Alternate enchantment system - brainstorming

[mlangsdorf]

I expanded your table with a rough estimate of the number of aborts caused by critical failures:

Average Days to enchant a 500 energy "baseline item", counting crit successes:

Skill	MoS	Success   Aborts(MoS)  Aborts(Success)
12	30	34           45%                  50%
13	28	30           43%                  43% 
14	27	27           42%                  42% 
15	25	25           40%                  40%
16	22	23           10%                  11%
17	21	23	      10%                  11% 
18	20	23            9%                   11%
19	19	23            9%                   11%
20	19	23            9%                   11%

Curse you, iterative probability!

The sharp knee in the failure rates at skill 16 is caused by the fact that a roll of 17 is no longer a critical failure. It's a bit unsightly to me. I'd recommend saying that a critical failure losers half the accumulated energy, and only a roll of a natural 18 aborts the project.

High skill enchanters will still add a lot of value, especially on large projects, but even a skill 12 enchanter has an 80+% chance of successfully completing a baseline project.

You get a more sensible situation where a low skill enchanter can expect to perform short, simple projects (80% of the projects under 250 energy come in on time) but can't even expect to attempt really big projects (less than a 25% success rate on 1000 energy projects). If the knight wants a really powerful sword, he'll need to quest for a skill-20 enchanter who can be expected to complete it.

[Bruno]

Interesting bit of trivial - Assuming 50% chance of at least one critical failure is the threshold for unacceptable risk of early project termination and time wastage (arbitrary figure), a skill 6-16 caster can go 37 iterations, and a skill 17+ caster can go 139 iterations.

On a 100-per-success cycle on the Success Based system, that's a rough cap of ~2770 energy for Skill 12 mage (whether cycles are weekly, fortnightly, or monthly, he's not going to be able to pull of a bigger enchantment than that with any sort of predictability). For skill 15 guy that's 3700, and for skill 20 guy that's a staggering ~14,950 energy.

Breaking cycles down to smaller units of energy for a per-diem system seriously throttles maximum enchantments. On Success Based on a per-cycle of 20, those caps are ~455, 740, and 2990 energy for skills 12, 15, and 20. Cycles that small start pushing minimum enchantment skill back up into very high ranges again; too much rolling, too much risk of a critical failure.

You can tinker with the acceptable risk threshold of course, but either way chance of critical failure is going to be a cap on your enchantment sizes.

This is of course the entire control on the Monster Hunters ritual magic system, and what's stopping an individual witch from immolating the planet with just a pocket full of NoDoze. Same issue here.

NINJAD in my own thread! Oh the humanity

[Bruno]

Originally Posted by mlangsdorf

High skill enchanters will still add a lot of value, especially on large projects, but even a skill 12 enchanter has an 80+% chance of successfully completing a baseline project.

If your risk tolerance is at the 80%-on-time mark, instead of 50% on time, then you can go on average 12 cycles with a skill 6-16 mage (on my system), 45 cycles on a 17+. You could get the reference mage (skill 12) to complete the reference project (500 energy) on time within that tolerance if each cycle is 42 energy or higher (in fact up to 894 energy on average if it's the 100-per-cycle system). Which still has the same sharp "knee" of effect of course.

Don't ask me how Luck impacts these numbers, I flat out refuse.

EDIT: The benefit of going with higher energy per cycle instead of tinkering with failure conditions is that you get the reference project coming in on time a useful percentage of the time, without having a zillion dice rolls ;) This also greatly reduces the chance of quirks on the final result. This may or may not be desirable.

I'm not sure how to calculate percentage of reference projects quirked. Hrm.

[Anthony]

Originally Posted by Bruno

I'm not sure how to calculate percentage of reference projects quirked. Hrm.

If you use my method (which requires a modified skill of 15), and remember that ritual magic always fails on 16 and crit fails on 17, you can simply use a lookup table for quirk rates on powerstones, it's going to be the same.

[Kuroshima]

Originally Posted by Bruno

I'm not sure how to calculate percentage of reference projects quirked. Hrm.

Write a damn script, and explore all the probabilities!

Now seriously, for the number of quirks, you can go with a binomial distribution. There are many calculators online for this.

[Anthony]

Originally Posted by Kuroshima

Write a damn script, and explore all the probabilities!

Now seriously, for the number of quirks, you can go with a binomial distribution. There are many calculators online for this.

It's not actually a binomial, because a failed roll not only adds a quirk, it doesn't make any progress, and thus you can in theory get an infinite number of quirks out of a single roll.

[Kuroshima]

Originally Posted by Anthony

It's not actually a binomial, because a failed roll not only adds a quirk, it doesn't make any progress, and thus you can in theory get an infinite number of quirks out of a single roll.

I know, but for large enough projects, it's a good approximation.

[Bruno]

So I made a script. 10,000 cycles each.

Reference wizard (skill 12), reference enchantment (500 energy), simple success scheme, regular crit-fail zots the enchantment.

100 energy per cycle - 88% success rate, taking 6.182 cycles, 0.374 quirks.
20 energy per cycle - 54% success rate, taking 24.366 cycles, 1.4136 quirks.

If we use mlangsdorf's "kind and gentle" crit-failures, which just "dump" half the current energy tally and count as a failure towards quirking, and the enchantment is only zotted on a natural 18, then the reference wizard with the reference tally has the following:

100 energy per cycle - 97% success rate, taking 6.660 cycles, 0.444 quirks
20 energy per cycle - 85% success rate, taking 34.035 cycles, 2.273 quirks.

So the Kind And Gentle failures significantly improve success rates, in exchange for taking longer (all those 'recovered' failures are big setbacks in progress) and more quirks (taking longer makes more chances for quirks).

Comparing at skill 15, reference enchant, harsh critfails

100 energy per cycle - 91% success rate, taking 4.875 cycles, 0.007 quirks.
20 energy per cycle - 65% success rate, taking 19.000 cycles, 0.024 quirks.

Quirks are clearly a problem for 'lesser mages'.

And again, at skill 15, reference enchant, kind-and-gentle critfails

100 energy per cycle - 98% success rate, taking 5.180 cycles, 0.012 quirks.
20 energy per cycle - 88% success rate, taking 26.29 cycles, 0.051 quirks.

Even with Kind and Gentle allowing longer attempts, quirks are still a problem for lesser mages.

One of the issues I have with Kind and Gentle failure is that the risk of rolling for your enchantments is even further reduced. I'm not sure I want it that routine... With big-energy cycle there's just not a lot of rolling going on, so I'm not sure it's worth it. With small-energy cycles there's just too much rolling unless you plan on resolving it all with a macro.

I'm obviously fine with resolving it with a macro but I've got players who like rolling the dice themselves (if not required to roll 26 times to resolve one action ;) ).

[Bruno]

As a side note, the Kind and Gentle crititcal failures remove the "knee" and replace it with a nice flat line :)