulas finally come to light. All I did were approximate graphs (and tried to back-fit my experimental data) and a bunch of trials with the ever-handy Twilight Flamereavers (Fire Shield is go).

My results (at 60) were here:

http://oth.arathianknights.googlepag...cs-resistances
http://oth.arathianknights.googlepag...s-resistances2

Note, I did see the magical cutoff value on my Felhunter at a 55% average damage resisted (I found out later with testing on myself that it cut out at about 200/300 FR, or 50% ADR), which seems to match closely with the '67% of maximum possible resistance' value.

Also, I did a spreadsheet, but yours are prettier.

This is using the trend lines that heel suggested.



I should add that the 0% won't actually arc back like that at 100% because the constant is 0, not whatever the regression thinks it is.

I don't mean the 25% and 50% curves with respect to each other, I mean the 25% and 50% curves in his plot with respect to the ones in the data.

Your functions however are much closer to the truth whereby the 25% curve peaks at around 40% chance and the 50% curve peaks at around 50%.

Oh and it would be interesting to put the numbers that Blizzard gives us (here) on there to compare.

Yeah, I get it bidby, I just noticed that after making the trendlines above, theres a discrepancy. However, this is also experimental vs theoretical, but he did do a relatively large sample set. Shrug.

Sorry I should have really said as a coder more or less piecewise linear would have been my preferential for implementing since means I can pick a few points and quickly implement it.

Gathering few data points now for missing spots to try to clairify.

Clearly this isn't accurate. Maybe for PvP or something.

As we've seen with the fact that the rate of 0% resists can in fact bottom out at 0%, there's something shady about that chart anyway.

Some "spells" can fully resist. Perhaps its more apt for outgoing damage, perhaps its more apt for PvP damage. Perhaps it works like this for incoming fireballs that we can fully resist, but not melee elemental? I don't think it means its totally debunked.

Not to mention they wouldn't need to deal with the negative %'s we're seeing on these graphs.

The full resist not being affected by resistances is not present for melee attacks only, but for spells also. I'm doing AOE on Illhoof imps with 352 fire resist and based on the combat log parsing I only had 4.5% full resists out of ~3000 imp fireballs. This comes purely from to hit mechanic I think as miss for level 69 mobs against me is 5% and 4% for level 70 (imps are 69-70).

But then you're stuffed, because if it passes through the origin, then at some point it has to drop *below* the x axis. That's clearly bogus - you can't have a *less* than zero chance of a 100% resist.

Whatever curves you fit, on whatever theoretical grounds, they have to obey the constraint that
y >= 0 for all x given 0 <= x <= 100%

No offense, but thats basically the stupidest thing i've read on EJ in a long time. Going below 0 is perfectly legal. Why in the world would it not be?

At 495 defense, your chance to be crit is negative according to the equations, but you don't receive negative crits, you receive the absolute... zero. You obtain a deficit of such that would be seen if the baseline was increased. Even linear equations will go to zero when extended beyond the zero point.

Shall I make a chart of a straight line for defense going from 5% crit, to 0% crit over 490 defense, and have it keep going? The equation is Y=490-5*D - nothing, NOTHING, in that equation stops the "line" from going negative when you pass 490 defense. Yet, you don't get negatively crit. This is basic coding here... The conditional is applied on the code. It is so corollary it is almost insulting to have to explain it.

The chart is clearly rounded off, and it clearly stops at 68%. Any quadratic function would do the same. The variation at 100% is due to the graph using "estimates" of its trendline, whereas my original equation for 0% passes right back at 0% chance of 0% resist at 100% resist gear, and stays at or below 0% before 68%.

Because then the *true* damage reduction (being the weighted average of the curves) would have weird blips in it where the trough of each curve gets flattened out on the X axis.

And given a choice between your figures, which give a -ve chance of a 0% resist at 80% resistance, and the official Blizzard figures which give a 1% chance, I know which I'd go for.
http://www.worldofwarcraft.com/info/...sistances.html

Note: no figures below zero, and all weighted sums work out correctly. Any graphs we try and fit really have to obey those two constraints IMO. And having no figures below zero is a necessary prerequisite of having the weighted sums work correctly unless you end up fitting some really weird functions (i.e. matching discontinuities in the other curves to counterbalance the one getting flattened at zero).

[Edited to point at the official figures]

BTW based on the data I'm getting at the moment you are going to have an extremely hard time fitting quadratic curves to the new data. So wouldn't spend any time trying to make them better (getting a few more data points then will post the updated results).

I think I see his point. Although these graphs are made on the assumption that the weighted average is a linear function, the assumption relies on the fact that all points (both x and y values) along the curves can happen in a real scenario. Yet we know this isn't possibe.

Plus its worth noting that they're not against using piecewise functions. Just look at the team rating/arena point graph!