Let's figure out scroll infusion lifetimes

[Goat]

I read something interesting on Krakiipedia recently, added by Drafix in March. I quote:


Scrolls have intrinsic silver value, as shown by appraising them at the pawnshop.
Invoking a scroll reduces the value, quick research shows approximately every 1 mana invoked, 10 silvers of value is lost.
Infusing a scroll with near 0 value will almost certainly lock the scroll.
Scrolls with high cost spells start with a higher intrinsic value.
Infusing a scroll may reduce its intrinsic value (requires testing to verify)


I have done some testing recently to expand on this. Early findings:

Both invoking and infusing lowers a scroll's pawnshop value. The value drop for invoking is constant on a per-charge-infused basis, and also constant on a per-invoke basis. Or rather, almost constant. It can go +/- 1. I presume there are several opportunities for rounding to cause the +/-:


Function that translates remaining scroll lifetime to base value
Function that translates base value to base pawn offer
Function that translates base pawn offer to trading/inf/race-adjusted pawn offer


I believe you can infuse "past" 0 on your final infuse. That is, if you have a scroll with a pawn value of 1, it has one charge of 303 on it, and it's unlocked for 10 charges. I think you can infuse up to 10 on that last attempt, if you would normally be able to do so in one shot. Then it'll lock after that one try, whether you got one charge in or ten.

Since both invoking and infusing reduce value, but you can continue to invoke after reaching 0 value, you figure to get slightly more overall use out of your scrolls by keeping them close to fully charged. That way, you get a full scroll's worth of 'free' invokes, which never counted against your scroll's value. You have to balance this against the fact that it is harder to infuse an almost-full scroll than an almost-empty scroll - you're more likely to lock the almost-full one if you're not comfortably trained to infuse it.

Scrolls do lock when their pawn value hits 0. This can happen whether you are infusing or invoking. You only get messaging telling you about the lock if it came while infusing. If it happens from invoking, you won't get any unusual messaging.

I have observed infuse costs from .8 per mana infused (115) and 1 per mana infused (105) to 7.9 per mana infused (215). Yes, the cost is NOT fixed per spell level; it depends on the spell.
Invoke costs seem to be pretty steady at right around 3 per mana invoked (I suspect it's exactly 3 when all the rounding errors and trading bonus are accounted for).


Some preconditions to note:

I check pawn value at FWI, so should have no racial modifier.
Between INF and trading skill, I have a 4% trading bonus.


It seems possible to build a catalog of every spell, and what it's infuse cost is. From that, we could build a script that appraises your scroll, takes into account town, race, trading skill, inf, and tells you how many of each spell you'll be able to infuse/invoke over its lifetime. It won't be perfect, because you may invoke a bit more than you infuse, but it'll be very close otherwise.

So if you're inclined, infuse a scroll, note what you infused and how many charges, figure out the cost per change, and post here. Note your race, town where you get your pawnshop quote, INF bonus, and trading skill. Bonus points for doing the path and figuring out what the base value is, before taking into account race/town/inf/trading, based on http://www.krakiipedia.org/wiki/Trading. The trick will be verifying that a given spell always costs the same to infuse across different scrolls.

Also consider confirming all of the other claims I've made here, especially the 3 per mana invoked cost.

[Ceyrin]

One of the things I always assumed (but never confirmed) was that invocation was a consistent drain on the silver value of the scroll. While the infusion 'drain' is probably based on a number of factors that likely included the level of the spell, the rarity of the spell (things like heroism for example likely have an extra multiplier), and how far outside the circles of magic it is in relation to the sorcerer and potentially the relation this has to the mana training the sorcerer has.

I can't log in to help you figure this out, but good luck. I expect this will require substantial data mining.

[Goat]

I'm slowly working on checking infusion costs on everything, but in the mean time, here are infusion costs for most things that a sorcerer would care about in practice. I will come back and edit some of the very relevant missing stuff (e.g. 313, 618), but I'll just publish a different set of tables entirely if I ever get a really comprehensive list.

These costs are relative to a dark elf with no trading at the FWI pawnshop, no FWI citizenship. (Which should be a 0% trading modifier)

Note that in all observed cases, the invoke cost for a spell is its spell level * 2.83, though I haven't tested that on every single spell listed. There's an exception, though - when you invoke the last charge on a scroll, apparently it doesn't reduce the scroll's value at all. It appears to be a "free" invoke.

For infuse costs, there is pretty much always some kind of rounding error involved, but it amounts to an error of less than 1 silver per infused charge.

I haven't included data for useless (e.g. 502) or less popular (e.g. 901) scrolls. However, with those included, it's pretty clear to me that infusion was designed such the higher level scrolls generally take more value to work with, BUT there's also a significant component built in so that "better" scrolls cost more, separate from the level consideration. Broadly speaking, it does little damage to your scroll's lifetime to unlock a low-level, crappy spell for 20 charges rather than unlocking it for 5 to minimize to infusing you do with it.

If you want to know a scroll's approximate lifetime: Go to the pawnshop and appraise it. Assuming you're only interested in one spell on it, divide the pawn value by the third column for that spell (infuse+invoke cost). That is roughly how many charges you'll be able to put into it beyond what it started with. I may write a script someday to get something closer to exact (e.g. taking your trading modifier into account), but it will always depend a bit on how you use it (e.g. it is better to keep it closer to fully charged, since you can keep invoking after you can no longer infuse, but it's also 'free' to invoke the last charge currently on the scroll).

Spell|Infuse cost|Infuse+Invoke cost
202 | 8.25 | 13.91
207 | 14.3 | 34.11
211 | 38 | 30.8
215 | 114 | 156.45
219 | 57 | 110.77
303 | 14.75 | 23.24
304 | |
307 | 17.14 | 36.95
310 | 32.35 | 60.55
313 | |
315 | 22.66 | 65.11
318 | 236 | 286.94
503 | 9 | 17.49
507 | 14.14 | 33.95
508 | 38.33 | 60.97
509 | 24.6 | 50.07
511 | 18.5 | 49.63
513 | 21.25 | 58.04
601 | 3.85 | 6.68
602 | 9.8 | 15.46
603 | |
604 | |
606 | 31.28 | 48.26
613 | 26 | 62.79
618 | 39 | 89.94
905 | 14.25 | 28.4
913 | 34.14 | 70.93
1119 | 34.2 | 87.97
1204 | 8.5 | 19.82
1208 | |
1215 | |
1601 | 8.5 | 11.33
1605 | 14.2 | 28.35
1617 | 52.58 | 100.39
1701 | 3.75 | 6.58
1708 | 11 | 33.64
1711 | 34.33 | 65.46
1712 | 14.8 | 48.76
1720 |

[Allereli]

I think pawnshop values are seriously flawed

[Fallen]

I think pawnshop values are seriously flawed

I definitely agree it's a tricky system to use to figure out the exact worth of scrolls using this process. Attempts have been made in the past, but I can't speak to the reliability of the data generated.

[Goat]

I think pawnshop values are seriously flawed

I welcome any counter-examples you can find. Everything has been consistent for me so far, and compares well to Nindon's earlier work (he shared a spreadsheet with me), suggesting it is consistent from sorcerer to sorcerer.

[Allereli]

I think the only thing that would be accurate is a bard loresong, ironically. But I have zero patience to do testing of this sort, have at it.

[Goat]

> I think the only thing that would be accurate is a bard loresong, ironically.
I expect pawn value on a scroll is an exact, consistent fraction of loresong value. As long as that holds, the only error introduced by using pawn value is rounding error, which I mentioned up top and will never be off by more than a full silver per infusion in terms of pawn value.

If it's just that you prefer to go with your intuition and (admittedly substantial) anecdotal experience about how these things work rather than relying on my data, I guess it's one of those "agree to disagree" things.

[Allereli]

I definitely agree it's a tricky system to use to figure out the exact worth of scrolls using this process. Attempts have been made in the past, but I can't speak to the reliability of the data generated.

if Fallen says it, it is true.

[Goat]

I did a fixskill which included dropping to 24 ranks EMC and SMC. Findings:


1711 costs 13 mana to infuse a charge instead of 11, but 511 still costs 11 per charge.
Late edit: 1215 costs 25 mana per charge.
The increased per-charge mana cost does not impact the pawn value drop per charge infused - so low mana controls do not impact your scroll's lifetime.
It may be possible to determine precise relative scroll difficulty by reducing EMC/SMC further and seeing which spells have which penalties for mana used per charge. I have no plans to pursue this myself.

[Fallen]

Glad you're still plugging away at this, Goat.


However, with those included, it's pretty clear to me that infusion was designed such the higher level scrolls generally take more value to work with, BUT there's also a significant component built in so that "better" scrolls cost more, separate from the level consideration.

I don't have them saved, but the GMs at the time mentioned the order would be Defensive > Utility > Offensive. One has to wonder what leeway they have to set a spell's worth based off of their subjective opinion of it, versus values based off of some sort of standardized weighted formula.

I'm not great with numbers, but it would be interesting once you have all of your data if you could find a way to graph it so that you could predict a spell's value by comparing it to all the others. From there, you could see if there is any rhyme or reason to the "penalty" to good spells, and see if there is a system in place there too.

[Goat]

I don't have them saved, but the GMs at the time mentioned the order would be Defensive > Utility > Offensive.
Neat, I never knew a GM said that explicitly. That seems roughly accurate when we limit the "offensive" bucket to one-time casts. Persistent offensive buffs have similar, or maybe somewhat higher, costs compared to defensive ones. A maybe more useful heuristic is "long-lasting buff > one-time cast".


I'm not great with numbers, but it would be interesting once you have all of your data if you could find a way to graph it so that you could predict a spell's value by comparing it to all the others. From there, you could see if there is any rhyme or reason to the "penalty" to good spells, and see if there is a system in place there too.

Interesting idea, but I don't know that I'll ever gather a full enough set of data. I have scrolls on me to gather costs for almost all of the remaining (IMO) useful spells, but I may never get to the others.

We can get some idea about design leeway by taking a look the known costs, e.g. 318 vs 219 and 1119. We hypothesize that utility will be less expensive than defense, but an infuse+invoke drains nearly 3x as much value as 219, and more than 3x value of 1119. Of course, we can also expect 318 to be an outlier based on the fact that it is deemed too valuable to show up on scrolls any more. 215 vs 1119/219 is also interesting, as they all appear in the modern treasure hopper. Heroism is ~80% more expensive that 1119 and ~40% more expensive than 219.

[Rheisia]

I can't find the quote for you now (it was from years ago), but the GMs have previously confirmed that the more valuable spells like 215/211/etc DO in fact drain more quickly. So there is a modifier there. Like Fallen, I also recall hearing that the general order of cost was Defense > Utility > Offense. Though this was years ago when the spell was first released.

And Goat is correct that it doesn't matter how quirky the pawnshop values are- as long as they are consistent for the same item and the same person, then the results are valid. Goat is testing the draining effect, not the original value of the scroll.

Goat- this is fantastic work you're doing here. We definitely need more sorcerers to test the same spells with similar stats. The mana control issue is one I hadn't really considered before (even though it's listed as a factor, I always assumed it was based on whether or not you had 24 ranks) One thing that I've learned over the years- GMs do a lot to throw players off. As in, they add lots of randomness inside of an overall consistent process to make it harder to determine exactly how it works. And no GM did that more...thoroughly...than Nilven.

[Goat]

Goat- this is fantastic work you're doing here. We definitely need more sorcerers to test the same spells with similar stats.

Thanks. For what it's worth, Nindon shared his spreadsheet with me from when he started down the same path. I have only spot-checked mine vs his, but I have yet to find a discrepancy.