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Let's Investigate: The Ring of the Erudite!

  • Member
    April 23, 2014


    UPDATE 5/24: James has dropped in and explained definitively how the Ring of the Erudite works. His explanation renders the rest of this post quite obsolete, so I highly suggest you go read it directly from the horse's mouth by clicking here. Thanks, James -- you nailed it!

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    I don't have access to the Creation Kit or command console, but I thought I'd try my hand at exploring something that I can test -- at least to some degree. If there's interest, I can try to turn this into a regular segment. I have a couple ideas for other things to investigate next....

    So, most of us know that the Ring of the Erudite buffs Magicka Regen by a noticeable margin. Ponty once reported that the ring multiplies effective Magicka Regen (i.e., actual Magicka restored per second) by 5/3, but I don't know whether his test was exhaustive. And no one has ever confirmed his findings to my knowledge. So I decided to give it a shot.

    This is going to be a detailed account of my testing, with a fair bit of math and deduction. If that doesn't interest you, feel free to skip on down to my conclusions at the end of the post.

    My initial testing setup was with the base 100 Magicka, and no active forms of Magicka Regen to conflict with the Ring. I did three tests where I'd drink a custom potion of +100 Magicka to simulate the +100 Magicka on the Ring of the Erudite, and then cast two Revenant spells simultaneously. This left me with net 64 Magicka. It took an average of 22.89 seconds for that to fully recharge (+5.94 Magicka per second). I will use this same process as a control in all future rounds of testing.

    I then did three more tests where I did NOT drink the potion, but did wear the Ring of the Erudite. Again, dual Revenant took me from 200 down to 64 Magicka. In this case, the average time was 13.73 seconds to fully recharge (+9.91 Magicka per second).

    9.91 ÷ 5.94 = 1.67

    So far, this verifies Ponty's findings. Accounting for variations due to rounding error and human error, we're pretty much right in line with +66.7 Magicka Regen.

    Next, I decided to test with active Magicka Regen from a second source: the Apprentice Stone. I ran the same tests with the Apprentice active for +100% Magicka Regen. My results were as follows...

    • Without Ring of the Erudite: 11.73 seconds to fill (+11.59 Magicka per second)
    • With Ring of the Erudite: 7.24 seconds to fill (+18.79 Magicka per second)

    18.79 ÷ 11.59 = 1.62

    This time, it's a little harder to be certain whether it's multiplying the effective Magicka Regen rate by 5/3 or not -- rounding error and human error both could have made +66.7% look like +62.1%.

    So I ran another series of tests, this time with the Apprentice stone and a custom Magicka Regen potion @ 125% magnitude. I also threw in a Circlet of Extreme Magicka to see if a higher base Magicka pool might have any effect. So my base Magicka at this point was 150 -- (250 after accounting for the potion or ring) -- and my base Magicka Regen was +225%. My results...

    • Without Ring of the Erudite: 6.24 seconds to fill (+21.79 Magicka per second)
    • With Ring of the Erudite: 4.06 seconds to fill (+33.50 Magicka per second)

    33.50 ÷ 21.79 = 1.54

    At this point, I don't think we can reasonably write off this difference to human error or rounding error. So after running this last round of tests, I conclude that the Ring of the Erudite does NOT multiply your effective Magicka Regen by a static 5/3.

    The really interesting thing is that it does't appear to be a static percentile addition either. With +225% base Magicka Regen, a flat +66.7% effect would not have made such a noticeable difference.... I'm not enough of a math wizard to figure out exactly what the effect may be. But I can conclude that it's neither a static +x% to Magicka Regen, nor is it a static ×5/3 to whatever your Magicka Regen was prior to applying the ring. It's something else entirely -- something that I don't know how to identify.

    Also of note: I tried several times equipping the ring after that Magicka Regen potion, and several times before the potion. The Magicka Regen rate added by the ring seemed unaffected by that order.

    I decided at this point to run one final series of tests, with the Apprentice stone, the Blessing of Julianos, and that Circlet of Extreme Magicka from the previous test -- but without the Magicka Regen potion. So now my base Magicka was 175, and my base Regen was +100%. My hope here was that the same effective +62.1% from Test #2 would carry over. If so, I could determine that the size of your Magicka pool does not affect the Magicka Regen rate added by the Ring of the Erudite. Results...

    • Without Ring of the Erudite: 9.78 seconds to fill (+13.91 Magicka per second)
    • With Ring of the Erudite: 6.00 seconds to fill (+22.67 Magicka per second)

     

    22.67 ÷ 13.91 = 1.63

    In this case, the difference between Test #4 and Test #2 was negligible -- less than 0.01 after accounting for rounding. Throw in variations due to rounding error and human error, and I think it's safe to conclude that the rate is the same. Magicka pool size has no impact on the percentile Magicka Regen rate: With 100 Magicka vs. 175 Magicka, the ring effectively provides the same boost.

    Phew!

    Alright, with all that in mind, here are my conclusions:

    1. As Magicka increases, the impact of the percentile Magicka Regen added by the Ring of the Erudite is unchanged.
    2. As Magicka Regen increases, the impact of the percentile Magicka Regen added by the Ring of the Erudite decreases.

    • With no other buffs or debuffs to Magicka Regen, the Ring of the Erudite augments effective Magicka Regen by roughly 67%.
    • With +100% Magicka Regen (prior to the Ring of the Erudite), the ring augments effective Magicka Regen by roughly 62.5%.
    • With +225% Magicka Regen (prior to the Ring of the Erudite), the ring augments effective Magicka Regen by roughly 54%.
    • With +350% Magicka Regen (prior to the Ring of the Erudite), the ring augments effective Magicka Regen by roughly 52% [see comment below].
    • With -50% Magicka Regen (prior to the Ring of the Erudite), the ring augments effective Magicka Regen by roughly 64% [see comment below].

    Final note for clarity: By "effective Magicka Regen", I mean actual Magicka points restored per second. In all other cases where I don't explicitly use the word effective, I am talking about the Magicka Regen rate expressed as a percentile, e.g., +100% from the Apprentice stone.

    If there's any interest, I can run a test with even more Regen -- e.g., that +125% potion, the Apprentice stone, and Expert Robes = +350% Magicka Regen (before the ring).... For now though, I'm going to call this one. Hope this was of use to someone! Went ahead and ran this test, along with one other. See comments below for details.

  • Member
    April 23, 2014

    Ah, I was too curious to sit on that last test.

    Used the components listed there -- +125% potion, Expert robes, and the Apprentice. Total +350% before equipping the Ring of the Erudite. I ditched the Circlet of Extreme Magicka and the Blessing of Julianos, figuring that less effective Magicka regen per second would allow for more accuracy. Findings...

    • Without Ring of the Erudite: 5.65 seconds to fill (+24.07 Magicka per second)
    • With Ring of the Erudite: 3.71 seconds to fill (+36.66 Magicka per second)

    36.66 ÷ 24.07 = 1.52

    Interesting ... that's barely worse than the Test #3 where I had +225% regen. Which suggests either my margin of error is worse than I thought, or else there's just no linearity to this. I really have no clue how to nail down the true effect; I might have to try it out with the Atronach and see how stunted regen figures into the equation. May give that a look tomorrow....

    For now, I think we can basically leave it at:

    With no additional regen, the Ring of the Erudite increases cumulative ("effective") Magicka Regen by roughly 68%. As you add additional regen effects, the Ring of the Erudite's cumulative ("effective") increase to Magicka Regen approaches 50%.

    If you really maximize your Magicka and Magicka Regen together with the Ring of the Erudite, you can get to a point where you're recovering 100 Magicka per second -- with the gear used in that last test, it takes less than 5.5 seconds to completely refill your Magicka from an empty state!

    Who needs cost reduction, right? 

  • Member
    April 23, 2014

    Alright, got too curious again. 

    This test was with the Atronach stone and no other effects on Magicka Regen, for -50% Magicka Regen (prior to equipping the Ring of the Erudite).

    • Without the Ring of the Erudite: 36.57 seconds to fill (+3.72 Magicka per second)
    • With Ring of the Erudite: 22.27 seconds to fill (+6.11 Magicka per second)

    6.11 ÷ 3.72 = 1.64

    So actually a tad worse than the percentile buff with no Regen. Honestly, if any math experts can chime in and try to plot this cure or something.... Because it makes no sense to me!

    Ah well, if nothing else, this gives a pretty good indicator of the range of aid that the ring can grant depending on your other Magic Regen effects.

  • Member
    April 23, 2014

    I looked in Creation Kit and here is what I found (screenshot below). This is a comparison between magicka regen of the Ring of the Erudite (top window) and that of the Expert Robes of Destruction (bottom window). I'm not sure what to make of it, one theory is that the name "AbFortifyMagickaRate" implies "absolute" meaning it's essentially x2 multiplier. However it may work of base regen only, unaffected by any other magicka regen bonuses...

  • Member
    April 23, 2014

    Thanks Vaz, interesting. As my tests show, it's not doing x2 in practice, from the base regen (Test #1) nor from the cumulative effective regen (Tests #2-6). But that CK effect indicates that it's probably multiplying something by x2....

    If you have a chance to check, could you confirm whether the Apprentice stone also uses the FortifyMagickaRateConstant (I assume that's what that last word is there)? Just curious because the in-game description says that it doubles regen, not that it adds +100% regen. If that one is also using an "AbFortifyMagickaRate" effect, then it could explain some of my test results. I may need to do another test where I'm using a stone other than the Atronach OR the Apprentice....

  • Member
    April 23, 2014

    Good thinking, I'll see what I can dig up 

  • Member
    May 23, 2014

    Happy to see this awesome theorycrafting, sad to see it stopped so abruptly.  Hopefully I can shed some light on this subject.

    To understand what the 'Ring of the Erudite' does you first need to understand that your character has things called 'Actor Values'.  These values are quite extensive and are the building blocks for the calculations that the game engine is doing underneath the hood while you run around punching mudcrabs...as one is wont to do.  I'm going to try and do this all off the top of my head so there very well might be something incorrect said, hopefully nothing too terrible. 

    The two important AV's that we are interested in for this discussion are the following:

    1. MagickaRate
    2. MagickaRateMult

    MagickaRate:

    This is your character's BASE rate of magicka regeneration as a percentage.  In turn your character has two BASE rates, one for when you are out of combat and one within.  The BASE rate outside of combat is 3.00% and while beheading Nazeem for mouthing off (AKA in combat) your BASE is 0.99%.

    MagickaRateMult:

    This is an additional multiplier that is applied to your character's MagickaRate.  When you are crouching in the corner of Ysolda's bedroom at night, while naked, your character's BASE MagickaRateMult is 100.0%.  When your shame overtakes you and you silently slip on your crusty college robes that have the enchantment description "Magicka regenerates 50% faster" your new MagickaRateMult becomes 150.0% (an increase of 50%). 

    The 'Ring of the Erudite' has a unique enchantment (as you can see in the pictures Vazgen posted) that actually modifies the MagickaRate AV.  From what I remember, this +2 magnitude to the 'AbFortifyMagickaRate' actually bumps your characters BASE MagickaRate to a ridiculous 5.00% outside of combat and 2.99% while engaged.  I remind you that this value is the overall % of your magicka, per second, that you recover under these circumstances.

    So let's look at a brief example to help clarify things.

    100 BASE magicka, no Regeneration enchantments:

    Outside of combat you recover 3% of your total magicka per second, a total of 3 magicka per second.  If you were to cast a spell that costs 60 magicka, you will be back up to full after 20 seconds of regenerating.

    200 BASE magicka, no Regeneration enchantments:

    Outside of combat you recover 3% of your total magicka per second, a total of 6 magicka per second.  If you were to cast a spell that costs 60 magicka, you will be back up to full after 10 seconds of regenerating.

    CONCLUSION: The higher you base Magicka pool, the more you'll regenerate (total) per second since the regeneration % remains a constant value.  3% of 200 magicka is more than 3% of 100 magicka.  Very straight forward!

    When we start modifying the MagickaRateMult AV things start getting more interesting.  If the character in the above scenario has a BASE magicka pool of 200 and is outside of combat we now know he'll regen 6 magicka per second.  If he now puts on robes that boost magicka regeneration by 100% (eg. Adept Robes) we now must multiply the BASE MagickaRate by our new MagickaRateMult so our character now has a regeneration rate of 6% of the total magicka pool when outside of combat and 1.98% while fighting.  When we have a badass mage who is rocking 400% magicka regeneration what we really have is a character that regens 12% off his pool outside combat and 3.96% inside.

    A mage with enchantments giving him 400% magicka regeneration and a magicka pool of 500 will be regenerating a massive 19.8 magicka per second while fighting!

    So what does this all have to do with this smelly vampire ring?!?

    While wearing the 'Ring of the Erudite' your character now has a new BASE MagickaRate of 2.99% while in combat (original 0.99% plus the 2 from the enchantment).  If we also wear standard magicka regen robes we boost this new 2.99% in the same way as before; a mage with 400% regen will now be able to regen 11.96% of their total magicka pool per second while in combat.  If we take the previous example of a 500 magicka pool our badass wizard can generate almost 60 magicka per second. 

    If we look at your original numbers we can see this in action perfectly:

    My initial testing setup was with the base 100 Magicka, and no active forms of Magicka Regen to conflict with the Ring. I did three tests where I'd drink a custom potion of +100 Magicka to simulate the +100 Magicka on the Ring of the Erudite, and then cast two Revenant spells simultaneously. This left me with net 64 Magicka. It took an average of 22.89 seconds for that to fully recharge (+5.94 Magicka per second). I will use this same process as a control in all future rounds of testing

    You're regenerating 3% of your total magicka pool per second giving you 6 magicka per second thus it should take roughly 22.6 seconds to fully regen.

    I then did three more tests where I did NOT drink the potion, but did wear the Ring of the Erudite. Again, dual Revenant took me from 200 down to 64 Magicka. In this case, the average time was 13.73 seconds to fully recharge (+9.91 Magicka per second).

    You're now regenerating 5% of your total magicka pool per second (base 3% plus 2 from the ring) giving you 10 magicka per second thus it should take roughly 13.6 seconds to fully regen.

    I think the confusion was coming from the calculations involving multiple variables being multiplied together rather than only one which is why it seemed to be changing.  This was all from memory so I hope I covered everything.  This site needs more brain storming and experimentation so I'd absolutely love to see you (or someone else) start up another discussion!

    -James

    P.S.

    Did anyone here miss my pedantic prose?

    P.P.S.

    I resisted the urge for far too long.  MagickaRate.  MagicKARATE.  MAGIC KARATE!!!

  • Member
    May 23, 2014

    Ah, the inability to like comments on Ning...  James, you're awesome! 

  • Member
    May 23, 2014

    My mom says I'm specul

  • Member
    May 24, 2014

    I would absolutely LOVE this to be a regular segment.