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SkarmCents and BlissCents: Beta v0.2. With an "Attack tiers" this time
- Thread starter Dragontamer
- Start date
You have to be extremely careful when commuting division though, because doing it wrong can potentially mess up your answer.
In fact, the only way to reliably commute division is to treat it as multiplication of the reciprocal.
I like this concept. It's just the kind of thing my mind might have devised if I considered this problem.
EDIT: fixed a typo. Put multiplication where I meant division.
In a purely mathematical sense, they are commutative. But, in reality, with computing devices and the inherent inability to properly represent fractions with floating point numbers -- you can screw up the results of a series of multiplication/division operations very, very easily. Basically, if you are using a calculator or a computer, you can't count on getting the exact same results if you switch the order of operations. For the types of numbers and the number of operations being discussed here, the variance is likely irrelevant in practical terms. But, your point about "being careful", is absolutely true.
Actually, in a purely mathematical sense division is not commutative. For it to be commutative, x / y = y / x must be true, and it is not.
Division is only commutative in the sense that you can treat it as a multiplication of the reciprocal. x / y = x * (1/y) = (1/y) * x is a true statement.
Addition and multiplication are commutative, subtraction and division aren't.
Sorry, I misinterpreted your meaning of "be careful". Yes, division is clearly not commutative. And I was assuming the multiplication of reciprocal as a substitute for division in my statement about commutativity. For example, I might call the following operations an example of commutativity:
x / y * a / b
x * a / y / b
x / b / y * a
In a strict sense, the series is not commutative because of the division. However if I substitute the division operations with multiplication by the reciprocal, then it is. I was assuming that the divisors must always be divisors, which is a poor way of saying "multiply by the reciprocal" - but IMO, didn't really need to be spelled out.
I really shouldn't have used the term "purely mathematical sense", but I thought you were referring to issues of numeric precision. You were right, I was wrong.
x / y * a / b
x * a / y / b
x / b / y * a
In a strict sense, the series is not commutative because of the division. However if I substitute the division operations with multiplication by the reciprocal, then it is. I was assuming that the divisors must always be divisors, which is a poor way of saying "multiply by the reciprocal" - but IMO, didn't really need to be spelled out.
I really shouldn't have used the term "purely mathematical sense", but I thought you were referring to issues of numeric precision. You were right, I was wrong.
Lol, Earthquake on a Skarmory would do 0% damage.
One thing that I have qualms about is that the Special side and Physical side are based on two different scales. Special attacks and Physical ones are treated exactly the same in the damage formula, so there is no reason why both scales can't be based off of the same standard, such as Skarmory's physical defense. It might seem odd basing the effectiveness of a Special attack off of another Pokemon's Physical defense, but it makes sense when you consider that both Physcial and Special attacks use the same damage formula.
Normalizing the two scales like this would allow easier comparisons between a Pokemon's Special and Physical capabilities. For example, a standard Bliss has 67 SkarmCents and 100 BlissCents, but trying to use these numbers to determine how much more effective Blissey is at tanking Special hits than Physical ones is pointless unless you have a way to convert SkarmCents to the equivalent amount of BlissCents or vice versa. Normalizing the scales would remove the need for this intermediate step.
Genius.
Is finding the max damage really as useful as these charts would make it seem? I know it's cool to see if something will OHKO, but these seem like they would not be very useful for in-battle calculations. Ex: My +1 Gyarados @ 10%HP is facing my opponent's Skarmory@ 38%HP....do I risk losing Gyarados because I rolled lower than max damage for a chance to sweep? This system would not be a reliable way to determine that =\
This data looks useful for EVing, but with the response that this has gotten you would think that it is a revolution in damage calculating.
edit: wow that sounds a lot harsher than I intended it to. I'm not trying to undercut any of the work put into this by Dragontamer, I'm just saying that the applications for this are too specific for it to be a "new concept in team building". The charts are just written versions of what should be common sense to anyone who has actually played. Easier damage calculations are always welcome, and things like this make it easier for the rest of us. Thanks, Dragontamer!
p.s. Skarmory is not in the SkarmCents chart this time around >_>
This data looks useful for EVing, but with the response that this has gotten you would think that it is a revolution in damage calculating.
edit: wow that sounds a lot harsher than I intended it to. I'm not trying to undercut any of the work put into this by Dragontamer, I'm just saying that the applications for this are too specific for it to be a "new concept in team building". The charts are just written versions of what should be common sense to anyone who has actually played. Easier damage calculations are always welcome, and things like this make it easier for the rest of us. Thanks, Dragontamer!
p.s. Skarmory is not in the SkarmCents chart this time around >_>
Multiply by 0.85, and maximum damage turns into minimum damage.
Multiply the final value with .85 if you want to calculate the minimum damage. Multiply the final value with 1 (obviously) if you want the maximum damage.
To find the average damage, multiply with .925.
EDIT: beaten >_>
That is true. However, one of the primary purposes of BlissCents / SkarmCents is to fill a void where Defense Tiers (and their complement Attack Tiers) are difficult to use. If you wish to compare that sort of information, Defense Tiers work perfectly fine already. There, you can compare say... SpecsMence DracoMeteor vs BandHeracross Close Combat. (118.19 vs 117.51 on the Attack Tier scale if you're curious)
Defense Tiers are not obsolete by SkarmCents / BlissCents, instead, these two systems complement each other.
Lol, beaten in your own thread.
The tier system has the advantage that logarithms turn multiplication into addition, but t is not really useful in determining how much more powerful certain attacks are relative to each other. People tend to think in proportions, not logarithmically. And when comparing 118.19 to 117.51, it's not immediately easy to see that Draco Metoer is 6.7% stronger than Close Combat in this case.
Tiers are useful for mass damage calculation, but the Cents are easier to compare the power of two Pokemon.
Actually, for small values it is quite close. Watch.
118.19 - 117.51 == .68
1 Tier == 10% difference.
.68 Tiers == about 6.8% difference (really, 6.7%)
For values close to 1, it is reasonably accurate. (I admit that it gets less acurate the further away you get from 1)
Anyway, 1 tier difference is always 10%, so tier 100 vs tier 101 is 10% difference. Tier 120 vs tier 121 is 10% difference in strength. It is uniform throughout the entire tier set. This way, we can really say that Weavile vs Machamp is like comparing Skarmory to Steelix (both comparisons are ~3 tiers apart)
But SkarmCent 50 vs SkarmCent 55 is 10% difference. SkarmCent 60 vs SkarmCent 65 is a 8.33% difference. A difference of "5" changes depending where you are.
Scyther (40 SkarmCents) vs Blastoise (50 SkarmCents) is a bigger difference than Weezing (89 SkarmCents) vs Slowbro (99 SkarmCents), even though the difference is 10 SkarmCents for both, the comparison doesn't hold true. Blastoise is 20% tougher than Scyther, while Slowbro is only ~10% tougher than Weezing. Thats the kind of comparison I'm talking about.
EDIT: This isn't a particular point that probably should be argued normally, but I do have reason. I'm planning to eventually write a SkarmCents / BlissCents and Defense Tier guide, and understanding when to use one system over the other would be key. If I'm misunderstanding the general mindset of people who do use both systems, then that is something I should understand.
The issue I'm getting at is that when comparing things, it is easiest for people to think proportionally rather than logarithmically. 100 is twice as great as 50. 220 is 10% greater than 200. It's easy to compare the two numbers and envision just how big of a difference it is between them when you can think in terms of a proportion.
Logarithms are a different story. Taken from the Sp.Def tiers, Blissey is in tier 128 and Magikarp is in tier 99. The initial reaction of someone first seeing that data is that that difference isn't that big. It isn't until you work out the math and change the logarithms into proportions that you can find that Blissey has 16 times the walling power of Magikarp.
Tiers have their use in allowing rapid calculation of specific operations, such as calculating KOs under a variety of conditions. At that, they are very good, very efficient, and very capable. However, the tier's logarithmic base robs people of the ability to easily compare and envision the power difference between two Pokemon.
This Cents idea here has its main application in allowing people to easily envision that difference in power between Pokemon. A Pokemon with 336 SkarmCents is 3 times as powerful as a Pokemon with 112 SkarmCents, for example.
As already mentioned, the only thing I see wrong with this system is that the physical and special scales are based off of different standards. Alakazam is roughly as powerful at special attacking as Tyranitar is at physical attacking (Alakazam is actually just a bit stronger), but Alakazam only has 156 BlissPoints max while Tyranitar has 244 SkarmPoints. The difference between these two numbers makes it hard to envision the difference in damage that these two Pokemon would deal to similar targets, such as a mixed Bronzong. Normalizing the two scales to be based on one standard means that Alakazam's and Tyranitar's Point values would be about the same, accurately reflecting the closeness they have in power.
Another benefit to normalizing the two scales is that you would be able to accurately gauge the difference in how well a Pokemon could tank a certain class of attack over another. For example, a standard Blissey - having a Defense stat of 130 and a Sp.Def stat of 306 - is approximately 2.35 times as effective at tanking special hits than physical ones. This difference is not accurately reflected in Blissey's Skarm- and BlissPoints scores (67 and 100, respectively).
Logarithms are a different story. Taken from the Sp.Def tiers, Blissey is in tier 128 and Magikarp is in tier 99. The initial reaction of someone first seeing that data is that that difference isn't that big. It isn't until you work out the math and change the logarithms into proportions that you can find that Blissey has 16 times the walling power of Magikarp.
Tiers have their use in allowing rapid calculation of specific operations, such as calculating KOs under a variety of conditions. At that, they are very good, very efficient, and very capable. However, the tier's logarithmic base robs people of the ability to easily compare and envision the power difference between two Pokemon.
This Cents idea here has its main application in allowing people to easily envision that difference in power between Pokemon. A Pokemon with 336 SkarmCents is 3 times as powerful as a Pokemon with 112 SkarmCents, for example.
As already mentioned, the only thing I see wrong with this system is that the physical and special scales are based off of different standards. Alakazam is roughly as powerful at special attacking as Tyranitar is at physical attacking (Alakazam is actually just a bit stronger), but Alakazam only has 156 BlissPoints max while Tyranitar has 244 SkarmPoints. The difference between these two numbers makes it hard to envision the difference in damage that these two Pokemon would deal to similar targets, such as a mixed Bronzong. Normalizing the two scales to be based on one standard means that Alakazam's and Tyranitar's Point values would be about the same, accurately reflecting the closeness they have in power.
Another benefit to normalizing the two scales is that you would be able to accurately gauge the difference in how well a Pokemon could tank a certain class of attack over another. For example, a standard Blissey - having a Defense stat of 130 and a Sp.Def stat of 306 - is approximately 2.35 times as effective at tanking special hits than physical ones. This difference is not accurately reflected in Blissey's Skarm- and BlissPoints scores (67 and 100, respectively).
Initially, yes. However, a logarithmic scale is far more similar to humans and is actually far more natural than most think. Psychologically speaking, sight (brightness specifically), hearing (both frequency and loudness), and feel/strength are all in a logarithmic scale to the human brain. And as such, these things tend to be measured logarithmically in practice (octaves, decibels, richter scale, and even pH are all logarithmic based).
Initial reactions, I can agree with. SkarmCents / BlissCents were designed after all so that they would be easily figured out with little use (kind of like an "introductory" defense tier). But I argue that after some amount of use, the Defense Tiers feel more natural. After all, logarithmic scales are based on proportions, and are in fact used to visualize proportions.
(bold is to match a piece of you're quote with mine, thats all)
I see the benefit. However, re-normalizing the scales would get rid of a very specific advantage of these scales. All pokemon currently are compared to the most popular Special Wall in the game (and who arguably takes the most special hits in all of Shoddy), and all pokemon are compared to the most popular Physical Wall in the game (who arguably takes the most physical hits). Well... at least at the time I made them, Skarm was slightly more popular than Cresselia on the Shoddybattle statistics... I dunno about now.
To anyone who has played Pokemon competitively, they should have a natural feel of both Blissey and Skarmory. Both are in the top 15 lists of used Pokemon in the Shoddybattle ladder. People probably know how much Stone Edge does to a Skarm naturally, and similarly people probably know how much Draco Meteor does to a Blissey. Now, they can compare that to every pokemon in the game with this list.
If one these scales no longer applied to real pokemon, they would lose a key benefit. Unless there is a very common pokemon who has as much Physical Def as a Standard Blissey's Sp. Def, or vise versa with Skarm (who is also used often), I'd say that the costs outweigh the benefits.
Attacks are also more simple to calculate and figure out. To compare say, Alakazam's Sp. Attack to T-Tar's Physical Attack... why not just pull up Serebii, look at Alakazam's 135 Sp. Atk base, and T-Tar's 134 Base Attack, and then go "Oh, they're about the same"?? I doubt they need any tiers or complicated calculations to compare at all now that I think of it.
Items like Pikachu's Light Ball and abilities like Medicham's Pure Power are not factored in. The stats shown are the ones assuming there is no item like the aforementioned Light Ball, or ability like the aforementioned Pure Power, in play.
Blisscents = Skarmcents x ~1.57
Lol, never thought of them in that way. I ought to put that into the first post somewhere. Thanks.