Sacred Underworld: Chance to land a Critical Hit, a handy reference.

[xeyp 53]

You know those pesky "Chance to land a critical hit: X" 
If you've ever gone beyond 5, you would've noticed something strange upon hovering on the plus icon next to your character's portrait.
There these modifiers would be summed up and expressed as Chance to land a critical hit x (y%). 
Let's call x critical rating, the game uses some kind of formula to derive a critical strike percentage or y from this rating.
The fact of the matter is, the more you invest in slotting or having items with critical rating, the less each point does. 
Armed with a handful of "Chance to land a critical hit: 5" rings bought by my level 1 Dwarf (@lvl 33 Trading) and a just recently created lvl 9 Battle Mage
with a equipment full of 22 holes to fill (15 equipment, 4 sword, 3 shield) I decided to do you and future me a favor and slot them one my one while documenting the results.
Here's going from 5 to 110 Critical Rating and its relation to critical chance:
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Legend:
Critical Rating | Critical Chance Total | Percentage Increase per 5 Critical Rating increase
5                   5%                  5%
10                 9%                  4%
15                 13%                4%
20                 17%                4%
25                 20%                3%
30                 23%                3%
35                 26%                3%
40                 29%                3%   <
45                 31%                2%
50                 33%                2%
55                 35%                2%
60                 38%                3%    <<
65                 39%                1%
70                 41%                2%
75                 43%                2%
80                 44%                2%
85                 46%                2%
90                 47%                1%
95                 49%                2%
100                50%                1%   <<<
105                51%                1%
110                52%                1%

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If you veterans have ever reached 100% Critical Chance, please let me know at what number that occurs. For the rest of us, especially for lower leveled toons
where itemization is quite limited in terms of the quantity of Critical Rating given I suggest 3 breakpoints <, <<, <<< to use as a guide for investing in critical strike chance.
  The First one at 40 rating gives you almost 30% Critical chance. It's the moment where 3% per 5 rating dries up.(excluding the little rounding up that happens at the next break points)
This is our best bang per buck for the least investment made, it's best for early game characters who could even consider going as low as 25 critical rating for an almost 'free' 20% Critical Chance.
  The Second one is at 60, a nice rounding up giving us our last 3% per point. At almost 40% Crit Chance it feels substantial enough to warrant the increased investment into Critical rating.
This is a good 40-80 character level spot, or until itemization drastically starts to increase the Critical Rating on items to reduce the Equipment Slot / Jewelry slot investment.
  The Third, and probably final logical place where one could aim to take critical rating is at 100, giving us a nice and round 50% critical chance. This I would consider a the gold spot for post 100 character level.
As with their much higher inherent Critical Ratings, Weapon, Equipment and Socketables/I.e. Jewelry make it possible to reach that number without sacrificing too much else - additionally, going past 100 Rating introduces significant diminishing return, judging by the trend in the third column we're 10-15 Rating away from 5 Rating giving less than 1%. That is if it drops below 1% per 5 Rating, however, since the 5 Rating
increments are an arbitrary way of measuring decided by myself and additionally the fractional rounding up and down present in the column - it seems very likely this will be the case and with such rapid decreases
reaching 100% might not be possible through Rating alone - here's where a set like Andiell's Malevolence comes into play w/ 4 pieces supposedly increasing the Critical Percentage directly by 21%.

Now, veterans are definitely welcome to shed some light here, because I'm not aware of how the Critical "Rating" meshes with Direct Critical Strike Increases. 
The best case scenario would be that they are two separate factors that increase the Critical Strike chance, if that is correct - the best strategy would be to max
your Critical Rating at 100 and then use Direct Critical Strike Increases like the Andiell's Set to reach higher percentages. 

@SLD @Sethi22 @gogoblender Are welcome to shed some insights they might have on the matter and help me provide a more complete Critical Strike Chance reference.

[SLD 524]

3 hours ago, xeyp said:

Now, veterans are definitely welcome to shed some light here, because I'm not aware of how the Critical "Rating" meshes with Direct Critical Strike Increases. 
The best case scenario would be that they are two separate factors that increase the Critical Strike chance, if that is correct - the best strategy would be to max
your Critical Rating at 100 and then use Direct Critical Strike Increases like the Andiell's Set to reach higher percentages. 

If there were critical rating and seperate %crit values the "best case" would not be two "seperate factors" as factors would be multiplied. Adding the two chances would give the greatest results ol course. But maybe that is what you meant...

3 hours ago, xeyp said:

  The Third, and probably final logical place where one could aim to take critical rating is at 100, giving us a nice and round 50% critical chance

100 gives 50%? That's an interesting pair.

3 hours ago, xeyp said:

additionally, going past 100 Rating introduces significant diminishing return, judging by the trend in the third column we're 10-15 Rating away from 5 Rating giving less than 1%.

That stinks a lot like 200 rating giving 66% 300 rating 75% and 400 rating 80% etc. That would also obviously mean that:

3 hours ago, xeyp said:

reaching 100% might not be possible through Rating alone

makes sense.

3 hours ago, xeyp said:

here's where a set like Andiell's Malevolence comes into play w/ 4 pieces supposedly increasing the Critical Percentage directly by 21%.

This one I highly doubt though. There is no way without massive empirical testing to be sure but I think these "21%" will just be 21 additional crit rating.
Now why the confusing "%"? Well back in the day when the game first came out crit was a % based mod and it stacked additively with no diminishing returns at all. At some point that was changed to the new crit rating system. Things that still say % are probably just an oversight from the change. As always, I'm not sure when the change was implemented, but it was probably either with the Underworld addon or a patch past that.

3 hours ago, xeyp said:

@SLD @Sethi22 @gogoblender Are welcome to shed some insights they might have on the matter and help me provide a more complete Critical Strike Chance reference.

Gogo may have some light () to shed but I think on such mechanical matters he's mostly in the dark. Oh boy, I'm outdoing myself again
Swthi22 could maybe provide more numbers but I don't think we need any.

As for a "more complete reference", my theory of
[crit chance]=[crit rating]/(100+[crit rating])
seems to create quite accurate results.

The only thing that certainly none of us could "know" is wether I'm right on the assumption that crit% would do the same as crit rating. One would have to make a statistically relevant aniubt of hits and measure the results.
The easiest setup for this would probably be one that would reach 100% if the two potentially adding crit values were working as hoped and looking for non crits. Not sure how reasonable that test setup would be to achieve. Mostly depends on wether you could find more simultaneously usable % bonuses. Once decided what to use, Lindor has some downloadable high level characters with matching gear for such testing purposes.

Edited August 7, 2024 by SLD

[alfchaval 196]

This is easy to test, just cheat some item to give you lot of chance to land critical hit.

Clearly the formula converges at 100%, it is impossible to reach that value.

[SLD 524]

36 minutes ago, alfchaval said:

This is easy to test, just cheat some item to give you lot of chance to land critical hit.

Clearly the formula converges at 100%, it is impossible to reach that value.

We've already determined a formula (though I must admit it must be slightly off otherwise the picture should say at least 99%). The thing remaining to test is if sources like the mentioned

6 hours ago, xeyp said:

Andiell's Malevolence

does anything different like

6 hours ago, xeyp said:

increasing the Critical Percentage directly by 21%.

or just states "%" to cause confusion.



On another note, welcome to the discussion
Always nice to have more active people around!
 

[alfchaval 196]

The previous picture included the bonus of Andiell set (and some extra of two Fadalmar sets).

Anyway, Andiell incorrectly states to increase the chance by 21%, what it really does is adding 21 points.

[Sethi22 373]

Don't count on me! I may have played lots and lots of Sacred, but the amount of info I've collected is really low. No calculations about crits on my part! (The only thing I remember about crit strikes is that they were the reason I couldn't get the maximum 6 points at the end of "The Path to Becoming a True Fighter Series" quest. I kept mortar grenading the 3 dudes again and again and again, and although they seemingly died at the same time, from the same hit, I never got the 6 points. And then finally after God knows how many attempts, I realized I had some stuff, especially rings with crit chance on them, causing all the mess with the different damage numbers. So I took everything off, and mortared them to the afterlife properly in the end. All three died at exactly the same time, and I got my 6 points.) And that is everything I can tell you about this

Edited August 7, 2024 by Sethi22

[alfchaval 196]

4 hours ago, SLD said:

As for a "more complete reference", my theory of
[crit chance]=[crit rating]/(100+[crit rating])
seems to create quite accurate results.

The formula should be something like this:
chance = maxchance * (1 - (1/whatever))

50 ≈ 1/3 and 100 ≈ 1/2 suggest it should be something like this:

chance = 100 * (1 - (1/((X/100)+1)))

That 98% is still weird.

Edit: I just checked the difference of results and both formulas are equivalent 

Edited August 7, 2024 by alfchaval

[xeyp 53]

4 hours ago, SLD said:

If there were critical rating and seperate %crit values the "best case" would not be two "seperate factors" as factors would be multiplied. Adding the two chances would give the greatest results ol course. But maybe that is what you meant...

Yeah, factors not in the purely mathematical sense, but in a more verbal sense - as in "two contributing factors". So absolutely that's what I meant.
 

4 hours ago, SLD said:

As for a "more complete reference", my theory of
[crit chance]=[crit rating]/(100+[crit rating])
seems to create quite accurate results.

Nice, had something similar in mind as soon as I saw 100 rating = 50% chance, but I refuse to do numbers at 2am, you saw what happened to your name in the CA DMG Cap thread :))
This is indeed a very useful thing to have for people who want to chase higher numbers and want to know exactly how much crit rating they need for that 75% Crit Chance.

----------------------

@alfchaval Thank you so much for doing the testing! That resolved a lot of questions and confusions I had about critical strike.

----------------------

So it turns out Direct Critical Strike Increases are but a typo in the current version of the game.
This more than confirms that 100 critical rating is the most you should go for(a soft cap if you will), only having more if your equipment simply has 
item properties that add up to over 100, otherwise the investment of Jewelry and Socket slots will definitely be badly spent.

I actually enjoy the steep diminishing returns, the game clearly tells you to choose your battles :))
So the result is, at lower level you need a relatively massive investment to reach the 'soft cap' and as your level increases the gear offers more and more
of the Critical Rating, until you can fairly easily reach the soft cap, opening a lot of Jewelry and Sockets for other things! 
It seems very similar to the situation with Life Leech - in the beginning you don't do much damage so you need a higher %, but the % in modifiers on items
isn't as high, and as you go up in levels both your damage and the life leech % per modifier increases so you end up only needing one.
I do not know if this is intentional or not, but this definitely would make me feel better for focusing on socketing for defense & resistance, as usually 
in every RPG I've played I felt bad for investing in defense as it felt like a detraction from my offense (well until you meet that one boss that you can't quickly finish and have to survive haha)

[gogoblender 3,583]

2 hours ago, alfchaval said:

The formula should be something like this:
chance = maxchance * (1 - (1/whatever))

50 ≈ 1/3 and 100 ≈ 1/2 suggest it should be something like this:

chance = 100 * (1 - (1/((X/100)+1)))

That 98% is still weird.

Edit: I just checked the difference of results and both formulas are equivalent 

Alfchaval!

wanted to say that I am sorry about the dev nor responding to the NL request  

HOWEVER...dang you're already living the life up here at DarkMatters in this busy topic

(And DANG... check out yer fancy avatar 

 

... show me da  bar guys lets all chat crit together!

I'm not a power sorcerer when it comes to numbers BUT... one of my friends from years ago when Underworld was released when crazy with what he called a crit machine build... and dontcha know it.. Alloooo Andiell ... he even put a vid... and some then lovely music...

 

At the time then everything in game was fresh...and seeing someone max crazy crazy crit levels in a build and being successful was tasty stuff

gogo

[SLD 524]

16 hours ago, alfchaval said:

The previous picture included the bonus of Andiell set (and some extra of two Fadalmar sets).

Anyway, Andiell incorrectly states to increase the chance by 21%, what it really does is adding 21 points.

Great, now we know it all

15 hours ago, alfchaval said:

Edit: I just checked the difference of results and both formulas are equivalent 

yeah, yours just looks a lot more complicated

[SLD 524]

On 8/7/2024 at 6:19 AM, SLD said:

[crit chance]=[crit rating]/(100+[crit rating])

there is currently no right place for this so I'm slapping this information on here:

Spell resistance, stun resistance and the chance to banish undead mods all follow the same formula as crit.

The "Shock opponent" mod is different (Example value 28->9%)

[Sethi22 373]

Well done all of you, thanks for all this calculating! I forgot to check back to this thread, but you've done a great job here. I of course love crits, (who doesn't?) If I find something nice with crit on it, I instantly fall in love with it usually,  I just never calculated it like this. I wanted as many of them as I could squeeze in. But it seems, it's a bit more complicated than that... This "soft cap" and "diminishing returns" thing I've never even thought of. So thanks again for the hard work, guys! This is my "Path to Becoming a True Fighter": to learn from you, who actually calculate things!

Edited August 11, 2024 by Sethi22

[SLD 524]

On 8/11/2024 at 12:05 PM, SLD said:

there is currently no right place for this so I'm slapping this information on here:

Spell resistance, stun resistance and the chance to banish undead mods all follow the same formula as crit.

The "Shock opponent" mod is different (Example value 28->9%)

Just stumbled upon the formula for mf.
sqrt(Itembonusvalue/100)=actualMF
example values: 100 -> 1=100%
                          400 -> 2=200%
                          900 -> 3=300%
                          20   -> 0.4472...=44%