Proposed Changes to Base DamageEdit
I'm don't want to make many changes to the wiki page, since I'm new here, but I wrote up what I think the Base Damage Section should look like. Feel free to take what ever pieces of it you like (if any):
Described in-game as the "Character's basic skill damage". Derived from primarily from Might, Strength, and Accuracy, as well as Stamina, Solidity, and Talent: Ultimate Strength. There are several parts to the calculation of Base Damage as follows:
Note that these intermediate values are not shown in game, but they simplify the derivation of the final values.
First add in the extra stats to the basic ones. Solidity adds a percentage of Stamina to Might so:
Effective Might = Might + (Stamina * Solidity)
And each level of Talent: Ultimate Strength adds 10% to Accuracy, but Accuracy cannot be greater than 100% so:
Effective Accuracy = Min(Accuracy + (Ultimate_Strength_Levels * 10%), 100%)
Then calculate some in-between values.The Minimum before Accuracy brings it closer to the Maximum is:
Proto-Minimum = (Eff_Might * 29/300)
And Damage "Spread" (the difference between Proto-Min and Max) is:
Spread = (Eff_Might * 2/300) + (Strength/5 * (100% + Eff_Accuracy))
Finally, the values you see in game are:
Maximum Base Damage = Proto_Min + DmgSpread Minimum Base Damage = Proto_Min + (DmgSpread * Accuracy)
Some conclusions to make based on those formulas:
- Might contributes to Base Damage at a rate of 10 Might to 1 Damage
- At 0% Accuracy, Strength also contributes at a rate of 10 Strength to 1 Damage
- At 100% Accuracy (if possible), Strength would improve your damage at a rate of 10 Strength to 4 Base Damage
- Part of Minimum Base Damage is affected by Accuracy twice (i.e. one of its terms contains Accuracy^2), meaning that Accuracy becomes more valuable as you get more of it.
- For a tanky character who already wants a lot of stamina, Solidity can be a good investment. But for dps-focused characters, there are many other, more valuable stats for damage.
184.108.40.206 04:08, July 25, 2015 (UTC)
- I really like this breakdown, and I think we should put it on the main page. Nice job! Some feedback:
- Conclusion #4 could be expanded on: the fact that accuracy is exponential means that it is a very good stat for damage Accuracy^2. Some commentary on how stamina stacks up against the other two independent variables would be welcome (unless you have solidity, it is equal to might). Also, a full equation (with evaluated fractions) at the beginning or end of the entry would be a good addition. Lastly, I think "proto" is a bit of a turnoff for normal readers... but I don't have a better suggestion. Thoughts?
- Unless others think otherwise, I'll go ahead and put it on the main page in, let's say, 24h.
- Unislash (talk) 23:43, July 25, 2015 (UTC)
- Alright, I editted conclusion #4 and added a #5 about Solidity. We could replace Proto-Minimum with Pre-Minimum. I'm not sure though. I can't think of any less akward names for it :\
- 220.127.116.11 05:25, July 26, 2015 (UTC)
Here are the Russian damage formulas Edit
This just surfaced on one of my reddit threads. Kudos to /u/Chazzers for this information! Notice that the Russian formulas are _also_ influenced by _Stamina_ (!!!!), "Solidity" (a bonus from certain chapels) and by "Ultimate Strength" (of which there are 6 related talent nodes in the upper atlas). I've copied the spreadsheet linked in the reddit comment below and am playing with it....
..... Prelim results using values from the spreadsheets thrown around here so far are..... If you factor out everything except Strength, Accuracy, and Might, you get essentially the same results we've seen so far with /u/Lucai's version of the formula. But when you start factoring in Stamina, Solidity, etc. you see how things change.
Also, by playing with the same exact amount of Might and Strength, and varying only Accuracy, you can see that the ratio of contribution to average damage starts swinging heavily in favor of Strength. For example, try 0 accuracy, 10% accuracy, and then 20% accuracy. At 0 accuracy, Might contributes 49.9 percent, and Strength contributes 51.1 percent. At 10 accuracy, the ratio is 45.1 to 54.9. At 20 accuracy, the ratio is 40.8 to 59.2.
And here's a fun experiment: put in values of 1000 each for Might, Strength, Valor, Luck, and Stamina. Then put in values of 20(%) for Accuracy, Temper, Crushing Blow, and Solidity. The "Breakdown" section tells the entire story. Clearly: Strength, Luck, and Valor all contribute the most to your average damage. Might comes in next, contributing only about 70% as much as the first three. Crushing Blow and Solidity contribute the least.
At this point, I call for the main page to be converted to the Russian formulas and to provide a link directly to /u/Chazzers' Google Sheet. This will enable people to make their own copy from Chazzer's and use it as a private damage calculator
(Yokai) 18.104.22.168 18:18, July 24, 2015 (UTC)
- Wow, interesting. Well, we should definitely test this out, specifically the stamina interaction. Will do when I get home.
- Awesome, thanks for the info! I have also updated my spreadsheet (https://docs.google.com/spreadsheets/d/1VwIXJZhBbFxvlAIxleM3QkvmnpgT0MPtFhsADT3lHVo/edit?usp=sharing) to include these formulas; they definitely seem to line up well for the data points I have. Unfortunately I didn't record stamina or my bonus talents at the time, and I cannot connect to the game ATM to try and grab those #'s. Will have to wait until the server likes me to verify this further but looks solid so far...
- Nezroy (talk) 19:33, July 24, 2015 (UTC)
These formulas make sense. The only thing new here is that Solidity and Ultimate Strength are factored in, and they do so like they should. Solidity * Stamina is added to Might, and Ultimate Strength is just 10% extra accuracy. And of course the new formula takes note that accuracy can't be more than 100%. From here I suggest we break this up and make it easier to understand piece by piece. If we break it up as much as possible we get:
- Effective Might (Mht) = Might + (Solidity * Stamina)
- Effective Accuracy (Acc) = Accuracy + (Ultimate Strength Level * 10%) (Note: Hardcapped at 100%)
- Strength (Str)
- Max Base Damage (Max) = (Mht * 0.1033) + (Str * 0.1967 * (1 + Acc))
- Min Base Damage Before Accuracy (Min) = (Mht * 0.0967)
- Actual Min Base Damage = Min + ((Max - Min) * Acc)
- If we put these together a bit more, into a bigger picture we get the following:
- Min Base Damage = (0.0967 * Mht) + (0.0067 * Mht * Acc) + (0.1967 * ((Str * Acc) + (Str * Acc^2)))
- Max Base Damage = (0.1033 * Mht) + (0.1967 * (Str + Str*Acc))
- These are just two different ways of composing Min and Max damage, but I think they both show different things. With the first version you see how Accuracy directly add Max to Min to "Bring Min closer to Max", and with the second you can see that there is a Acc^2 term when you work it out (which means that Accuracy gets even better when you get a lot of it). Also, you may notice I tried putting the constant coefficients in front in the second half, which I prefer simply because that's how I do algebra. Take what you will from this, but those are my thoughts on "readable formulas".
- 22.214.171.124 20:28, July 24, 2015 (UTC)
- Ha, I updated the wiki along these lines almost at the same moment you were making this comment :) I followed a similar thought, ultimately focusing on a concept of "damage spread", though the squaring of Accuracy is certainly notable and I also like the idea of "effective might". Probably worth at least mentioning in there somehow, but for the moment I'm going to stop staring at it.
- Nezroy (talk) 20:36, July 24, 2015 (UTC)
- Server is still down for maint (or at least, I can't connect :), but based on the general fit to all my recorded values so far, and the (unverified but I'm trusting) Russian source, I updated the wiki with the formula from Chazzer. Note that I re-derived it in a different format that 1) re-uses fewer repeated terms across the min/max values and 2) I think makes it more clear which values are affecting which bits; particularly with regard to how accuracy is truly working to pull the min closer to the max.
- Nezroy (talk) 20:29, July 24, 2015 (UTC)
- The equations are basically the same except the constants are a little different. I posted a comment in the original reddit thread https://www.reddit.com/r/Skyforge/comments/3eg4fs/my_guide_might_be_substantially_wrong/ctez6s5 describing this. It's also interesting to learn about the Ultimate Strength + Accuracy cap (although I'm not sure you could hit it).
- Lucaj (talk) 20:34, July 24, 2015 (UTC)
- Yeah I'm curious to know if bonus damage formula has a similar cap from the talent contributions as well, since it has a similar form. The Russian source/spreadsheet does not include a cap but definitely something to keep an eye out for when people start approaching those limits.
- Nezroy (talk) 20:50, July 24, 2015 (UTC)
- Oh, speaking of the slight differences in constants, I had good results when using the "damage spread" concept that I updated the wiki with, and rounding it to an int before plugging it in to the max/min dmg derivations. This is how my current spreadsheet does it and the #'s line up perfectly. If true, it makes more sense for a number of reasons (from a programming perspective), and keeps mostly "nice" constants in the overall formula (such as the straight 20% constant on Strength). The only odd value at that point becomes 0.0968, which I assume is their intentionally arcane scaling/tweaking factor for balancing.
- Nezroy (talk) 20:55, July 24, 2015 (UTC)
- Hmm.. I have other numbers in a very similar range that work out properly (980 might, 284 str, 11.7 accuracy). Further, based on those numbers, the calculated values for your numbers fall about where I would expect. That suggests the baseline formula is OK but that something else may be adding to your final total displayed in game (particularly to the max #); could there be other gear effects or damage boosting talents being applied that are unique to your build?
- Nezroy (talk) 16:33, July 25, 2015 (UTC)
Based on current formula by /u/Lucai, Strength is only marginally better than Might Edit
Since /u/Lucai's formula seems to be the current accepted formula for min/max damage calc (with Accuracy factored in), I did a spreadsheet to confirm/disprove 2 specific things:
1. Is the in-game description for Accuracy correct (it raises min damage within the base damage range)? Per the current forrmula here, the answer is "not in any significant way, but technically yes".
2. Is Might really truly terribad compared to Strength? Per the current forrmula here, the answer is a resounding "NO". Everyone who has focused on the 10% multiplier per point for Might versus the 20% multiplier for Strength (myself included) is WRONG if /u/Lucai's formula is actually correct. Why? because of that damn (1-Accuracy) in Lucai's formula for Min Damage, versus the earlier formula for min damage here that used (1+Accuracy).
I'd still prefer more testing and verification of the curent formula, because these two conclusions fly in the face of statements from the Russian community, and that's puzzling to me. However, if it's true, then it's true, and its good to know that because it changes how we all should look at Might versus the relative power it's buying you for every new point of prestige.
Here's my sheet so you can verify my conclusions for yourselves: https://docs.google.com/spreadsheets/d/164g8yNNmTjRznjZOsqDFNBTahHDXEh6YO3ZZwZE6JDQ/edit?usp=sharing
(/u/yokaiichi) 126.96.36.199 13:42, July 24, 2015 (UTC)
Yokai, thanks for your analysis. I had similar thoughts when I was comparing Might and Strength yesterday. Would this mean that specific classes could invest more heavily in Might to offset a lack of Strength in favor of another stat? I can't say either way now since I don't know if there are limits to how you acquire Strength and Might as you progress in Prestige. It seems like a tricky balance that changes relative to what amount of Strength and Might you have access to at a given time. But, since you have only so many Ascension Atlas nodes and ring slots available, efficient stat distribution is bound to come up eventually. It's just unclear to me if this is a problem at any particular Prestige as you claim. Should not the greater concern, perhaps, be in investing in more stamina than you need relative to your Prestige, not in Might, as long as your other stats are balanced for your class accordingly?
- If the formula is accurate, even if it's only accurate at lower prestige ranges < 10,000, it still means that for new players in their first month, there is no harm at all in swapping out their founders/collectors weapons for ones with much higher Might on them, and there's no harm at all in dumping millions of credits into accelerated Adept Missions to quickly rank their Province temples (Might/Stam/HP%) and gain as many temples, as their investment into Greatness nodes will allow. It's _possible_ that the formula is still wrong, or it's _possible_ that the game algorithms aren't properly executing the design intent behind the stats, or it's _possible_ that the damage formula changes at some point with typical "diminishing returns" fall-off for one or more stats, but we won't see such falloff until much higher prestige levels.
- Regardless, the impact on _new_ players < 10,000 prestige is pretty clear if the current formula is true: Rank the hell out of your Order and get as much juicy Might and Stam/HP% as you like. Upgrade to any weapon with more might and useful stats and keep those founders/collectors weapons around but idling in a bag slot "just in case" for later.
- Yokai 188.8.131.52 15:53, July 24, 2015 (UTC)
- Yea, I suspected that might/strength may be, for all intents and purposes, extremely similar in terms of contribution to base damage. Even if the current equation is wrong and accuracy doesn't effect might negatively in min damage, by far the most important thing to do is to balance your strength and might. The balance point might not be exactly equal (again, depends on the true equation), but it should be pretty close. Thus, I think the reason why we hear "invest in strength over might" all the time is because people generally have far more might than strength--so of course strength is going to contribute more in that case if the equation is square(ish).
- That being said, take a look at my findings with the Skill Tooltip Damage#Findings. Bonus damage may infact be an extremely bountiful stat to contribute to--even more than strength or might.
- Unislash (talk) 18:47, July 24, 2015 (UTC)
- An easier way to think of the min base damage formula is to consider the min base damage value at 0 accuracy:
MinBaseDamageAt0Accuracy = Might * 0.0966
- and from that adjust it so it is accuracy closer to the max base damage.
MinBaseDamage = MinBaseDamageAt0Accuracy + (MaxBaseDamage - MinBaseDamageAt0Accuracy) * Accuracy = MinBaseDamageAt0Accuracy + MaxBaseDamage * Accuracy - MinBaseDamageAt0Accuracy * Accuracy = MinBaseDamageAt0Accuracy * (1 - Accuracy) + MaxBaseDamage * Accuracy
Accuracy description in game might actually be "correct" Edit
EDIT (/u/yokaiichi): This opening statement is now obsolete per the most current formula in favor. If the effect accuracy has on min and max damage is even close to your current guess at this timestamp, then the in-game description isn't actually wrong. I work with Ukrainian and Russian devs and am familiar with the quirks of the way they often translate into English.
Your formulas so far would make both the min and max damage rise per each percent of Accuracy. However, the min would rise much more than the max. This effectively "raises the minimum base damage" _relative_ to the maximum. See, it's the stuff they assume you get and therefore leave out. The devil is often in the details. BTW this is yokaiichi from Reddit.
184.108.40.206 03:02, July 23, 2015 (UTC)
- However, I'll also point out that per order of operations in your formula for max damage the above is true. But I wonder if you have your parentheses corrrect? Did you really mean to write Max per accuracy as this instead? Based on how you constructed max damage _without_ accuracy, this would be more accurate:
- ... and if so, then my supposition above would be wrong and both the min and max would raise equally due to Accuracy. It would also make Accuracy probably the best overall stat to acquire, since it would effectively raise damage by the exact percentage value of your total accuracy. That's even better than a fair amount of extra crit chance. (Yokaiichi again).
- 220.127.116.11 03:11, July 23, 2015 (UTC)
- Hmm, I didn't come up with the equation for min/max base damage, but they match up perfectly to my ingame numbers as they are currently written on the page: Might * 0.1034 + Strength * 0.197 * ( 1 + Accuracy )
- As for the ingame description, the description for Accuracy is pretty accurate, but technically I think the last part should read "... increases your Strength's influence on _maximum_ base damage." However, the incorrect description indicated on the page is referring to Strength's description, which is indeed completely wrong. Minimum base damage simply has nothing to do with Strength.
- On a different note, @Yokaiichi, I could really use your help deriving the skill tooltip numbers. They are very interesting to me, as it appears that bonus damage (and thus Valor) directly influences the max tooltip value quite significantly--but not the min value at all.
- Unislash (talk) 05:21, July 23, 2015 (UTC)
- All I'm getting at is that not everyone understands math order of operations, so IMO when writing to a general audience, it's always better to explicity use parentheses and brackets to group the terms you want to evaluate first.
- Some people will misconstrue the formula ad do the order of operations as I've demonstrated above. There is a significant difference in these two versions, and more people that you would suspect will interpret the formulas as they exist at this timestamp like the first sample below.
- (Might * 0.1034 + Strength * 0.197) * (1 + Accuracy)
- As for your request, I'd love to help but don't have enough different gear pieces to make enough datapoints for my own analysis, and I don't have the kind of time it takes to do this kind of testing and analysis. (Yokaiichi)
- 18.104.22.168 13:01, July 23, 2015 (UTC)
- I have removed some noise from the min/max damage formulas (we don't really need the non-accuracy baselines at this point), and I've added explicit parens to make order of ops clear. While I don't have much gear to test with (2% accuracy ring), my numbers work ONLY when accuracy is applied to the strength term alone in the max damage formula. I will keep testing though as I get more gear.
- Nezroy (talk) 13:45, July 23, 2015 (UTC)
- For what it's worth, these are the numbers I get: https://docs.google.com/spreadsheets/d/1e9hG9jLu9EurxiPgpHE1ghv3-y8F1ZebzkR3zGqtoN0/edit?usp=sharing
- They seem to fit with the in-game description of accuracy, i.e. accuracy moves Min Damage closer to Max Damage.
- 22.214.171.124 01:33, July 24, 2015 (UTC)
- Changing the min might coeff to 0.0967 gives a better fit, and better than the current formula. I will update the main wiki to reflect. Also, see https://docs.google.com/spreadsheets/d/1VwIXJZhBbFxvlAIxleM3QkvmnpgT0MPtFhsADT3lHVo/edit?usp=sharing for more data points.
- Nezroy (talk) 06:06, July 24, 2015 (UTC)
- Seems quite a bit more complicated. It might fit your data better, but maybe it's the rounding error talking? The equation was already predicting things quite well for me. Keep in mind that the real equation in code is probably rather simplistic to save on server computations...
- Unislash (talk) 09:52, July 24, 2015 (UTC).
Accuracy maximum damage Edit
Can someone confirm that contrary to the description, accuracy also improves maximum damage? Have no gear to test it atm...
- I tweaked the scaling values to work better with the numbers I have. I also changed the way accuracy is added into the max dmg based on the 2% accuracy ring I have around to try it out with.
Stats Google Sheet Edit
I've put my #'s into a google spreadsheet with the formulas we're currently trying to figure out. Still some slight discrepencies, especially with critical damage values. Feel free to edit to add your own data/formulas.
Luck * 1/3 * (1 + (#_of_T:MR / 10))
"At 50% Critical Chance and 6 Talent: Maximum Recoil, Luck would improve your average damage at a rate of 10 Luck to ~5.33 average Critical Damage."
How does 10/3 * 1.6 * 0.5 (crit chance) = 5.33 ? Did someone forget to factor in Crit chance? Or is there a 2x number that I'm not seeing? This should be 2.66.
126.96.36.199 16:32, October 19, 2015 (UTC)