Crit / BPE / Resist / Mitigation Ratings :: How they convert to % based on level

[Dom12]

Unfortunately, the previous threads that led to the initial formulas were sacrificed to the forum purge gods. Further down this thread is some of the discussion that led to the formula revamp. Here's the resulting formulas that can be used to convert your ratings to % based on your level:

Variables

• % :: this is your base percent chance versus on-level mobs (assuming it's below the cap)
• Rating :: this is the rating shown on your character sheet for the stat in question
• Level :: this is your level :: as explained below, I believe you can substitute the mobs level here

Mitigations (Common, Fire, Frost, Shadow, Lightening, Acid)
% = Rating / (150 * Level + Rating)

Everything Else (Avoidances / Resistances / Criticals / Crit Def / Offence / Defence / Healing)
% = Rating / ((1190/3) * Level + Rating)


The primary purpose of these formulas is to determine what your percentage would be for a given rating. For example, let's say you're at L65 and your character screen shows that you have 3000 crit rating and hovering over that shows a 10.4% crit chance. You want to know what you would gain from a piece of gear with +212 crit rating, so you plug in 3212 rating into the formula to see that your chance would go to 11.1%.

However, I believe you can also use them to determine what your percentage is against a mob of a given level. IOW, if you're L65, and you want to know what percentage your crit chance would be against a L67 mob, you would plug the mob level into the formula instead of your own. You could also use it to figure out what rating you would need to have to maintain a certain percent against a higher level mob, for example, to keep your crit chance capped at 15% (with L65 as the starting point, adding approximately 70 rating per level keeps crit/BPE/Resists capped)

Some round sample values:

15% crit at L50: 3500
15% crit at L60: 4200
15% crit at L65: 4550

20% mitigation at L65: 2437
30% mitigation at L65: 4178
40% mitigation at L65: 6000
50% mitigation at L65: 9750

Credit goes to LagunaD and Moebius92 for coming up with the original formulas.

EDIT1: to appease the formula police
EDIT2: to note that the BPE/Crit formula also applies to pretty much everything else
EDIT3: changed formulas from the original ones by LagunaD¹ to the more accurate ones suggested by Moebius92²


¹ For anyone interested, these are the old formulas:
Mitigations (Common, Fire, Frost, Shadow, Lightening, Acid)
% = ((0.0000106516) * ((Rtg / Lvl)^3) - 0.003593648 * ((Rtg / Lvl)^2) + 0.653753685 * (Rtg / Lvl)) / 100
Everything Else (Avoidances / Resistances / Criticals / Crit Def / Offence / Defence / Healing)
% = (0.25*(Rtg / Lvl) - 0.0005*(Rtg / Lvl)^2) / 100

² Moving to the new formulas brought the max error of what was shown in-game vs. what the formula gives from 0.256 down to 0.050 for the crit formula and from 0.159 to 0.055 for the mitigation formula. The total error for the 89 values I gathered ranging from L13-L65 for the crit formula went from 0.941 down to 0.056. The total error for the 29 values I gathered in the same level range for the mitigation formula went from 0.434 down to 0.144.

[Chazcon]

tag for future reference

[Ruthelia]

You need to explain the variables in the formulae and where players can get them from. Any and every acronym should be also written out fully the first time you use it, with the acronym immediately following it in brackets. Other than that it looks ok.

[Chazcon]

LOL that's funny, the formula police...

[bubbajman]

wonderful. I cannot count how many times I wanted to figure this out.

[ironmosquito]

I just thought I would bump this - hold off the purge elementals for a bit longer

[moebius92]

Formula shows some inaccuracies.

For example, I happen to know that at level 65, a rating of 539 will report a 2.0%, while a rating of 540 will report a 2.1%

0.25 * 539 / 65 - 0.0005 * (539 / 65)^2 = 2.03, rounds to 2.0%
0.25 * 540 / 65 - 0.0005 * (540 / 65)^2 = 2.04, rounds to 2.0%

The second value is wrong. I suspect the error in the formula is less than +/-0.1%, but if you need to know the actual percentage, it's probably going to be a bit off.

[LagunaD]

Formula shows some inaccuracies.

Yes, although the basic formula seems to be unchanged from MoM, we now have tooltips up to higher values, and it looks like the offense/crit/b/p/e/resist formula has a small (positive) cubic term.

For your test points, my current best fit formula still isn't perfect, but:

539/65 -> 2.041
540/65 -> 2.045

So it is pretty close to rounding properly.

Also, I think it is likely that the unrounded numbers are used internally, so the error is probably even smaller than the 0.05% suggested by rounding to 3 digits...

I didn't actually use any points that low, by the way. My lowest point in the fit is 750 Rating (at L65).

The coefficients I get are:

Linear: 0.250928948
Quadratic: -0.000583285
Cubic: 8.69771E-07

[moebius92]

Try this one out. Let R be the rating, and L be the level.

p = R / (L * 400)
Actual percentage = (p / (0.991665 + p)) * 100

539 and 540 return the proper values, and the other ratings I have on hand give the correct answer.

[Dom12]

Fighting off the purge.
..books are burning!

[TheAnticat]

Tag for reference.....

[Mael5trom]

Tag for future reference.

[Malephor]

Anyone have the dev crit formulas on hand, or is there a way to get to dev crit from the crit formula here?

[Dom12]

Anyone have the dev crit formulas on hand, or is there a way to get to dev crit from the crit formula here?

You gain dev crit at roughly 1/3 the rate of crit. I find that dividing crit % by 3.14 comes up w/ a pretty close approximation - on my hunter at least. I haven't taken the time to really look at it across multiple levels or classes tho.

[Feybobiam]

Devastates are crits divided by pi.

/nods sagely

[moebius92]

Anyone have the dev crit formulas on hand, or is there a way to get to dev crit from the crit formula here?

From what I can tell all rating to percentage conversions use the same formula:

percentage = rating / (constant * level + rating)

You can solve this for rating and constant to get:

rating = percentage * constant * level / (1 - percentage)
constant = rating * (1 - percentage) / (percentage * level)

For resistance, avoidances, criticals, critical defenses, and offenses, constant = 1190 / 3. This gives us two points of interest, 15% (0.15) and 30% (0.30). Plugging in the two percentages, we get:

rating = 0.15 * 1190 / 3 * level / (0.85) = 70 * level
rating = 0.30 * 1190 / 3 * level / (0.70) = 170 * level

(I believe someone else has noted the 70 * level and 170 * level thing before.)

For devastating criticals, we can take that a rating of 58 at level 1 gives you 4.2% (0.042), and plug in to get the constant (remember that percentages are rounded off, so it's really anywhere from 4.15% (0.0415) to 4.25% (0.0425)), and you get

constant = 58 * (1 - 0.0415) / (0.0415 * 1) = 1339.6
constant = 58 * (1 - 0.0425) / (0.0425 * 1) = 1306.7

So, it's probably somewhere between 1339.6 and 1306.7. I'd use 1330, just because it's a round number and plugging in a percentage of 5% (0.05) gives you:

rating = 0.05 * 1330 * level / 0.95 = 70 * level

...which means that whatever rating gives you exactly 15% critical gives you exactly 5% devastating criticals. (I don't know if that's actually true though - I suspect it isn't, just because I mostly chose it because it looks pretty.)

[Dom12]

From what I can tell all rating to percentage conversions use the same formula:

percentage = rating / (constant * level + rating)

You can solve this for rating and constant to get:

rating = percentage * constant * level / (1 - percentage)
constant = rating * (1 - percentage) / (percentage * level)

For resistance, avoidances, criticals, critical defenses, and offenses, constant = 1190 / 3. This gives us two points of interest, 15% (0.15) and 30% (0.30). Plugging in the two percentages, we get:

rating = 0.15 * 1190 / 3 * level / (0.85) = 70 * level
rating = 0.30 * 1190 / 3 * level / (0.70) = 170 * level

(I believe someone else has noted the 70 * level and 170 * level thing before.)

For devastating criticals, we can take that a rating of 58 at level 1 gives you 4.2% (0.042), and plug in to get the constant (remember that percentages are rounded off, so it's really anywhere from 4.15% (0.0415) to 4.25% (0.0425)), and you get

constant = 58 * (1 - 0.0415) / (0.0415 * 1) = 1339.6
constant = 58 * (1 - 0.0425) / (0.0425 * 1) = 1306.7

So, it's probably somewhere between 1339.6 and 1306.7. I'd use 1330, just because it's a round number and plugging in a percentage of 5% (0.05) gives you:

rating = 0.05 * 1330 * level / 0.95 = 70 * level

...which means that whatever rating gives you exactly 15% critical gives you exactly 5% devastating criticals. (I don't know if that's actually true though - I suspect it isn't, just because I mostly chose it because it looks pretty.)

Nicely done! That's a lot more simple than the old forumla and actually resolves some errors that I've noticed in the latter levels using the old formula. I'm gonna go do some spot checks of some of my characters across different levels, but then I'll update the OP w/ your formula.

Have you looked at the formula for mitigations? At a quick glance using a few screen shots I have on hand in the L50-60 range, a constant of 150 fits pretty well, giving:
Mitigation % = Rating / (150 * Level + Rating)
The data I have on hand to test it against is pretty thin, but the widest variance I'm seeing is 0.042% from what the tooltip shows. Using a more obscure constant of 2254/15 tightens it a bit bringing the max variance down to 0.029%. But again, that's limited to sample data between L50&60, so not much use going too far w/o more data.

Thoughts?

[moebius92]

Have you looked at the formula for mitigations?

Your guess is probably better than mine. I looked at mitigations briefly, but all I remember is that the constant should be in the 100s. Could be anywhere from 50 to 500, really.

I was mostly looking into the rating formula because I needed more accurate tactical offense and healing percentages to calculate the base values for the LM's skills. I hadn't even looking into devastates until a couple days ago.

[Dom12]

Alright, it took me a while to get back to this, but I think I've done enough spot checking that I'm pretty confident in the new formulas (one formula really, just with two different constants). It's proven to be significantly more accurate than the older one. And it's much more simple, which is definitely a good thing IMO. So I'm gonna go back and edit the OP with the new formula.

[Evendale]

Thanks for the update. These formulas are very nice, and the 70/170*level rating for cap is also an extremely useful piece of information

[bastiat1]

Excellent work and contribution to the community LagunaD, Moebius92 and Dom12. Thanks very much for sharing.

[Tovarashh]

Everything Else (Avoidances / Resistances / Criticals / Crit Def / Offence / Defence / Healing)
% = Rating / ((1190/3) * Level + Rating)


However, I believe you can also use them to determine what your percentage is against a mob of a given level. IOW, if you're L65, and you want to know what percentage your crit chance would be against a L67 mob, you would plug the mob level into the formula instead of your own. You could also use it to figure out what rating you would need to have to maintain a certain percent against a higher level mob, for example, to keep your crit chance capped at 15% (with L65 as the starting point, adding approximately 70 per level keeps crit/BPE/Resists capped)

Against higher level mobs, I think there might be another term for level differences, like the damage formula, that makes it more complicated. I can see from reducing the terms for a capped % of 15, that the coefficient is 70. That puts the cap at 4760 when fighting a mob of level 68. I measured the melee defense cap vs a level 68 mob and it was around 5300. I'm not sure how that relates to the formula.

[Amphoras]

So, it's probably somewhere between 1339.6 and 1306.7. I'd use 1330, just because it's a round number and plugging in a percentage of 5% (0.05) gives you:

rating = 0.05 * 1330 * level / 0.95 = 70 * level

...which means that whatever rating gives you exactly 15% critical gives you exactly 5% devastating criticals. (I don't know if that's actually true though - I suspect it isn't, just because I mostly chose it because it looks pretty.)

I did a few tests using this formula, and the suggestion earlier in the thread that dev crit was crit/pi.

Firstly, I noticed in-game a while ago that getting ~4500 crit rating gave 15% crit chance and also 5% dev crit chance. This made me suspicious of the crit/pi formula as it doesn't match up. I then saw the quoted formula which does match up. I then tried taking off my champs gear piece by piece and comparing the dev crit chance from each formula with the value given on the character sheet.

The crit/pi formula is not that far off the actual value at ~1500 rating. When you round it you get the same value. However, as the rating increases, the crit/pi formula gets further and further away from the true value. At 3966 rating you have 4.4% dev crit chance but the formula gives 4.233% which is a fair bit off.

The % = rating/(1330*level + rating) formula gives much better results. At every point I tested, it gave the same value as the character sheet when rounded. It seems much more likely that this or something very similar is the formula used, especially as it is in the same format as the others.

Edit: Tested it with a few values of Partial Block/Parry/Evade and it seems to hold for them too.

Also, if its of any use, I noticed that your Partial Block/Parry/Evade Mitigation is 20% + Block/Parry/Evade % and caps at 35%. Skills like Pledge, Guardian's Defence/Parry that add a % to Block/Parry/Evade don't seem to add anything to the Partial Mitigation unless they specifically say they do (eg. Guardian's Defence/Parry).

[drfacts]

Would the Mitigation formula work for partial mitigation as well?

[Amphoras]

Would the Mitigation formula work for partial mitigation as well?

Not exactly. Your partial mitigation is a combination of multiple factors. If we take blocking common damage as an example. Firstly, your partial block chance is determined by your block rating. Then your partial block mitigation is 20% + block% + any gear bonuses. So if you have a 15% block chance, and relics that give +10% partial block mitigation, then your partial block mitigation is 45%. If you're taking common damage, this is then added to your common mitigation. So in total you get that your partial block mitigation against common damage is 20% + block% + partial block % gear bonuses + common mitigation. So using the previous numbers, if you have a common mitigation of 45%, then any time you partially block a common damage attack, you'll mitigate 90% of the damage it does.