Rune Theorycrafting - Attack, Damage %, Crit and Skill

TLDR Summary: Attack runes are by far better than Damage % runes in increasing overall damage output. However, Attack rating does not increase damage from effects such as Burn and Poison, where Damage % runes will. Attack runes also increase overall damage output more than Crit and Skill runes, but Crit has other benefits for certain heroes and in certain circumstances.

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There are 4 rune stats that can increase damage output: Attack, Damage %, Crit and Skill. Skill runes don’t appear to be working properly at the moment, except that they do at least increase the Crit value slightly (but not as much as comparable Crit runes). For that reason, at least for now, Crit runes are better than Skill Runes.

Crit runes and Damage % runes increase damage by a fairly similar amount in the long run, as the relative % value you get from comparable runes are fairly similar. For example, Greater 3 Star Rare runes give you about 4.4% crit (as the primary stat) compared to 3.7% for damage runes. So over a long fight, crit is a slightly better stat for increasing direct damage. Crit rune damage will be more spikey, in that when you crit you get 2x or 2.5x damage, while the Damage rune will give you a more consistent % damage with each attack. If you are trying to knock out a hero in one hit, then Crit will be better potentially, in those circumstances. Also, certain heroes benefit more from Crit in that they might proc specials (like on Goblin teams, Indigo, etc.) and they might also get a higher multiplier (like Black Diamond).

That leaves Attack runes to talk about. I’m going to compare these to Damage % runes, since they serve similar purposes in that they consistently increase the damage output of each attack, but in different ways. In the first table below, I’m comparing the damage output of Bovus attacking Tsume (both level 65, six stars and fully ascended, but without runes) using a basic attack. In the first two columns I’m showing the damage output comparing Attack versus Damage %. I used the average Attack rating and Damage % provided by Greater 3 Star Rare runes, which was Attack of 214 and Damage of 3.7%. You can see that the damage output when adding Attack was 1,483 compared to 1,232 when adding Damage %. One reason is because Attack gets double benefit from being increased. Base damage amounts are calculated on Attack rating (49.5% of Attack in the case of a basic attack) and Attack rating also increases the damage multiplier (multiplier is Attack rating/defender’s defense rating). It seems that DB did not assign high enough values to Damage % runes to make them comparable to Attack runes.

In the second and third columns, I’m showing that it would actually take a Damage % rune of 25% to be equivalent to an attack rune of 214. Even Greater Legendary 5 Star runes only provide about 7.6% damage increase, so this just reinforces that they undervalued Damage % runes by a significant amount.

Damage % will outperform Attack at very high levels of Attack, so I’m showing in the fourth and fifth columns the level of Attack at which Damage % runes start being more effective than Attack runes. It would require an Attack rating of 11,670 before this would happen, so effectively it is out of play in the current environment.

I know the question of whether the defender’s defense rating makes a difference is bound to come up, so the second table below address that. Similar to how the attacker’s attack rating doesn’t matter when comparing the value of defense and life runes, the defender’s defense rating doesn’t matter when comparing the value of Attack and Damage runes. For comparison purposes, I left everything exactly the same as in the first table, except I used Alexandros equipped with 3 legendary bulwark runes to bring his base defense up to around 4,000. As you can see, the results are identical to the first table in terms of comparing the benefit of Attack and Damage runes. It still takes a Damage rune of 25% to be equivalent to an Attack rune of 214, and the Damage rune starts being better at the same 11,670 Attack rating.
As mentioned in the TLDR summary, Damage % runes will increase damage from effects such as burn and poison, where Attack runes don’t increase that damage. However, I don’t think that benefit is enough to outweigh the benefit of Attack runes, as “damage over time” effects are more situational.

The question of stacking Damage % may also come up. Unfortunately that doesn’t really help the situation and actually only makes it worse for Damage runes. The third table shows what happens when you stack three Greater 3 star Legendary Attack runes compared with three Greater 3 star Legendary Damage % runes, taking it to the cap of 30%. The result is that you do more than 3x the damage with stacking Attack compared with stacking Damage %. A lot of this has to do with the double benefit you get from Attack rating. Also, to achieve the same damage results as adding 1,935 in Attack rating, you’d have to add runes that would provide 324.2% increase damage (well beyond what is available and also well beyond the 30% cap).

Hopefully DB will recognize the issue and not only give Damage % runes a boost, but also consider doing the same for Damage Reduction and Resist runes, as they are also underpowered.

As always, if you have comments or suggestions, or find some error in my logic or math, I’m happy to hear about it.

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Comments

  • I'm going to go ahead and suggest a compilation of all your posts be made in one organized thread and stickied. @Joveth

    A great analysis of the current large inequality between rune stats. I don't think the double/triple dipping affect I have referred to in other posts was really considered during balancing.
  • BunkbotBunkbot Member
    edited September 2016
    Great post. I think It is also worth nothing that for slow heroes and heroes with a boost to attack from epics the % increase is applied after adding the boost from the rune. I.e. If you add a rune giving +100 attack to a slow hero with an epic giving +5% attack, you actually get +130 attack.
  • Curious how much extra you would count how much +Att is on a rune compared to other stats like +Dam, +Crit or +Skill?
    e.g. if you had a 3* Improved Uncommon rune with +Att as primary and secondary stats (118/59) and were comparing them to another rune you had that was a 3* Greater Uncommon rune with +Dam as primary and secondary stats (3.7%/1.8%), which would you consider was the superior rune according to your logic above (assuming no +Att buffs)?

    What would be your comparison for evaluating stats against one another? i.e. w Att = x Dam = y Crit = z Skill? Assuming no other factors or course. e.g. Att is 20% more effective than equivalent amount of Crit, 30% more than Dam and 50% more than Skill.
    I am sure you have some kind of factor or comparison rolling around in your head. Care to share?
  • MattCauthronMattCauthron Member
    edited September 2016
    Curious how much extra you would count how much +Att is on a rune compared to other stats like +Dam, +Crit or +Skill?
    e.g. if you had a 3* Improved Uncommon rune with +Att as primary and secondary stats (118/59) and were comparing them to another rune you had that was a 3* Greater Uncommon rune with +Dam as primary and secondary stats (3.7%/1.8%), which would you consider was the superior rune according to your logic above (assuming no +Att buffs)?

    What would be your comparison for evaluating stats against one another? i.e. w Att = x Dam = y Crit = z Skill? Assuming no other factors or course. e.g. Att is 20% more effective than equivalent amount of Crit, 30% more than Dam and 50% more than Skill.
    I am sure you have some kind of factor or comparison rolling around in your head. Care to share?

    The answer is already there for you Satan. Avoid Dmg% always essentially. That being said he also already gave you a ratio! 214 atk = 25 % damage.

    So now let's take a look at your example! If we take the ratio above down to a denominator of 1% we get that 8.6 atk = 1% dmg. This may seem a little confusing at first, but that's only because of how absurdly underpowered dmg % is! In your example, the uncommon rune has a total of 177 attack. This is the equivalent of 20.5% damage!! (Assuming a defense of 1826). They aren't even in the same ballpark! (Really they shouldn't even be in the same game).

    As for your question regarding crit that is quite a bit more complicated. Similar to dmg% there is a certain tipping point where crit becomes more valuable than attack. For Dmg% that attack point isn't really attainable (Though you can get close with Brom), and though Foozle (nor I) have done the math yet I don't know the exact point for Crit, but I believe it is obtainable. What complicates this further however is the calculation changes depending on sustained dps verse burst dps and this game is far more often about burst dps.

    I do want to say I slightly disagree with Foozle comparing Crit % to dmg % in any way. Essentially saying they give you similar damage output but one overtime while the other very quickly. Though this may be true, in a game like this the burst damage is FAR more important. Being able to one hit opponents before they can 1)Heal or 2) Use their abilities is what wins matches. There's really no comparison here, it's crit % every time. In my mind for most offensive heroes you watch to push attack as high as possible and with your non attack slots focus on capping out crit %. In your tertiary slots try and pick up defense if possible or health.

    Edit: To iterate on your example, I want to go into it a little further. I know you said ignoring passives, but we should NOT be ignoring passives! That only swings the favor FURTHER in attacks favor which is already completely unbalanced. Runes benefit from ALL passives given how they are calculated. So if we look at a hero like Brom and look at 214 attack vs 3.7% damage that's not a real comparison. Let's say I bring Ember Zen Brom Kozar. I use Ember Zen Kozar and then Brom goes. Let's take a look at that 214 attack now.

    214 x 1.8 (Ember buff) x 1.3 (Epic buff) x 1.25 (Slow buff) x 2 (This number is estimated but is the most powerful factor)

    That 214 is now ONE THOUSAND TWO HUNDRED FIFTY ONE (1,251). Suddenly we see why Ember Zen Kozar is running around one shotting everything regardless of whether Kai is there or not.

    I want to touch just a little on the relevance of the Kozar debuff. The lower a persons defense the more each points of attack is worth since attack/defense is a multiplier in the damage formula. I'm not entirely sure what Kozar's debuff % is (You could calculate it) but let's assume it's 50%. If you'r opponent has 1000 defense and you have 1000 attack your attack multiplier is 1. Lower their defense by 50% and your attack multiplier becomes 2 (It doubles!!!). Each point of attack is now worth two attacks. And when you put all the multiples together things get crazy. Damage % on the other hand still sits there completely useless.

    If Foozle ran those comparisons again with 1,251 attack instead of 214 vs 3.7% dmg the results would be so absurd they wouldn't even be believable. You'd have to wonder how anyone could release runes like this and think they were balanced. I personally believe runes should not be getting these double/triple/quadruple benefits like they currently are and we are going to see some major changes.



  • @MattCauthron - Thanks for the reply. I agree with you that crit is almost always better than damage %, but I was just pointing out mathematically they are the same overall damage over the long run (assuming same percentage crit as damage %). As you say, though, crit has many more benefits than damage % and generally burst damage is superior to consistent damage over time. Crits trigger secondary benefits on many heroes, and you do often need that high burst damage to kill an enemy, especially if they have healers on the team. You do also get a slight benefit with Damage % runes when dealing "damage over time" effects like burning and poison. I haven't really paid attention, but I'm not sure burn damage and poison damage crits, but it might - I just don't recall seeing.

    There are three situations I can think of where damage % might be better than crit. One is where the enemy has the Vendetta passive and they retaliate every time you crit. The other is when the boss has a cap on how much damage they can take per attack. There is at least one of those in boss mode. So any additional damage from the crit might be lost in those instances. And finally, if your hero is already crit capped (Black Diamond gets that way very quickly), then Damage % runes would be better than adding additional crit obviously. However, I think these situations are so rare that I personally would always choose Crit runes over Damage % runes. And even if I didn't need to add anymore Crit, I'd still rather increase my Attack value rather than damage %, so basically I can't ever see myself using Damage % runes, unless they just happen to be on a rune as a secondary stat and the rune, otherwise, is very good.

    I think you are spot on with your analysis of multipliers. I did some testing and confirmed that Ember is providing an 80% attack buff. My Kozar, who is only 3 stars and Level 65 fully ascended, is providing a 35% defense debuff with his first ability. Perhaps this percentage increases as you increase the hero level -- I'd need to retest later when I hit level 70.
  • @Foozle

    I'm curious if your damage calculation formula is "official" or if it's based on experiments. I've been trying to find damage calculations with no luck until this post; that is:
    DMG = (ATT/DEF)*(0.495*ATT) where ATT = attacker's attack rating and DEF = defender's defense rating

    IF the above is correct, then THANK YOU for this post!
  • MattCauthronMattCauthron Member
    edited September 2016
    bphammy24 wrote: »
    @Foozle

    I'm curious if your damage calculation formula is "official" or if it's based on experiments. I've been trying to find damage calculations with no luck until this post; that is:
    DMG = (ATT/DEF)*(0.495*ATT) where ATT = attacker's attack rating and DEF = defender's defense rating

    IF the above is correct, then THANK YOU for this post!

    Where did you get .495*Attack from? Also every attack has a +/-10% variance.

    Damage = Damage base (Every ability tells you what this is) x ATK/DEF x type multiplier (Fire vs Nature getting 1.3) x crit multiplier (If crit) x .9-1.1 random roll

    Most buffs increase either attack or defense which changes the initial ratio. This has the largest affect on the outcome.
  • I got the 0.495*ATT from the original post where the author writes base damage from normal attacks is 49.5% of ATT

    The formula you just provided is extremely helpful. Thank you very much!
  • FoozleFoozle Member
    edited September 2016
    Yes the .495 is correct, except for epic heroes and then it changes to .50. They really didn't explain why it is different. I asked in a different post. I think pontifex is the only non epic hero where the value is also .50. Also, heroes that have non-standard basic attacks, like Furnace and Aria have lower values.

    And actually each special attack is also a percentage of attack rating. It is the same percentage no matter what level you are and at all star levels. I have a list somewhere I can post at some point.

    This is another reason attack runes are powerful. They increase the base damage of the attack and also increase the attack/defense multiplier.
    Post edited by Foozle on
  • A question was raised to me in a PM about whether the Attack stat really has a double benefit as I described above. In the link seanlucky posted above, it shows the damage formula to be:

    [Total Damage] = [Base Damage]*[Attack Stat]/[Defense Stat]*[Product of All Modifiers]*[Rand(0.9,1.1)]

    That formula is still correct, but I am just taking it further and showing where the "Base Damage" comes from. I think it is confusing because in the ability tool tip, the base damage is shown as 49.5% (for most heroes) of base attack rating. Before the days of runes, the tool tip amount was correct 90% of the time because there were not that many modifiers to base attack (a few heroes did have small modifiers, but most didn't). With the introduction of runes, Attack rating is boosted on many more heroes because Attack is a common stat on many runes that are used. My theory was that even though the tool tip is showing the base damage as 49.5% of base Attack, the actual base damage being delivered is 49.5% of Adjusted Attack (including passives, runes and epic bonuses).

    The table below supports my theory. For my test, I used a totally unruned Shadowblade (level 65, fully ascended, 6 star). I chose Shadowblade because he doesn't have any passives that would affect his damage output. I also chose, as the defender, Pontifex (level 56, fully ascended, 4 star), because he doesn't have any special damage mitigation like armor. In the 2nd column from the left, you can see the results of 20 attacks against Pontifex by Shadowblade, included a calculated average of 1,257. I did 20 attacks and took the average because damage has a +/- 10% randomness built into it.

    The first step was to calculate Pontifex's defense rating. I have been keeping track of my heroes' stats since around level 50, so I could look back and see that a level 56, 4 star, fully ascended Pontifex has a base defense rating of 1,245. The opponent's team did not have any heroes that would boost Pontifex's defense. Also, their Pontifex appeared to be un-runed, because when I calculated the defense based on the damage I was doing to him, it came very close to my predicted defense of 1,245. You can estimate his defense by using the following formula: Base Damage * Attack Rating / Damage done. Plugging in the actual known amounts yields an estimated defense of 1,216 (870 * 1757 / 1257), which is very close to my expected defense amount of 1,245. It is important to estimate Pontifex's defense rating for the 2nd part of the test -- adding runes and attacking again.

    After completing this, I added runes that increased Shadowblade's attack rating by 270 points. I then did 20 more attacks against the same Pontifex and recorded the amounts in the 4th column at the bottom of the table. I also calculated the average damage to be 1,651.

    In the 3rd and 4th columns (at top of table), using the estimated Pontifex defense, plus my known Attack rating (after adding 270 attack from runes), plus the base damage (either using the tool tip amount -- column 3 or using my predicted amount of 49.5% of Total Attack Rating -- column 4, I'm calculating a predicted damage amount after adding the attack rune. If the game only uses the base damage amount (per the tool tip), then column 3 should be close to what we see as actual damage. It would simply be the base damage from the tool tip (870 ) * Attack Rating (2027) / Defense rating (1245) = 1416 estimated damage.

    If my theory is correct and attack rating increases from runes have a double effect of increasing the damage multiplier (attack/defense), and also increasing the base damage (total buffed attack rating * 49.5%), then column 4 should be close to what we see as actual damage. It would be the calculated base damage of Attack rating (2027) * 49.5% or 1003, then the 1003 base damage * Attack Rating (2027)/Defense rating (1245) = 1634.

    As you can see, the 4th column yields a damage number that is very close to the actual damage observed of 1,651. The amount predicted by column 3 is well below that amount. Damage does have a +/- 10% random variation, but using 20 sample attacks mitigates. So based on this test, it does appear that Attack rating increases damage in two ways: by increasing the damage multiplier and by increasing the base damage.

    The implication of this is that you may not be able to stack enough Defense (using comparable runes) to offset an attacker who stacks entirely Attack. Making things even worse is that it appears that comparable runes give more Attack rating than Defense rating. For example, the average Greater, 3 Star, Rare Bulwark rune adds 185 defense (primary stat on the rune), compared to a Battle rune adding 214 to Attack. So Attack gets a double effect, and it also gets greater base stats on comparable runes. From a PvP perspective, things only get worse when considering the attack buffs that can be applied before the opponent has a chance to apply any defense buffs.

    Let me know if there are any questions or thoughts.

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  • Once again an excellent write up. It would appear as if each ability (Non basic attack) also is a % base off of attack power. For example BD's tooltip damage of her first ability is 65% of base attack. This tooltip is incorrect however as you mentioned, as in reality the base damage is 65% of her runed attack. This is a big reason why we are seeing top geared BDs/MKs able to one shot entire teams. I would imagine every single ability is a certain% of attack power. The higher the % the more "additional" benefit they get from attack runes.
  • FoozleFoozle Member
    edited September 2016
    Here you go. Damage multipliers for all the abilities. Note that all basic attack multipliers are 49.5%, except for the following exceptions: 50% for any hero with an epic equipped, Aria is 35% because her basic attack has a special attached to it, The Furnace is 17.5% because his basic is an AOE attack, Pontifex is 50% despite not having an epic weapon. Interestingly, Selwyn has the highest single target attack multiplier at 185% for his Chilling Blast attack and Igorak has the highest AOE damage multiplier at 100% for his Polar Pounding attack - although I have to admit I came up with these by eyeballing the numbers, so please correct me here if I'm short changing some heroes.

    Note that I put "n/a" (not applicable) when an ability didn't not have a damage component, like heals, taunt, etc.

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  • This information seems incredibly useful for creating defenses. Kozar's high percent explains his ability to one shot people through Kai. Bovus also has a relatively high percent and is capable of doing the same thing. Excellent chart.
  • This is pretty dang awesome. I had started almost this exact spreadsheet last week, and got as far as putting in my heroes and their attack values before my will petered out. Thanks for doing this and posting.
  • ItchytorturepoxItchytorturepox Member, Dungeon Boss Guru, Volunteer Moderator
    If anyone is skimming this thread and just looking for some quick tips:

    Look at heroes like Igorok, where using runes to increase damage output seems like the obvious thing to do (i.e. where you don't have to use too many rune slots to mitigate weaknesses).
    Next, look to see if that hero has an additional benefit from landing a Crit. Some additional benefits from Crits, such as freezing or putting disease on an applicable target, according to @Foozle's findings, do not appear to be weighted in damage multipliers (the way that some specials on are). For Igorok, we see double freeze potential on PP and an unweighted freeze potential on his basic. An additional benefit from landing a Crit potentially gives this type of hero a statistical advantage over heroes that do not have such a benefit. Now go ahead and max Crit and add +Attack runes to this hero, as well as any required enhancements to defense.

    Another tip (in reply to the original post) is to think twice about placing multiple skill and crit runes on heroes that have auto-crit abilities (e.g. Willow and SB). Probably better to focus on enhancing attack and mitigating weaknesses, instead.
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  • @Foozle Can you tell me how you arrived at your numbers? I'm coming up with very different numbers for my heroes. Maybe we're not looking at the same things. For instance, my Abigail has the below stats. She has no +dmg runes to muck up the calculations.

    Attack 2756
    Basic 927 34%
    Skill1 2621 95%
    Skill2 749 27%
    Skill3 1310 48%
  • @Foozle Can you tell me how you arrived at your numbers? I'm coming up with very different numbers for my heroes. Maybe we're not looking at the same things. For instance, my Abigail has the below stats. She has no +dmg runes to muck up the calculations.

    Attack 2756
    Basic 927 34%
    Skill1 2621 95%
    Skill2 749 27%
    Skill3 1310 48%

    You didn't say, but since your basic attack damage is 927, you must be level 70. To recalculate the numbers that show up in the tool tips in game, you need to multiply the percentages in the table above by the base Attack amount, not the final Attack amount. Abigail's base Attack stat at level 70, 6 star, FA is 1872, which means you must have runes plus her attack passive that gets you to a total of 2756 Attack.. So, 1872*.495=927 (basic attack). 1872*1.4=2621 (ability1). Same for Ability 2 and 3.

    The real damage you do is actually more than what shows in the tool tip. You do damage equal to 2756*.495=1364 for a basic attack in your case.

    Let me know if that makes sense.
  • Ahh, I see. I had assumed that the damage numbers on the Abilities tab were adjusted for runes, but I just removed one and the number was unchanged. Your numbers make sense now, thanks.
  • Ahh, I see. I had assumed that the damage numbers on the Abilities tab were adjusted for runes, but I just removed one and the number was unchanged. Your numbers make sense now, thanks.

    Would be a nice addition if they would update the game so that the actual damage was reflected in the abilities tab, but likely a low priority behind a lot of other stuff they can work on.
  • So when it comes to crit chance runes over skill, which is more effective at raising crit level? I would assume critical, but I would also assume damage runes would be more impactful than attack runes, and as we know that's very wrong.
  • Scroom407 wrote: »
    So when it comes to crit chance runes over skill, which is more effective at raising crit level? I would assume critical, but I would also assume damage runes would be more impactful than attack runes, and as we know that's very wrong.

    Skill gives less than half the amount of crit as an equal level crit stat. It's suppose to increase healing as well to balance this out, but doe not currently. At the moment skill is just a pretty bad stat : /
  • 4tom4tom Member
    edited September 2016
    Awesome stuff as always Foozle.

    Here's another thing I was wondering that this helped me to better understand; Crit vs Att for vamp healing.

    Att raises dmg, which means you heal more. Crit raises dmg like Att, but it can also increase heal outputs (since heals can crit as well). Also, both the hit and heal can crit, which provides a x4 heal!

    As an example, consider if you deal 100 damage per hit and have a 50% crit rate and 10% vampire ability. 25% of the time you get no crits and vamp +10 hp. Another 50% you get a crit with your hit or heal (but not both) for +20 hp. Finally, 25% of the time you crit for both your hit/heal for +40 hp. Ultimately, +50% crit = +125% vamp healing.

    Which is better?


    A 4.4% increase to crit is a 4.4% increase to dmg and a 11% increase to healing output. 214 Att provides lvl 65 Bovus with 25% increased damage/healing, so in the case you present [att > crit].

    If you do the same equation as above for Tsume/Bovus, crit starts to catch up to att in value at around 4000 att. I'm guessing that in a rare few scenarios (like on a Zomm that already has lots of att stacked), crit might start to be worthwhile if you want to up the healing being done. However, most the time [att > crit].
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  • bvs72bvs72 Member
    edited October 2016
    nevermind
    Post edited by bvs72 on
  • @4tom Good analysis. Yeah, at a high enough Attack level, adding crit would be more valuable in terms of healing. Do we know how often the vampiric trait procs? That would also be a factor, I suppose, in determining how valuable that increased healing is.
  • @Foozle I have unfortunately nothing to add to this great thread, but I had to say this: You've done incredible work on your theorycrafting posts. Thank you so very much.
    IGN: Xanathra
  • Silvanus wrote: »
    @Foozle I have unfortunately nothing to add to this great thread, but I had to say this: You've done incredible work on your theorycrafting posts. Thank you so very much.

    Thanks. Happy to contribute!
  • 4tom4tom Member
    edited October 2016
    Foozle wrote: »
    @4tom Good analysis. Yeah, at a high enough Attack level, adding crit would be more valuable in terms of healing. Do we know how often the vampiric trait procs? That would also be a factor, I suppose, in determining how valuable that increased healing is.

    Vamp procs about 30% of the time (my short test showed 15/50). I don't think it's worthwhile except on Zomm/Brom (though Brom already heals like a boss). When they are paired with Yorick (for extra defense) and Ponti (def + att), it gets a bit ridiculous and the vamp helps keep big heals a bit more consistent. Maybe a few other heroes could get use out of it (e.g., aria/hansuke), but the secret combo is high def + high damage, which not too many heros have.

    Previously, I've been using it on Zomm/Hansuke to auto-run boss island dungeons, but my combo was lots of crit + vamp. Now I realize I need to focus more on att and drop some (but not all) of my crit.
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  • 4tom4tom Member
    Again, this thread needs to be bumped up.
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  • Does the skill stat incress effects like burn and poison
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