Ascension and relative power levels

DNA3000DNA3000 Member, Guardian Posts: 19,652 Guardian
I was trying to make some ascension decisions the other day when I decided to actually calculate precisely where Ascended champs fall in the power spectrum of champion rarity. How does an ascended 6* compare to 7* champs? Are ascended 5* champs viable competitors to 6* champs? That sort of thing.

There's no way to do a perfect apples to apples comparison, because there are other factors at play. There's awakening and signature levels, for example. Lower rarity champs are easier to awaken and sig up. And then there are some other scaling effects that are difficult to perfectly quantify and compare - combat power rate, for example, or abilities that have their own scaling. So this is just looking at the factors we can compare - attack and health scaling.

Ascension scales champions attack and health upward by a fixed amount, although that amount differs by rarity. According to the table given in the Ascension announcement (https://playcontestofchampions.com/news/ascension/) 4* champs gain 30% attack and health when ascended, 5* champs gain 20%, and 6* champs gain 22%. If we focus on the percentage change and look at one of the two stats affected by Ascension, we can take a sample champ (I picked Angela, as she's available at 7*) and see how her attack value scales upward with rarity, rank, and ascension:



I've sorted in descending order from highest to lowest. This is what it looks like in pretty picture form:



We can see that Ascended 6* R5 is almost identical to 7* R2. I don't think that's a coincidence. I've color coded 7* champs in red, 6* champs in green (ascended champs in a lighter shade) 5* champs in blue, and 4* champs in brown. I'm not sure that helps, but there you go.

These numbers don't fully express the actual difference between rarities and ranks however. When you increase attack by 20% and health by 20%, you don't make the champ 20% stronger. Consider a fight where you are dealing damage and taking damage. You win if you deal enough damage to defeat the defender before you take enough damage to die. There is, in theory, a maximum amount of damage you can deal before you die, if you are constantly losing health. If you increase your attack by 20%, you will deal 20% more damage. But if you increase your health by 20%, you will also deal 20% more damage - because you will live longer and deal more damage before you die. If you increase both, your damage per second goes up and also how many seconds you live to deal damage goes up. The total amount of damage you can deal before you die goes up by a factor of 1.2 x 1.2 =1.44. So in situations where you are challenged and taking damage, increasing damage and health by 20% increases your overall damage dealing ability by almost 50%.

If we scale everyone down to where 5* R1 = 1.0, we can come up with a combined power table that reflects that combined benefit:



And of course:



Now, the order of the champions remains the same, because in effect all we're doing is squaring the numbers. If a < b, a^2 will also be smaller than b^2 (at least here, where power levels start at 1.0 and go up). So the order is the same, but the magnitude of the differences goes up substantially. 7* R2 and 6* R5 ascended look pretty close to 7* R3 in the one dimensional scaling table, but in the combined relative power table 7* R3 is far higher than both. This shows the exponential growth of champion power over time.

The first table does have uses. By focusing on one dimension, we can ask questions like "is a 6* R5 ascended running a 20% champion boost competitive with a 7* R3? The 6* R5 ascended is around 5000 and the 7* R3 is a bit above 6000, so yes, a 6* R5 Ascended champ running a 20% boost is going to be, at least when talking about health and attack, comparable to a 7* R3. Also, if you are in fights where you are pretty sure you aren't going to die, the main advantage of higher rarity is more damage and quicker kills. In that case, more health is not a noteworthy advantage and in those cases the first table better reflects the advantage differences between rarities.

But I think for most players in most reasonably challenging content, it is the second set of data that better quantifies the relative strengths of the different rarities and where ascension places champs, at least before considering the stats ascension does not affect the scaling of, like combat power rate, ability effects, critical rate, etc.

Overall, to me it does look like Ascension roughly does the job it was intended to do. If you're a player that is currently using a mix of 5* and 6* champs, then 5* R5 ascended is at least competitive with a 6* R3, and for such players 6* R4s will likely be still difficult to get. For players using mixes of 6* and 7* champs 6* R5 ascended is very competitive with 7* R2, with 7* R3 champs currently extremely constrained - but those highly expensive and difficult to get rank ups are standing head and shoulders above the rest, as they currently should.

Presumably, almost no one is going to ascend champs that are not either at max rank or one tier below, but I put them all in there for completeness. But I think the best candidates for Ascension are 6* R5, 6* R4, 5* R5, 4* R5, and maybe 6* R3 and 5* R4 (for lower progress players). i would not recommend ascending other ranks.

Comments

  • HeattblasttHeattblastt Member Posts: 254 ★★
    Great work man.Have nothing to add but just want to bump thread so others can also see.
  • captain_rogerscaptain_rogers Member Posts: 9,505 ★★★★★
    But If 4* r5A champs scale equivalent to 5* r3, and 5* r5A champs scale equivalent to 6* r3, then it is logical to conclude that 6* r5A champs should scale equivalent to 7* r3 right? But it seems that it is equivalent to 7* r2. Why this anomaly? Does 7* champs base stats increase a lot between 7* r2 and 7* r3? Is this even intended? Why there is a huge difference between 6* r5A and 7* r3?

    If we consider the difference between 4* champs and a 5* champ at base level is x/y, I assume the difference between 5* champ and 6* champ will be the same x/y right? Then 6* champ and 7* champ will have the same x/y difference ratio is attack and health. So the pattern I mentioned in the above paragraph must stay true right? @DNA3000
  • G-Hun-GearG-Hun-Gear Member Posts: 1,447 ★★★★

    But If 4* r5A champs scale equivalent to 5* r3, and 5* r5A champs scale equivalent to 6* r3, then it is logical to conclude that 6* r5A champs should scale equivalent to 7* r3 right? But it seems that it is equivalent to 7* r2. Why this anomaly? Does 7* champs base stats increase a lot between 7* r2 and 7* r3? Is this even intended? Why there is a huge difference between 6* r5A and 7* r3?

    If we consider the difference between 4* champs and a 5* champ at base level is x/y, I assume the difference between 5* champ and 6* champ will be the same x/y right? Then 6* champ and 7* champ will have the same x/y difference ratio is attack and health. So the pattern I mentioned in the above paragraph must stay true right? @DNA3000

    If you look at the graphs, the jump from 7r1 to 7r2 is huge… about 25%, while the jump from 6r1 to 6r2 is smaller, about 18%… With that in mind, it makes sense that an ascended 6* doesn‘t keep up with a ranked 7* the same way that an ascended 5* keeps up with a ranked 6*…
  • peixemacacopeixemacaco Member Posts: 2,954 ★★★★

    I ascended some champs cause my dust was expiring.

    That's my pointless story in 1 sentence.

    This item don't expire...
  • G-Hun-GearG-Hun-Gear Member Posts: 1,447 ★★★★
    edited January 23

    I ascended some champs cause my dust was expiring.

    That's my pointless story in 1 sentence.

    This item don't expire...
    Really? Not even in the overflow?
  • MrSakuragiMrSakuragi Member Posts: 5,215 ★★★★★

    I ascended some champs cause my dust was expiring.

    That's my pointless story in 1 sentence.

    This item don't expire...
    Really? Not even in the overflow?
    It does expire. I can’t remember if it’s 30 or 14 days in overflow though.
  • ButtehrsButtehrs Member Posts: 5,925 ★★★★★

    I ascended some champs cause my dust was expiring.

    That's my pointless story in 1 sentence.

    This item don't expire...
    The ones in your overflow most certainly do expire.
  • peixemacacopeixemacaco Member Posts: 2,954 ★★★★

    My Inventory - Tier Dust 2 and 1
    No time to expire.

    ☝🏻👍
  • DjjendjeenDjjendjeen Member Posts: 55
    Do we know if ascending a 6*r4 then taking them to r5 later results in the same stats as ascending a 6*r5?
  • GrandOldKaiGrandOldKai Member Posts: 789 ★★★★

    Do we know if ascending a 6*r4 then taking them to r5 later results in the same stats as ascending a 6*r5?

    There is no reason it shouldn't.
  • peixemacacopeixemacaco Member Posts: 2,954 ★★★★


    My Inventory - Tier Dust 2 and 1
    No time to expire.

    ☝🏻👍

    Once you hit that cap and have some in overflow/stash it most certainly does expire. If you don’t use it as you get it, you’ll eventually have some in overflow and have to either use it or lose it.
    Thanks!

    I never had more dust than I got...
  • PikoluPikolu Member, Guardian Posts: 7,720 Guardian

    But If 4* r5A champs scale equivalent to 5* r3, and 5* r5A champs scale equivalent to 6* r3, then it is logical to conclude that 6* r5A champs should scale equivalent to 7* r3 right? But it seems that it is equivalent to 7* r2. Why this anomaly? Does 7* champs base stats increase a lot between 7* r2 and 7* r3? Is this even intended? Why there is a huge difference between 6* r5A and 7* r3?

    If we consider the difference between 4* champs and a 5* champ at base level is x/y, I assume the difference between 5* champ and 6* champ will be the same x/y right? Then 6* champ and 7* champ will have the same x/y difference ratio is attack and health. So the pattern I mentioned in the above paragraph must stay true right? @DNA3000

    A r5 4* is about equal to a r2 5* in power, so an ascension brings them up to the next power level which is r3 5*. Believe it or not, but a r5 6* is really almost just a r1 7* with the exception of sunspot where a r1 7* sunspot has higher stats across the board than the r5 6*. Because of that, ascending a 6 star brings it up to the next power level which is r2 7*
  • G-Hun-GearG-Hun-Gear Member Posts: 1,447 ★★★★
    Pikolu said:

    But If 4* r5A champs scale equivalent to 5* r3, and 5* r5A champs scale equivalent to 6* r3, then it is logical to conclude that 6* r5A champs should scale equivalent to 7* r3 right? But it seems that it is equivalent to 7* r2. Why this anomaly? Does 7* champs base stats increase a lot between 7* r2 and 7* r3? Is this even intended? Why there is a huge difference between 6* r5A and 7* r3?

    If we consider the difference between 4* champs and a 5* champ at base level is x/y, I assume the difference between 5* champ and 6* champ will be the same x/y right? Then 6* champ and 7* champ will have the same x/y difference ratio is attack and health. So the pattern I mentioned in the above paragraph must stay true right? @DNA3000

    A r5 4* is about equal to a r2 5* in power, so an ascension brings them up to the next power level which is r3 5*. Believe it or not, but a r5 6* is really almost just a r1 7* with the exception of sunspot where a r1 7* sunspot has higher stats across the board than the r5 6*. Because of that, ascending a 6 star brings it up to the next power level which is r2 7*
    Can confirm… 2 examples of 6r5 vs 7r1 (where I have the 7* at r1, but not the 6*, so I can show the r5 stats)






  • captain_rogerscaptain_rogers Member Posts: 9,505 ★★★★★

    Pikolu said:

    But If 4* r5A champs scale equivalent to 5* r3, and 5* r5A champs scale equivalent to 6* r3, then it is logical to conclude that 6* r5A champs should scale equivalent to 7* r3 right? But it seems that it is equivalent to 7* r2. Why this anomaly? Does 7* champs base stats increase a lot between 7* r2 and 7* r3? Is this even intended? Why there is a huge difference between 6* r5A and 7* r3?

    If we consider the difference between 4* champs and a 5* champ at base level is x/y, I assume the difference between 5* champ and 6* champ will be the same x/y right? Then 6* champ and 7* champ will have the same x/y difference ratio is attack and health. So the pattern I mentioned in the above paragraph must stay true right? @DNA3000

    A r5 4* is about equal to a r2 5* in power, so an ascension brings them up to the next power level which is r3 5*. Believe it or not, but a r5 6* is really almost just a r1 7* with the exception of sunspot where a r1 7* sunspot has higher stats across the board than the r5 6*. Because of that, ascending a 6 star brings it up to the next power level which is r2 7*
    Can confirm… 2 examples of 6r5 vs 7r1 (where I have the 7* at r1, but not the 6*, so I can show the r5 stats)






    The 6* stats are without any masteries applied, but yeah, it won't be a big difference between the 2.
  • G-Hun-GearG-Hun-Gear Member Posts: 1,447 ★★★★

    Pikolu said:

    But If 4* r5A champs scale equivalent to 5* r3, and 5* r5A champs scale equivalent to 6* r3, then it is logical to conclude that 6* r5A champs should scale equivalent to 7* r3 right? But it seems that it is equivalent to 7* r2. Why this anomaly? Does 7* champs base stats increase a lot between 7* r2 and 7* r3? Is this even intended? Why there is a huge difference between 6* r5A and 7* r3?

    If we consider the difference between 4* champs and a 5* champ at base level is x/y, I assume the difference between 5* champ and 6* champ will be the same x/y right? Then 6* champ and 7* champ will have the same x/y difference ratio is attack and health. So the pattern I mentioned in the above paragraph must stay true right? @DNA3000

    A r5 4* is about equal to a r2 5* in power, so an ascension brings them up to the next power level which is r3 5*. Believe it or not, but a r5 6* is really almost just a r1 7* with the exception of sunspot where a r1 7* sunspot has higher stats across the board than the r5 6*. Because of that, ascending a 6 star brings it up to the next power level which is r2 7*
    Can confirm… 2 examples of 6r5 vs 7r1 (where I have the 7* at r1, but not the 6*, so I can show the r5 stats)






    The 6* stats are without any masteries applied, but yeah, it won't be a big difference between the 2.
    True, but I don‘t run suicides, so the masteries only give about 1.7% attack increase… Substract that from the 7* stats and that’s about it…
  • DNA3000DNA3000 Member, Guardian Posts: 19,652 Guardian
    Pikolu said:

    But If 4* r5A champs scale equivalent to 5* r3, and 5* r5A champs scale equivalent to 6* r3, then it is logical to conclude that 6* r5A champs should scale equivalent to 7* r3 right? But it seems that it is equivalent to 7* r2. Why this anomaly? Does 7* champs base stats increase a lot between 7* r2 and 7* r3? Is this even intended? Why there is a huge difference between 6* r5A and 7* r3?

    If we consider the difference between 4* champs and a 5* champ at base level is x/y, I assume the difference between 5* champ and 6* champ will be the same x/y right? Then 6* champ and 7* champ will have the same x/y difference ratio is attack and health. So the pattern I mentioned in the above paragraph must stay true right? @DNA3000

    A r5 4* is about equal to a r2 5* in power, so an ascension brings them up to the next power level which is r3 5*. Believe it or not, but a r5 6* is really almost just a r1 7* with the exception of sunspot where a r1 7* sunspot has higher stats across the board than the r5 6*. Because of that, ascending a 6 star brings it up to the next power level which is r2 7*
    I have a vague recollection of there being a few champs that don't scale like everyone else, that was discussed when either 5* rarity was released or 6* rarity was released (or both times). Sunspot is definitely one of them. I picked what I thought was a representative champ for the vast majority of champs in Angela, and she does seem to be in the majority of scaling, with Sunspot as the rare outlier.

    Here's the power scaling for a set of champs. I've scaled all the numbers to be relative to 4* R3 = 1.0 to normalize the scaling values. I specifically tried to pick a wide range of champs across years of release and various prestige and attack emphasis:



    Sunspot diverges significantly from the rest. Here it is in graph form:



    Everyone pretty much overlaps each other, except Sunspot who diverges significantly from everyone else, especially at the jump from 6* to 7*.

    This is what the rarity ranks look like for Sunspot, in descending order, ranked by attack scaling:



    It is not a huge difference, about five percentage points of attack or so, but it is there.

    The fact that everyone lands almost exactly at 9.0 at 7* R3 suggests to me that at some point someone decided to do something about the irregular scaling, both for big outliers like Sunspot and small deviations in other champs, and tried to make 7* R3 the place where everyone ends at the same starting point (relatively speaking). Ascendancy may have had something to do with that.
  • MagrailothosMagrailothos Member Posts: 5,954 ★★★★★
    Fabulous assessment as always, DNA.


    My Inventory - Tier Dust 2 and 1
    No time to expire.

    ☝🏻👍

    Once you hit that cap and have some in overflow/stash it most certainly does expire. If you don’t use it as you get it, you’ll eventually have some in overflow and have to either use it or lose it.
    Thanks!

    I never had more dust than I got...
    My overflow, right now:

  • 4baigssss1begum4baigssss1begum Member Posts: 1
    I just ascended my 6* R2 antman future but I saw that it didn’t affect its pi much
    I know took him to R3 but still it didn’t seem to bring much change
    I’m worried if it’s stats will differ from the one ascended after taking to r3 or any other higher rank
    Does ascending at a lower rank differ from ascending at a higher one?
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