Calculations of Stat Values for Sorcerers/Wizards (Agi vs. Int)

These calculations likely apply to other classes as well, I'm just using magicians as an example.

The purpose of all of the following is to allow understanding of how these stats work in conjunction with each other and to give the ability to optimize stats knowing the value of both INT and AGI.

Scroll to the bottom for a summary if you don't want to read through the math.

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All calculations are assuming 100% hit rate, 0% defense rate, and a target on an equivalent level.

INT - Increases 2 magic power per 1 INT ( and 2 parry for that's irrelevant for DPS purposes).
AGI - Increases critical rate by 4 per 1 AGI (and 2 dodge but that's also irrelevant for DPS purposes).

EDIT-Crit Rate % = (AGI / (400 * (1.05^(character level - 1)))) * 100 (Thanks synesthetic) -- This formula determines the damage value of AGI as it affects crit rate % in regards to character level (maybe monster level more directly?). Using this, one point of crit at level 37 gives about an extra ~.04315 % chance to critical strike.
This guide will be assuming a level 50 character as endgame is where stat optimization is particularly considered.

Critical - All basic attacks and skills have a (4 * AGI * ~.02289)% chance to critically strike.

Magic power (MP) - The effect of magic skills is increased up to (2 * INT + [Bonus MP])

Critical strikes effectively double the damage the spell would normally do with MP alone when they occur.
MP increases the damage done by a spell proportionally to what percent of MP is taken into account in damage calculations.

To give a detailed example of how these calculations are being done, I'll walk through the stat calculations for level 5 cold bolt.
Level 5 cold bolt scales 38% with magic power (assuming the tooltip is exact). The sample stats being used can be proportioned to any real stat value, these numbers are just being used for ease of calculation. All secondary stats are assumed to be the same, as any value of them in conjunction with AGI or INT will lead to the same results proportionally. Also bonus MP is assumed to be 0 for this.
AGI----------INT----------~AVG DAMAGE PER SKILL USE
0-------------500---------------380-------------(1000 MP * 38%)
125----------375---------------317.62---------(4 * 125 * .02289)=11.445% (% of crits) (750 MP * 38%)=285 (normal dmg) 285*2=570 (Crit damage) 100%-11.445%=88.555% (% of normal hits)------------------------------------------------------------(.11445 * 570 + .88555 * 285)
250----------250---------------233.49---------(4 * 250 * .02289)=22.89% (500 MP * 38%)=190 (N DMG) 190 * 2=380 (C DMG) 100%-22.89%=77.11% ---(.2289 * 380 + .7711 * 190)
375----------125---------------127.62-----------Follows above formulas
500-------------0-----------------0---------------Critical strikes of 0=0 damage

The conclusion we can make from the above information is that AGI increases DPS at a rate proportional to the amount of INT (or more directly, MP) that is had. With 0 non INT based MP, INT is clearly superior (with the stats at hand). We can calculate the value of these stats, assuming 0 bonus MP is had, using the same general formulas as used above:

1. 100 INT=200 damage=2 damage per INT (1:1 scaling hypothetical spell for ease of interpretation)
2. 102 AGI+100 INT =218.67820 damage------=18.678200 damage from agility--= .18312 damage per AGI (with 100 INT)
3. 101 AGI+100 INT =218.49512 damage------=18.495100 damage from agility--= .18312 damage per AGI
4. 100 AGI+100 INT =218.31200 damage------=18.312000 damage from agility----= .18312 damage per AGI
5. 100 AGI+101 INT =220.49512 damage------=2.1831200 damage from 1 INT (with 100 AGI)
6. 100 AGI+102 INT =222.67824 damage------=2.1831200 damage from 1 INT
7. 101 AGI+101 INT =220.68007 damage------=2.1849512 damage from 1 INT (with 101 AGI)
8. 102 AGI+102 INT =223.05176 damage------=2.1868024 damage from 1 INT (with 102 AGI)
9. 100 AGI+101 INT =220.49512 damage------=0.1849512 damage from 1 AGI (with 101 INT)
10. 101 INT=202 damage-----------------------------------------------------------------= 2 damage per INT
11. (.1868024-.1849512)=(.1849512-.1831200)=.0018312=Exact increase in damage from AGI per point of INT using the 1:1 scaling spell
12. (2.1868024-2.1849512)=(2.1849512-2.18312)=.0018312=Exact increase in damage from INT per point of AGI using the 1:1 scaling spell
13. Damage per AGI from (2.)=Damage per AGI from (3.)=Damage per AGI from (4.), therefore AGI's value stays the same if it is the only variable
14. Damage per INT from (5.)=Damage per INT from (6.), therefore INT's value stays the same if it's the only variable
15. AGI's value depends entirely on INT
16. INT has a base value of 2 (assuming 1:1 scaling), and its value increases at the same rate in regards to AGI as AGI does to it



These numbers can be adapted to any spell/stat amount by proportioning that spell's MP scaling with the hypothetical spell's MP scaling (1:1) listed above.
For example, if one were to cast cold bolt (5) with 375 AGI and 125 INT, the calculations that would proceed as follows:
375 * .0018312=.6867------; The extra value of 1 point of INT from AGI
.6867 + 2=2.6867------------; INT has a base value of 2 per point (1 INT= 2 MP)
2.6867 * 125=335.8375-----; The value of INT multiplied by the # of instances of INT= damage per spell (1:1 scaling)
335.8375 * .38=127.61825-; Average damage per spell of cold bolt with given stats (cold bolt (5) has .38:1 scaling), which checks out with the number listed in the table above

Because the directly above does apply to all scaling spells, scaling will have no effect on INT and AGI's values in proportion to one another.
.0018312 * AGI + 2 = Damage increase from 1 more point in INT-----------------------.0018312 * INT = Damage increase from 1 more point in AGI
z(((.0009156x)(2y)) + ((1-.0009516x)(y))) where x=AGI, y=MP, and z=MP scaling is a formula that can calculate the average damage of a spell (disregarding secondary stats)

Extra magic power is a major factor in determining stat values as every point of MP increases AGI's value by about .0009156 and increases INT's value by 0; this is a significant variable in determining which stat actually becomes more valuable and when. Because of this, assume every 2 extra MP=1 point in INT in the following:

Based on this, the value increase (not damage) per point of AGI or INT is the same for either, but INT will always have a base advantage of 2 assuming they're equal. As shown earlier, the value of both stats increases off of each other, and therefore one will become comparatively more valuable if there is more of the other. Since .0018312 is the base value increase per stat assuming 1 point of increase in the other stat and INT has a base value of 2 per point alone, AGI needs to have an extra ~1093 INT (2/.0018312) to become more valuable.
For example, assume one's stats are 1313 INT and 220 AGI. The increase of damage per one point of INT would be (.0018312 * 220 + 2) 2.402684, and the increase of damage per one point of AGI would be (.0018312 * 1313) 2.4043656. Therefore, INT is more valuable to put points into until its amount exceeds AGI's by 580.

The following calculations tell the approximate relative values of INT to AGI assuming extra MP as a variable and 500 of each stat (calculated by dividing damage increase of AGI by damage increase of INT(2 MP= 1 INT)):
2186 MP ------------- AGI=1.000515-----INT=1
2000 MP ------------- AGI=.9421045-----INT=1
1600 MP ------------- AGI=.8164906-----INT=1
1200 MP ------------- AGI=.6908767-----INT=1
0800 MP ------------- AGI=.5652627-----INT=1
0400 MP ------------- AGI=.4396488-----INT=1
0000 MP ------------- AGI=.3140348-----INT=1
Of course, since linear regression is in place and INT's base value of 2 becomes comparatively less significant as stats rise, AGI's value will lower or raise faster as extra MP lowers if the total value of stats lowers or raises respectively. 1160 MP will always be the point where AGI becomes more valuable than INT, however.

These numbers should be used to judge optimization of stats; it can be adapted to variations of actual stat values by converting INT into MP (every INT=2 MP) until you have an equal amount of INT and AGI. For example, if one had 500 INT, 400 AGI, and 600 extra MP, it could be adapted into this chart by converting 100 INT to 200 MP to make the amount of points in each stat equal. The resulting values could be read in the line for 0800 MP, although the actual AGI value would be slightly lower (about .029 less)

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Conclusion:

INT is ALWAYS a more valuable stat unless any of the following conditions are met:
1. 2186 non INT magic power is had
2. 1093 more INT than AGI and 0 extra MP is had
3. The amount of INT that is had over agility being converted into MP (1 INT= 2 MP) and added to current non INT MP causes that sum to be greater than or equal to 2186.

The table above that lists the relative values of stats can be used to determine how valuable each point of AGI is as opposed to INT.

The information in the math section above can be used to calculate the optimal stat build for someone depending on gear and cards. Until gear with higher MP comes out, INT should definitely have significantly more priority than AGI. and even 41/41 probably is not optimal for DPS until the amount of INT as opposed to AGI that is had is majorly skewed (top levels of gear, and I'm not entirely sure if its skewed enough to matter).

If anyone wants me to calculate the optimal stat builds for them, post your stats in a reply and I'll probably get back within a day or two. It's fairly simple to do yourself, however; use the table above to determine the relative stat values (manipulating the numbers using the methods stated), and go point by point in determining which stat will give more DPS. When one stat starts taking more points than the other, divide the amount it takes to level up AGI by the amount it takes to level up INT. If this number is less than the value of AGI that was calculated using the table, put points in AGI. If it's greater, put points into INT. Continue this process until all stat points are spent.

Please feel free to criticize this post and to post questions/comments. As a developer of SimulationCraft, I am very familiar with how these things work and will be more than willing to modify things that need modification and further explain things that need explanation.

Edited by Scorpadorp, 03 June 2013 - 07:56 PM.

I can't remember exactly where I read it (probably the (dont kill me pls) SeaRO2 forums) that for wizards, INT > AGI until you have reached a 2.2k Matk threshold. Not sure if that is in there somewhere because numbers scare me and I hate math..which involves numbers.

I'll be honest. I didn't thoroughly read through whole post. It got messy with the first table, but I had the impression that you were thinking on the right track, but.. I'm sensing a misunderstanding with how Rate calculations are done after seeing that ".04315" number.

Taking excerpts from this thread (where "stat value" would refer to something like Crit as opposed to Crit Rate):
http://forums.warppo...stats-guidefaq/

Given base stat values, all Rates are determined by this formula:

Rate % = (Stat Value / (400 * (1.05^(character level - 1)))) * 100

Note that because of this, Rates decrease as you level.
AGI builds who are unaware of this will be saddened or panic as they notice their 20% Crit Rate gradually drop.

For quick reference if you're level 50,

Rate % = stat * 0.0228

Crit Rate % = AGI * 0.0916

[...]

But really, which is better? STR/INT or AGI? Which will make me do more? Give me math and numbers.
It mostly depends on how much attack and crit rate you have.

There's a breakeven point varying with how much crit rate and attack you have.
If you have less attack than that point, then STR/INT will do more.
If you have more attack than that point, then AGI will do more.
The breakeven point if you have 0% crit rate is about 2184 attack.
Then for roughly every 5% crit rate, the breakeven point for attack increases by about 109.
By 30% crit rate, the breakeven point is 2839 attack.

The 2.2k figure electrolights mentioned would be the 2183 breakpoint calculated by verxified from the sea forums.
The latter section in my quote above was my conclusion after calculating average damage, taking crit rates into account. It all only applies to Lv.50's though.

I'm actually not much of a math person. If you come up with some new insight given the information I quoted, I would love to learn more.

Hi guys!

Im going to repost this here, I want to make a hybrid sorc and I need some help, im not sure if I should go 41/41/0, 51/27/3 or 27/51/3 maybe?
I want to be efficient Sorc on dungeons, raids and maybe colosseum?

This is going to be my skill build:
http://ro2base.com/b...1.1.1/0.0.0.0.0

Any suggestions, stat builds are welcome, thanks!

I'll be honest. I didn't thoroughly read through whole post. It got messy with the first table, but I had the impression that you were thinking on the right track, but.. I'm sensing a misunderstanding with how Rate calculations are done after seeing that ".04315" number.

Taking excerpts from this thread (where "stat value" would refer to something like Crit as opposed to Crit Rate):
http://forums.warppo...stats-guidefaq/


The 2.2k figure electrolights mentioned would be the 2183 breakpoint calculated by verxified from the sea forums.
The latter section in my quote above was my conclusion after calculating average damage, taking crit rates into account. It all only applies to Lv.50's though.

I'm actually not much of a math person. If you come up with some new insight given the information I quoted, I would love to learn more.

Thanks for this info, when I wrote this post I was basing the stat values off of a level 37 character and honestly was just hoping that values didn't scale with level haha. I've updated the OP with accurate calculations in regards to level 50s rather than 37s.

im not sure if I should go 41/41/0, 51/27/3 or 27/51/3 maybe?
I want to be efficient Sorc on dungeons, raids and maybe colosseum?

This is going to be my skill build:
http://ro2base.com/b...1.1.1/0.0.0.0.0

Any suggestions, stat builds are welcome, thanks!

As far as DPS goes 51/27/3 is probably the optimal choice of those three until you get particularly good gear. AGI becomes more valuable than INT earlier in gear phases in regards to healing, so if you value that more than your DPS i'd suggest 41/41.
It all really depends on your gear and cards though. Its likely that none of those 3 would actually be optimal if you're trying to min/max.

Edited by Scorpadorp, 28 May 2013 - 11:56 AM.

Firstly, thank you for taking the time to calculate all that. I am concerned with one thing though. Sorcs rely on procs followed by JT and VS to deal double damage. When this procs with a critical strike the damage is quadrupled. Is this a factor that would influence your INT/AGI calculations, and if so would you be able to guide me in the right direction to maximize dps. Thank you in advanced.

Firstly, thank you for taking the time to calculate all that. I am concerned with one thing though. Sorcs rely on procs followed by JT and VS to deal double damage. When this procs with a critical strike the damage is quadrupled. Is this a factor that would influence your INT/AGI calculations, and if so would you be able to guide me in the right direction to maximize dps. Thank you in advanced.

When the double damage thing procs, it essentially doubles the magic scaling of your next two lightning spells. If either of these spells critical strike, the damage is modified based off of this doubled magic scaling. The critical strike damage stays at the same 2:1 ratio that it is with all your other spells. For example:
If you have 1875 MP:
Normal VS:------------1500
Normal critical VS:---3000
Proc'd VS:-------------3000
Proc'd critical VS:----6000

Because the damage modification from critical strikes stays the same, the value of AGI in regards to INT stays the same.
So no, this would not influence the calculations.

Thank you very much for reply Scorpadorp, it help me a lot.

what about wizards dots? they cant critt right?

what about wizards dots? they cant critt right?

Assuming the tooltips for all the wizard spells are accurate (many engrish), the critical hits create a DOT that deals damage in a constant ratio to the damage that the initial spell inflicted. Therefore, the DOT's total damage when a critical occurs is equivalent to double the total damage of a DOT that is spawned from a normal hit, which means that a critical hit for a spell with a DOT is just as valuable as a critical hit from a spell without a DOT if its only used once.

Spells with DOTs are almost virtually like normal spells if their DOT's MP ratio was added to the base ratio; the DOT MP ratio becomes a variable if the DOT is renewed before it has ticked every time it normally would. This doesn't change the fact that the actual ratio of value for a critical strike to a normal hit stays the same as it would for a normal spell, it just means it may be logical to mix in spells that won't renew the DOT early if the spell critical hits (so the spell's critical DOT can finish ticking).

Fire flower may be an exception to this rule; I'm not entirely sure how that spell works. If it really can't critical strike then that makes INT an even more valuable stat for wizards.

I believe fire explosion also has some effect that makes a spell auto-critical, if this is so then this also makes INT an even more valuable stat for wizards as extra critical rate doesn't improve an 100% critical strike chance.

Sorc here.

I'm a little bit confused about your

1. 2186 non INT magic power is had

line. I'm looking at all my gear, and there's nothing that adds straight magic power besides my staff.

I've been suspecting that INT would be better than AGI for me, but here's my stats in hopes that you can concrete it so I know if I should invest in changing all my runes.

AGI: 335
INT: 797
Magic Power: 2+2521 (2523)
Haste Rate: 17.71% (774)
Hit Rate: 99.13% (4149+182)
Vigor: 582
Critical: 30.67% (160+1180)

I have 10 rune slots, so I can switch from 335 agi to 285 // 797 int to 847. How much of a DPS increase would I get from this?

Edit: I forgot to mention, I'm a 40/40/8 build. Additional question: How much would switching to a 27/51 build increase my damage?

Thanks in advance~

Edited by Meowshi, 03 June 2013 - 01:40 PM.

Sorc here.

I'm a little bit confused about your

1. 2186 non INT magic power is had

line. I'm looking at all my gear, and there's nothing that adds straight magic power besides my staff.

This condition won't be met by anyone until further expansions or until a staff with that much MP is realeased; I just put that condition in there because hypothetically it can apply. Remember, items can increase MP as well.

I've been suspecting that INT would be better than AGI for me, but here's my stats in hopes that you can concrete it so I know if I should invest in changing all my runes.

AGI: 335
INT: 797
Magic Power: 2+2521 (2523)
Haste Rate: 17.71% (774)
Hit Rate: 99.13% (4149+182)
Vigor: 582
Critical: 30.67% (160+1180)

I have 10 rune slots, so I can switch from 335 agi to 285 // 797 int to 847. How much of a DPS increase would I get from this?

Edit: I forgot to mention, I'm a 40/40/8 build. Additional question: How much would switching to a 27/51 build increase my damage?

Thanks in advance~

Keep in mind these values only apply to whatever stats you gave me

Your damage on a spell that scales 1:1 with MP would increase according to the following (assuming 0 resistances and 100% hit):
Average damage with current stats: -------------------------------------3296.8

With rune modifications only, your MP would be 2623 and your critical strike chance would be 26.09%. So...
Average damage with rune modifications only: ---------------------3307.5 (+10.7)

With 27/51 stat modifications only, your MP would be 2545 and your critical strike chance would be 29.48%. So...
Average damage with stat modifications (to 27/51) only: ---------3295.3 (-1.5)

With stat (27/51) and rune modifications, your MP would be 2645 and your critical strike chance would be 24.90 %. So...
Average damage with stat (to 27/51) and rune modifications: --3303.3 (+6.5)

Since you're so close to the breakeven point in the value of INT versus AGI in your gear, the two extra stat points you lose from the level up value becoming too high make the stat change inoptimal. However, because the runes are a 1 to 1 exchange and INT is still a more valuable stat at that ratio, the rune change would increase DPS.

41/41 is your optimal choice of stats for DPS, but clearly you realize this and value 8 VIT more so I'd suggest leaving your stats as is. It seems to be little known but 31/49 is actually the highest stat build for DPS for 50s with low-middle tier gear.

Keep in mind that these damage values can be scaled to any spell and the damage increases will stay the same proportionally. I didn't want to calculate actual DPS because its extremely variable and this information should suffice for your purposes.

If you want a more in depth explanation or have any other questions let me know.

Edited by Scorpadorp, 03 June 2013 - 09:35 PM.

low-middle tier gear.

Hehe


Thank you very much :]!