Saturday, July 28, 2012

Skill Enhancement

Any card with a skill can have that skill enhanced to a higher level. The cards skill always starts at level one. At level on the percentage boost is determined by the label (big, med, small, massive, etc).

For each additional level the card gains 1% in power. Nightmare for example gives a 13% Boost to Demons Attack at level one. At level five this would turn into a 17% Boost. It is a 4% increase because the card has increased four levels (level one doesn't count as a percentage). At level 10, the max skill level, Nightmare would have 22% Boost to Attack.

The process of leveling a skill is simple in principle. If a card with a skill is enhanced using cards with skills, it has a percentage possibility of gaining a skill level. The percentage possibility has three factors.

1) The rarity of the card being evolved.
2) The rarity of the cards being used as the evolver
3) The current skill level of the card.

I found the exact numbers from Ragetrades who got the information by translating it directly from Japanese sources. The far left column signifies the skill level, the top signifies the percentage gain for each card of that rarity. For example, an SSR at level two will gain .7% chance of gaining a level per High Normal card being used or 20% per SSR used.

Legend Cards


SSR


SR


High Rare


Rare


High Normal



The information that can be deduced from these graphs is as follows. 
1) Cards like Dark Knight Luciella or Popstar which have a Higher Rarity but the same power level of a lower Rarity (both about High Rare-SR power levels) are actually worse than the lower Rarity counterparts. This is because leveling the skills will be very expensive in comparison.

2) A High Rare increased in level to SR is most effectively leveled by using High Normals. You can do so from start to finish most the time at a cheaper rate than Devil Queens/Treasure HRs.

3) Devil Queens are the only true cost effective way to gain levels on cards SSR on up.

4) Treasure Rare cards are a less expensive way of attaining HR enhancers. 

I will note that buyers rarely see the proper value of a card with a higher skill level so if you plan on selling the cards shortly, it's better not to spend a huge amount of money enhancing the level.

44 comments:

  1. ok, NooB question regarding skills... if I take a stage 1 skill maxed to ten with another stage one maxed to ten and evolve them, does the stage 2 now have a "step up" in the skill, meaning instead of a "small boost to blah" it now has a "medium boost to blah" all the way up to stage for with "huge boost to blah"?
    I have seen cards that at stage one give small, but at final stage give big/huge boost... is this due to maxing the skill level prior to evolving or does it not matter?

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    1. I have never seen what you are talking about. To my knowledge once a card hits level 10, it remains Big Boost to (whatever) lvl 10.

      The only cards I could think of that at stage 1 give small but at final stage give big/great are Knight Luciella's and that's because it's a function of the card. It gains in rarity and skill power each time you upgrade it.

      Delete
  2. that is the card I was referring to and was wondering if it was a card specific thing or if ALL cards did that. Thank you! :)

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    1. It is a card specific thing. The cards that do increase their boost/hit are the referral cards. These cards are: Luciella, Hilds, and Princess Knights.

      Delete
  3. Hello, I was looking to get someone elses opinion on this because a friend and I have a difference in opinion on how to skill up a card. We are curious as to the best way to skill up a card and it seams that on most forums and guides people just use all 10 skill cards at the same time. I was thinking that it might be better to do them one at a time, for example. You have 10 cards that each give a 5% chance to skill up your card. If you use them all at once you have a 50% chance to skill up on your 1 enhancement. If you do them all seperatly you have 10 enhancementes each with a 5% chance of skilling up your card, but in the end has the same chance (5%x10=50%). The only difference between the two methods is that in example one your best case is that you only get 1 skill up, where as in example 2 you could get lucky and skill up 2 or 3 times. Please let me know what you think and if you see an error in either method and which way you think is best. Thanks.

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    1. Ouch. I actually did a post in my order on this. It hurts my head. You are the guy who sees red hit 14 times on the roulette table and says, 500000 on black! And then loses.

      The way odds work is they are each calculated individually. You do not add up the sequence since the previous skill ups have no bearing as to whether or not this skill up will be successful. For example if I do math the way you did. 5%x10=50, lets reverse that, 95% (the odds of failing)x10=950% chance of failure.

      Or to simplify. You have numbers 1-100. If you have an 80% chance, 80 of those numbers will result in a skill up when the computer picks one at random. You fail. An entirely new sequence occurs. Meaning, whether or not you failed before, has no bearing over the random number picked this time.

      It is best to maintain the highest percentage each time you enhance for skill. There are no instances where it is better not to. If you had success one time doing 5% enhancements 10x, you got lucky. 95x out of a hundred, you fail. 5x out of a hundred you succeed.

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    2. Hello again, this seams to be the answer I get from most people but the thing I point out is that you are not taking into consideration the material cost. I understand that that the odds do not change from enhancement to enhancement, but mathematically speaking 1 enhancement at 80% vs. 10 enhancements at 8% will on average have the same number of successes (in our case a skill up). The worst case scenario for both is that you get 0 skill ups (both have a 20% chance of that happening) but the difference is the best case scenario, in situation 1 your max possible skill ups is 1, where in situation 2 your max possible skill ups is 10(nearly impossible but just technically speaking). To relate to your roulette reference it would be like one guy bets on 10 numbers with 1 bet vs. another guy that bets on 1 number 10 times. They both have an equal chance of hitting, the only difference is if the guy that bets one at a time hits on his first try then he saves himself the 9 other bets. That’s where my question comes in, wouldn't you want to give yourself a chance to get lucky vs. using them all at once where you can never get lucky? Thanks for your feedback.

      Delete
    3. "The odds do not change from enhancement to enhancement, but mathematically speaking 1 enhancement at 80% vs. 10 enhancements at 8% will on avergage have the same number of successes (in our case skill up)."

      This is a mathematically fallacy. It will not on average win. You are wrong. There is actually something called Gamblers Fallacy that covers this.

      Quite simply, you are wrong, you don't realize it but what you're saying has been proven wrong and verified as wrong by thousands of mathematicians.

      You did not understand my roulette reference, I can tell because your alternate example using roulette is the same argument you made except using "10 numbers with 1 bet vs..." as the example.

      The one bet is 10/38 or 26% chance of winning. One bet. If he then uses 10/38 again his odds are NOT now 52%, they are an entirely new 26%. If he then uses 10/38 again, his odds are 26% NOT 78%. If he then uses 10/38 again, his odds are 26% NOT 78%.

      If you use 1/38 10 times, your odds are each time 2.6%, not 26% eventually.

      Please read Wikipedias post on Gambler's Fallacy. I can unequivocally tell you that it is better to use more cards until you hit the highest percentage, without going over 100%.

      Delete
    4. Alright one more post than I will leave you alone promise ha. I guess the part we are disagreeing on is the odds of having 1 successful chance. For instance if I flip a coin I have a 50% chance of getting heads, on any given flip. I understand that if I flip 6 tails in a row the odds of getting heads on the 7th flip is still 50%. My point is that the question being asked is what are the odds of getting heads once, if I flip a coin 10 times. The odds of getting heads once is not 50% they are much higher, because the goal is getting 1 successful hit out of multiple attempts. So when it comes to enhancing the goal is getting 1 successful skill up. Yes the odds of getting one skill up on any given enhancement is going to be lets say 5%, but the question is what are the odds of getting one skill up over 10 enhancements. I am a poker player and am well aware of what you refer to as the gamblers fallacy and that is not the situation here. I am not saying that if my first 9 attempts fail at enhancing then my 10th one has a 50% chance, I am saying the odds of getting 1 successful skill up out of 10 attempts at 5% each are roughly 50%. The big point that is being left out here is that in order to do say a 50% enhancement you have to use 10 cards, where at 5% you only use 1. Therefore you can have 10 times the attempts due to the reduced amount of cards used. The goal for both is to get 1 skill up. 1 successful hit out of the multiple attempts. The only difference is when you get the successful skill up when using 10 cards you still lose all 10 cards. However if you were to get the successful skill up when doing them one at a time, and the skill up came on attempt #8 lets say, then you have saved yourself 2 cards for your next enhancement. I guess my final example to prove my argument would be say you are drawing a random number out of a hat with numbers 1-100. If the number you are trying to draw is 25 and you have 100 attempts at it you can't tell me you think after all those attempts you chance of getting 25 is only 1%. Yes its 1% on any given draw, but if you have 100 attempts at it odds say you will draw it once. No its not 100% guarantee but statistics say you should have 1 hit per 100 attempts. This is what I am trying to correlate to enhancing in that I feel that cards are being wasted by using them all at the same time, doing them one at a time ensures you get maximum use out of each card, where as if you use them all at once you throwing away some of their potential.

      Again thank you for you time and your thoughts talking to you about this made me look into this quite a bit more and I feel that enhancing the cards one at a time maximizes there potential.

      Delete
    5. That's fine that you want to think that way, but I want any of my blog readers to know what wbalzari is doing has been mathematically proven to be less efficient.

      There is no instance in which his way will give the best results. Especially once you hit skill lvls 3+. Always use 9 cards to achieve the highest percentage chance of success. Unless of course you can achieve 100% with fewer cards.

      Delete
    6. @wbalzari

      Lucarda is right. It is about 'probability', you should revise your logic.
      E.g two(2) times of 50% DOES NOT equal to 100%.

      50% (0.5) * 50% (0.5) = 25% (0.25). That was 25% of success.

      Delete
    7. It's actually 75% chance but yep.

      Delete
    8. Ops.. My mistake.

      The 25% is to get both (2 times) success.
      So it was 75% success rate for 1 time.

      For that in mind, i have a scenario to think.
      Lets say i want to enhance a High Rare card's skill from lvl 4-5.
      Provided I had 40 High Normal skill cards, which is better way?

      1) Use 10 High Normal each enhancement for 4 times (each time 49% success)
      2) Fully evolve all High Normal to Rare, then had 10 Rare enhancement (80%)

      Delete
    9. Easy! 10 high normals at 49% :P

      The reason is 2 times is 74% chance, 3 times is something like 86%, leaving an entirely extra time.

      I used to think evolving to rare was worth it but after looking at the numbers HR is always the better option. Hate to say it though.

      Delete
    10. This comment has been removed by the author.

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    11. Good to know.

      I was thinking to evolve all to rare too. After study it mathematically, now i made up my mind to use HN all the way. :p

      Delete
    12. The math is correct but incomplete. Since the goal is not just to get at least one, but the most skill ups with the least cards.

      Example SR skill lvl 4->5 with 10HN at 4% each.
      all 10 at once has a 40% chance of success where individually has a 33.5% chance of at least 1.

      We also have to consider the outcome that you can get more than 1 skill up. The probability of get all 10 skill ups is .04^10 or .000000000001% (yea I know, minuscule), but the chances of getting 2 out of 10 5.2% when feed individually.

      To find the probability of each occurrence, you use the probability formula :
      P(k out of N) = (N!/(k!*(N—k)!) *p^k x q^(N-k)
      For each count, 1-9, the probabilities are:
      0.277013598329792
      0.051940049686836
      0.00577111663187067
      0.00042081058774057
      2.10405293870285E-5
      7.305739370496E-7
      1.73946175488E-8
      2.717908992E-10
      2.5165824E-12

      Then multiple each probability by the occurrence rate, then sum all values and you get 0.399999999999895 and add the 10 out of 10 % calculated above and you get a 40% skill growth coefficient when factoring in the occurrence rate versus probability of getting multiple skill ups using the individual method.

      Granted this doesn't take into the calculation that once you go from 4->5 the percentage decreases now for 5->6 so the coefficient of growth potential changes each level. This is just an example to show that the coefficient of growth rate does not change when feeding cards individually versus 10 at a time.

      I suspect they designed it this way on purpose. If anyone has any math to disprove this, I'd be happy to read it.

      Delete
    13. I wrote quick SQL cursor to do the calculations. You can sub in any number of feeder cards and the probability of success and failure and find the growth coefficient.

      select y.*,
      (FACTORIAL_n/FACTORIAL_K/FACTORIAL_NK)*power(p,k)*power(q,n-k) as probability,
      (FACTORIAL_n/FACTORIAL_K/FACTORIAL_NK)*power(p,k)*power(q,n-k) * k as growth_factor,
      sum ((FACTORIAL_n/FACTORIAL_K/FACTORIAL_NK)*power(p,k)*power(q,n-k) * k) over () as total_growth_coeff
      from (
      select x.*,
      EXP(SUM(LN(greatest(k,1))) OVER (ORDER BY k)) FACTORIAL_K,
      EXP(SUM(LN(greatest(k,1))) OVER ()) FACTORIAL_n,
      EXP(SUM(LN(greatest(n-k,1))) OVER (ORDER BY n-k)) FACTORIAL_NK
      from(
      select rownum-1 k, -- number of successes
      10 as n, -- number of cards
      .04 as p, -- Probablity of success
      .96 as q -- probability of failure
      from dba_users sp
      where rownum <=11) x)y
      order by 1;

      I'm a programmer, not a mathematician, so if anyone sees anything wrong with my math, let me know.

      Delete
  4. OMG cat fight made my eyes bleed -.-
    Just a simple quick Q.?
    Is it better MAX ENHACE the card and LVL UP SKILLS before u EVOLVE CARD /vs/ just MAX ENHANCE and EVOLVE then LVL SKILLS?

    ReplyDelete
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    1. haha.

      When you evolve a card, the skill level is reduced to lvl 1. So if you were for example to get a ++ to skill level 5, the final form would still be skill level 1.

      As such, max the enhancements level, don't worry about skill until its in the final form.

      Delete
  5. I think your advice to evolve HN's to rares is not quite right. Say we have a SR skill 7card we want to skill up. 10 HN's have a 20% chance of leveling the card (the game adds the odds of each card added). The chance of not leveling is 80%. The chance of not level your card with four sets of 10 HN is 41% (.8*.8*.8*.8 = 40.96%). So the chance of leveling at least once is 49%. Those same 40 cards evo'ed to 10 rares gives a chance of skilling up your card of only 30% per the table. Please correct me if I'm wrong. I'm here to learn

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    1. Haha, you're right on this one. For some reason I must have switched to the SSR chart at some point.

      I was thinking at halfway through they dropped to .4

      Sorry about that.

      Delete
  6. lucarda,
    From skill 9-10 ... is its only gonna be 1% diff or great amount of diff??? because i hear many people talking about if you get to lvl 10 instead of 9, its give the other cards a diff amount of % boost; not the 1% diff. am not sure what they mean and how much diff it is...
    so if you have time pls look into it :)
    thank you

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    1. From everything I found when looking into this before, that's a myth.

      The myth came from people not counting lvl 1 as a level. So if a card had a 10% boost at level 1, they said, oh, level 10 means it will have a 10% bonus so 20%! The people forgot to subtract the first level making it 19%.

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  7. so even they forgot about that lvl doesnt count, but from skill 9-10 is only 1% diff, not like a major boost that worth lvl up... because i have a card skill 9 and faid like 5 time at 30-40% few time to get to 10... am kindda giving up right now if its only for 1% diff :))
    but if its more like a bonus 3-4% between 9-10 then ill keep trying :))
    thank you lucada :)

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    1. Skill ups are something I consider a non priority. For example, if you have a deck of five cards, your lead card a skill 5 Nightmare (like mine) should you focus on skilling it to 10? Or replacing your inugami with another nightmare? Swapping out the inu gives a much bigger boost.

      Once you have your deck the way you want it or have a large influx of feeders, that's when you should be skilling up.

      The next event is a perfect time to skill up because there will be a large influx of skilled feeders.

      Delete
  8. hi, can you still leveling up a card if it is fully evolve and enhance?

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    1. Yes, when you select to enhance it when its maxed level it will only show skilled cards as options to combine with it.

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  9. Lucarda I just want to say that whatever my question may be, I always find myself here one way or another for some solid answers. Thx for that. As for skilling up, I can see both sides of the argument. If u want ur best chances, use your way. If you want to roll the dice, use the other. I personally have achieved skill up with like an 8%-12% chance a couple times, so occasionally I just throw a couple of hrs at a card and hope for the best. Probably the gambler in me, maybe im just cheap. Good luck yall, may there be many ssr in your future!

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  10. I teach probability and statistics and I have a bachelors degree in statistics. Skill enhancing is not like gambling, and comparisons to gambling (including gambler's fallacy) are inappropriate. I will start with the conclusion, and you may continue to read the mathematical details if you'd like.
    Single-Card Method: enhance with one X% card at a time.
    vs.
    Ten-Card Method: enhance with ten X% cards at once (total % <= 100%).
    Conclusion: Each method will *on average* cost the same number of cards to succeed in a skill up. The single-card method will have more variability (less consistency) than the ten-card method. Therefore, you should tailor your enhancement method to what "cold streaks" you're willing to endure for the occasional "hot streak," but in the long run, you'll spend the same number of cards.

    The math: This is not like casino gambling. In all casino gambling, first you bet money, second you either lose that money or you win more money, and third you quit when you have no more money or earn a set amount of money. In enhancement, first you "bet" cards, second you lose those cards, and third you quit when you have no more cards or when you skill up once. You do not win cards, and obviously you do not quit when you have earned a certain number of cards.

    If you still think enhancing is like casino gambling, here is a more specific (mathematical) explanation. Casino gambling can be described as something called a Markov chain- a list of values that you travel between based on probability. Let's assume that you start with $30, must bet $10, and will quit when you hit $0 or $60. You will bounce around the following Markov chain:
    $0---$10---$20---$30---$40---$50---$60
    If you're playing craps, you have a 49% chance to move to the right and a 51% chance to move to the left. If you really want to hit $60, the smartest bet is to bet $30 right away.
    Skill enhancing can also be described as a Markov chain, but it looks quite different. Let's assume you start with 5 enhancing cards (5ec), enhance one card at a time, and stop when you have 0ec or successfully enhance (E). You will move along the following Markov chain (pretend periods are blank space- there's html for you):
    0ec----1ec----2ec----3ec----4ec----5ec
    ........./......../......../......./......./
    ......0ecE...1ecE...2ecE...3ecE...4ecE
    You start at 5ec and either move to the left or down. There is no bouncing back and forth- you never gain an enhancing card. It is not the same as casino gambling. The optimum method used in casino gambling does not apply here.

    Skill enhancing is a geometric distribution, meaning you perform trials (sacrifice cards) until you get your first success (skill enhancement). It is well-established that the average number of trials it will take is 1/p, where p is the probability of success (expressed as a portion instead of a percent, i.e. 0.05 instead of 5%). Let's compare the single-card method to the ten-card method with a per-card percentage chance of enhancement of 5%.
    Single-card enhancement: 1 trial = sacrificing 1 card. Probability of successful enhancement = 1*0.05 = 0.05. Average number of trials until success = 1/p = 1/0.05 = 20 trials = 20*(1 card) = 20 cards.
    Ten-card enhancement: 1 trial = sacrificing 10 cards. Probability of successful enhancement = 20*0.05 = 0.50. Average number of trials until success = 1/p = 1/0.50 = 2 trials = 2*(10 cards) = 20 cards.

    As you can see, it is the same average number of cards required to achieve a skill enhancement regardless of the method used.

    (cont)

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    1. (cont.)

      (My apologies for my second Markov chain not lining up right.)

      Some will raise the point that, with ten cards, you could get 2, 3 or even 10 enhancements using the single-card method, while the ten-card method could never get you more than one, and therefore, the single-card method is better. Well, that sort of ignores that I just proved that the average number of cards you use is the same, but I should still address the flaw in reasoning (and I will have to ignore the fact that skill enhancement success decreases as skill level rises- let's just assume you're skilling up ten level 1 cards). The single-card method does allow for multiple enhancements, but it's also far more like to get you nothing. Here's the breakdown:
      Ten-card method (5% per card)
      0 successes: 50%
      1 success: 50%
      Single-card method (5% per card)
      0 successes: 60%
      1 success: 32%
      2 successes: 7%
      3 successes: 1%
      4+ successes: essentially 0%.
      You can see that the 2 or 3 successes balance out with the increased chance of 0 successes.

      I hope this straightens things out for everybody.

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    2. This whole debate by the way is why I never posted about skill ups until people harassed me to do it. And I'm sorry if I come off as a twat about it but it irritates the piss out of me.

      The issue I have is when dealing with geometric distribution is that in my opinion it only works properly when we are dealing with a massive sampling otherwise it's horribly unpredictable(thousands). Using a sample of 100 people using all the cards at 5% per card, and another sample of 100 people using each card individually at 5% per card (using your math which I'll assume is correct):

      Group 1: 50 get a skill up, 50 don't. (In theory)
      Group 2: 40 get 1 skill up, 7 get 2 skill ups, 1 person gets 3 skill ups (which equals 50 skill ups in total for those reading), 60 fail. (In theory)

      There are still fewer winners, and a very small amount of people who are big winners. In theory those losers are more likely to win on their next attempt but truthfully their previous attempts no longer have any bearing on their future attempts and they could just as easily get perpetually locked in losses and geometric distribution kicking in so far down the road that they never get there.

      I hate geometric distribution because it follows along the theory that as long as something is possible, and you try it enough times, it will eventually happen and all your losses will even out. It's basically mathematical karma.

      The truth is if you play against the odds, no matter how much you do it, you are more likely to lose than win.

      Delete
  11. Just looking for some thoughts, Im trying to skill up my Jormy and my Dark Dragoon. DD is only at 2 atm. What would you do to lvl them. Ive been dumping sets of 10 rares at a time for 7% chance and no luck

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  12. basically what it comes down to, is if you want to gamble to get possibly more than one skill up, or basically stick to even odds... Me, i stick to best odds i can do since i usually have horrible luck (didnt skill up with 95% 3 times in a row before). i However do have a question for lucarda, since i still believe in his opinion, no matter how many math heads try to dismantle his guides lol i have heard a brief summary of 'pyramid skilling' meaning you skill a rare or HR up on skill level which raises the percent that single card would raise a higher card, such as SR or SSR... but i however didnt read anything about that in this guide... is it a myth? or something overlooked? thanks for the great guides :)

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    1. Pyramid skilling does work and is very effective from skill levels 7-10.

      I actually have three different posts relating to skill enhancement that cover quite a bit of it. When you calculate it out though, you'll find that the cost of skilling up some of those cards equalizes the effect.

      Now, obviously I prefer getting as close to 100% as possible, but if it costs 6x more to get the 100% than it would for a 50%, you need to take that into consideration.

      That's why I recommend doing it when cards are leveling from skill 7-10. Those are the hardest levels to gain and where you will get the optimum effect from pyramid skilling.

      Delete
  13. I have a problem with skilling a SSr of any kind.

    If i use only Rare its to costly, but does it help if i take a event hr and skill it to a certain level let say for example skill 5 and then replace it with a rare to make the certainty of skill more bigger

    Is this the best way or doe people use other tactics. If so i would really like to know cuase i would like to have my ssr to lvl 10!!!!!

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  14. hi since this new upgrade to the game IM having problems getting skill leves on my cards when I enhance them in the past I have used High norms with skills or archangle quen and was able to obtain a skill level or two I prevelousy was able to enhace my prisoner Knight Lucillea to skill level three using this method but my last set since this new system I was not able to do so any advice my cards are at the fallen stage and I would like to be able to incresse their skill level before the finnial evole oh by they way it will be a ful eight card evole

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    1. If you evolve a card, it's new skill level is set to 0. So if you skill up your prisoner Luciella to say 3/10 and then evolve her to Fallen Luciella, her skill level is now 1/10. Say you up her to skill 7/10, and then evolve her into [Fallen Paladin] Dark Knight Luciella, once again her skill level is 1/10. I actually have a perfect 8 card evolve too, ATK: 13627 / DEF: 10774. I'm at 3/10 skill so far, and it's hard haha.

      However, as a general rule, don't skill up cards that aren't Final Form.

      Delete
  15. I'm currently using HRs and Rares to skill up HRs to SkL4-5 to then use those skilled HRs to work on my Legendary Alice. It's a ton of work...but I think far cheaper than grinding with SkL0 HRs. This is particularly true in my case where I don't like to buy cards for skilling other cards. So my supply of HRs is relatively low compared to those with a higher threshold for letting their HPs go to grinding cards. It's slow but it's steady.

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    1. HNs and Rares...that is...I'm not skilling HRs with HRs...hehe

      Delete
  16. It's all a big gamble with skilling up. I've skilled up a SSR (not meaning to just needed to finish her level) at 2.2%. Then there are numerous times that I've had 94-96% and didn't skill at all. Eventually, you're going to use lots of cards no matter which way you plan on skilling up. I do mine based on budget and what I can get as far as cards go. With probabilities, it's always a gamble. As in gambling, it usually favors the House in the long run.

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