# Research:Mother Twinter's Yarrow Enchantment

## Corrections

The washboard with wringer attachment from Esme's house weighs 200 deben:

weigh washboard on scales
You slip one Djelian talon into the slot.
The scales indicate that the washboard with wringer attachment weighs two hundred deben.
You weigh the washboard with wringer attachment on the pair of weighing scales.
weigh washboard on scales
You slip one Djelian talon into the slot.
The scales indicate that the washboard with wringer attachment weighs two hundred deben.
You weigh the washboard with wringer attachment on the pair of weighing scales.
weigh washboard on scales
You slip one Djelian talon into the slot.
The scales indicate that the washboard with wringer attachment weighs two hundred deben.
You weigh the washboard with wringer attachment on the pair of weighing scales.
weigh washboard on scales
You slip one Djelian talon into the slot.
The scales indicate that the washboard with wringer attachment weighs two hundred deben.
You weigh the washboard with wringer attachment on the pair of weighing scales.

re scales
You read the pair of weighing scales:
Written in neat hieroglyphs in Djelian:
For the convenience of ignorant foreigners, it is known under the bubble of the Sky Goddess Nesh that two
"pounds" of sand weigh nine deben.

This makes the washboard weight 44 4/9 lb.

The maximum enchant capacity is therefore floor(2.25 * 44 4/9 + 5) = 105.

Unfortunately, this slightly alters the data below.

I'll try to fix those numbers.

This means changing the formula as well. The graph of the first table's ma.sp.mi vs max thaums gives me an equation of

y = 0.054866 * x + 21.0485
with a R² of 0.990563

Since the code probably uses integers, integer math and floor, the best fit with round numbers seems to be:

%enchantment = round( ma.sp.mi bonus / 20 + 21 , 2)
max thaums = floor( %enchantment * max enchantment / 100 )

Anyway all new errors are mine. The original version is in the history. --Frazyl 10:23, 28 April 2011 (UTC)

## Max enchantment level

### Skills dependencies

The following tests were performed on a washboard (weight: 44 4/9 lb, max enchantment: 105 thaums), in a room without any background enchantment.

ma.sp.mi bonus ma.me.ph.ev bonus ma.me.ph.en bonus ma.me.ph.ch bonus Max thaums reached %enchantment reached
230 203 207 232 34 32.4%
244 190 255 258 34 32.4%
253 197 266 266 35 33.3%
328 259 285 361 39 37.1%
344 267 293 371 40 38.1%

When graphed against %enchantment, one finds that:

• enchanting vs. %enchantment is not a straight line graph
• misc vs. %enchant is an exact straight line graph.

Specifically:

%enchantment = ma.sp.mi bonus / 20 + 21

It's reasonable to assume that this max %enchantment level is consistent for objects of all weights before rounding down, and this is confirmed by further testing. The following tests were all performed on on objects of varying weights, in rooms without background enchantment, with ma.sp.mi bonus of 328 (37.4% expected).

Object Weight Max enchantment 37.4% of max enchantment Max thaums reached
Washboard 44 4/9 lb 105 thaums 39.3 39 thaums
Medium wooden shield 13 3/9 lb 35 thaums 13.1 12 thaums
Flatiron 6 1/9 lb 18 thaums 6.7 6 thaums
Meat cleaver 1 7/9 lb 9 thaums 3.4 3 thaums

In each case, it can be seen that the max thaums reached is the expected value, after rounding down. Note that the rounding down effect is what leads to the common perception that lighter objects are harder to enchant - the lighter the object, the more of a percentage difference rounding down by up to one thaum makes; therefore, the more likely it is that the rounding down will cross one of the 10% boundaries that demarcate differences in visible enchantment levels.

To illustrate this, consider for example a player with a 220 ma.sp.mi bonus. They would by default be able to enchant to 32% of an object's maximum, a value that just about puts them in the 'steady but dull' range. If they tried this on a washboard, they would get 33.6 thaums, which is then rounded down to 33 - this is 31.43% and thus appears as 'steady but dull' as expected. If they then tried this on a meat cleaver, however, they would get 2.88 thaums, which is then rounded down to 2 thaums - this is 22.2%, so now appears as 'softly pulses'.

### Background enchantment effect

I have rather less data here, however, here are some results for enchanting a washboard in a variety of background enchantment levels:

Max thaums reached  %enchantment reached Background enchantment level
39 37.1% - 38.1% 0 thaums
42 40.0% - 41.0% 300 thaums
44 41.9% - 42.9% 500 thaums

If we assume that with a ma.sp.mi bonus of 328 the actual 'exact' %enchantment level at 0 thaums is 37.4%, as per the skills dependencies section above, then a reasonable theory here is that every 100 thaums of background enchantment adds 1% to your max %enchantment level reachable (giving 37.4%, 40.4% and 42.4% respectively for the levels in the table above, all of which fit in the ranges shown). If anyone can do some more research to confirm this, that would be very useful!

Note that a magic circle has a variable background enchantment level related to the witch's ma.sp.sp bonus, often approximately 300 thaums in magnitude. Thus, casting within a circle could be expected to improve the max enchantment level by about 3%.

There are more therefore more efficient ways than circles to improve enchanting - a fully charged thaum bomb releases 500 thaums [Frazyl: only up to 500 thaums in the room.], and rooms near the hub have significantly higher enchantment levels. Thus, it's probably more in a witch's interest to seek out these rooms than use a circle, if she's really trying to eke out the last few thaums. [Frazyl: But above 1000 thaums casting is dangerous.]

Of course, a difference of 3-5% isn't likely to make much difference to a light object, due to the rounding effect (see the skills dependencies section above); but for a heavier object, it may be more useful.

## Improvement per casting

This is a dependency that's much clearer. The following are the enchantment levels I observed (using a thaumometer), while enchanting the washboard up to 39 thaums, and later up to 42 and 44 thaums (using high background enchantment) respectively:

 First run 0 13 21 27 31 33 35 36 37 38 39 Second run 0 14 23 29 33 36 38 39 40 41 42 Third run 0 14 24 30 34 37 39 40 41 42 43 44

Note the diminishing returns effect - the closer the item's enchantment level to the final value, the less extra thaums each enchantment brings.

Looking closely at the above figures, there is in fact an exact and simple formula being applied:

• First, calculate the maximum thaums that the witch can reach, based on her skills and background enchantment (as per the max enchantment level section above).
• The increase in enchantment level for each enchant is then given by:
Increase(thaums) = [if cur enchantment < max thaums - 3]              : rounddown((max thaums - cur enchantment) / 3)
[if max thaums - 3 <= cur enchantment < max thaums]: 1
[otherwise]                                        : 0

--Chat 00:47, 12 December 2009 (UTC)

[I tried to fix the numbers with the correct washboard's weight. Hope it's right. --Frazyl 10:23, 28 April 2011 (UTC)]

## More data

This was mostly done while holding the washboard, which gave me -1 to dexterity because it's heavy. --Frazyl 21:58, 28 April 2011 (UTC)

misc
bonus
evoking
bonus
enchant
bonus
chanting
bonus
Max object enchanted (thaums/sec) Max object enchanted / enchant capacity (%) Thaums added to the locale (thaums) Average of thaumometer readings of the locale (thaums) In circle? Details
311 206 286 309 38 36.2% ~0 ~0 No I got 39 on the first go but it must have been a fluke cast.
311 206 286 309 45 42.9% ~10 ~350 Yes Some thaums from the yarrow spell castings themselves.
311 206 286 309 48 45.7% ~500 ~870 Yes Charged with a thaum shard of 500 thaums.
318 211 293 316 49 46.7% ~500 ~880 Yes Holding a charged Klein bottle (+2 int)
341 206 286 309 39 37.1% 0 0 No Increased ma.sp.mi
341 206 286 309 45 42.9% ~10 ~350 Yes Some thaums from the yarrow spell castings themselves.
341 206 286 309 49 46.7% ~500 ~870 Yes Charged with a thaum shard of 500 thaums.
349 211 293 316 50 47.6% ~500 ~880 Yes Holding a charged Klein bottle (+2 int)
441 223 339 339 44 41.9% 12 24 No
466 233 353 353 45 42.9% 14 25 No
466 233 353 353 50 47.6% 5 426 Yes
466 233 353 353 54 51.4% 10 858 Yes
533 239 359 359 9 47.3684% 12 473 No Casting on a two-handed sword

I have stuff to add, but I don't understand where or how to put in the info :( What is a circle effect? Max thaums looks like it is for thaums added to the object, so what is "thaums added" supposed to be for? --Kartoffel 05:52, 17 June 2011 (UTC)

The max thaums reached is how many thaums per second the item radiates when you stop trying to enchant it after many attempts.
The thaums added means how many thaums you added in the room or in the circle, I guess environment thaums might be clearer? Basically outside a circle it's what the thaumometer tells me and inside a circle it's an estimate of how many thaums I've released by casting spells or smashing a 500 thaums shard.
In parenthesis is the average of thaumometer readings inside the circle which adds to the thaums you released a fluctuating amount.
I'll rename a couple of the columns so it's clearer. --Frazyl 07:34, 17 June 2011 (UTC)

Great, that makes a bit more sense. Maybe object enchant and room enchant might be better names? --Kartoffel 13:42, 17 June 2011 (UTC)

Well saying room could be confusing because it's meant to be the place where you enchant and if in a circle you don't want the room outside the circle you want the thaums added to the circle and in the next column how it's reported on average inside the circle. Of course the inside of the circle is also a room but when the room is mentioned it's usually to refer to outside the circle. --Frazyl 19:36, 17 June 2011 (UTC)