Trader gem selling bonus

The Trader bonus is used to increase the coin gained from when the Trader personally sells gems or skins, whether individually or in open, closed, or tied gem pouches or bundles. This bonus is based upon a Trader's Charisma, as well as their Trading and Appraisal skill.

When a Trader unlocks the ability depends on that stat and skills, there's no set or minimum circle. However, it will generally be about 15th circle. The exact formulas are below.

General Overview

1. When a Player Character attempts to sell a gem or skin to an NPC buyer, the base appraisal value (as seen with an accurate and precise appraisal) is the starting base value of the item.
2. The character's Trading Bonus modifies this, by adding a percentage multiplier to the base value. Non-Traders have a 0% Trading bonus and don't ever change. Traders have an inherent bonus that raises their base setting higher than 0%.
3. This is then further modified by a random +/- 10% in discrete 1% increments (accurate to at least 2 decimal places, such as 122.00xxxx%), easily confirmable with single gems/hides, tied/lumpy bundles, or tied gem pouches. However, in untied gem pouches, EACH gem gets a separate offer, so the % bonus is not a clean discreet percentage. But it can still be useful for making a rough guess to a Trader's bonus with little work of finding the precise bonus level, particularly if the gems are of fairly uniform value, as an untied gem pouch is 70 offerings rolled into one.

For an example, presume a hypothetical tied gem pouch worth precisely 100,000 kronar (10 plat kronar) when appraised certainly and exactly. When a non-Trader has an NPC gembuyer make an offer on it, they will see a range from 90-110% of the appraisal. That is, offers from 90000 to 110000 kronar, in increments of 1000 kronar (9 plat, 9.1 plat, etc., up to 11 plat).

According to the table of data formulas below, a 71st Circle Trader with 60 Charisma, 394 Trading, and 331 Appraisal has a bonus of 40%, and a bonus of 50% when under the effects of Finesse bonus. This Trader, with the same pouch, would see offers ranging from 13 to 15 plat in 1000 kronar increments (30% to 50%). If that Trader uses Finesse when selling, the offers can range from 14 plat to as high as 16 plat. (+/- 10% from a 50% base)

Formulas

The formula for the Trader bonus for selling is known to be a complicated function, the exact formulas of which has been determined.

It is what is known as a piecewise linear function, where the function changes over the domain, and each piece is a straight line. That, plus the random modifier, made it difficult to pin down a precise formula.

The player of Naniaki collected data over a period of years using 7-8 Trader alts (All but 2 below 40th), plus help from the player of Navesi (Aside from a good bit of more data, Navesi's experiences gave the realization that Naniaki's running assumptions at the time had to be wrong for grossly misfitting his own data, which gave the impetus for more research) and some others. It also helped to use Charisma reset potions a few times to get data over a wide range of Charisma value with little change, or to go back for specific points.

Tables were constructed in Open Office Calc and formulas reverse-engineered to fit known data, with refinements as new data was obtained.

Primary Formula

The primary formula, or the domain for the piece-wise function, is current/modified charisma times the sum of Trading and Appraisal.
Current Charisma*(Trading+Appraisal) = X.

This X is to be plugged into the piecewise functions. Y is the resulting bonus, before Finesse modifier (covered below).

Piece-wise Formulas

The first formula is for X equal to or less than 2100.
Y = (X/210), rounded down.
This goes on from 0% to 10% bonus.

The second step is for X greater than 2100 but equal to or less than 8400.
Y = (X/350)+1, rounded down.
This formula results in a bonus ranging from 7% to 25%.
By the formulas, it is possible to drop from the 10% to 7% as you move from the first step to the second step, and it does indeed happen, although the certainly apprentice Trader likely doesn't realize it happens because of a combination of the random modifier and lacking the skills to get certain appraisals of the object in question. It was quite a shock when first recorded.

The third formula covers all possibilities of X greater than 8400.
Y = ((X+444)/2211)+21, rounded down
This covers a range from 25% to at least 50%, and perhaps beyond if not for caps.
444 is correct, as 445 did not cause a rollover to the next point, but not tested at adjacent points.

Finesse

Finesse is composed of two parts:

1. A Charisma bonus that is used in the primary formula.
   
2. A direct bonus added to Y, of Circle/10, rounded down. This bonus does not scale with mana, it is in full effect as long as Finesse is active.

Formula Calculation Example

Assume a 40th Trader of 40 Charisma, 200 Trading and 160 Appraisal. This would be an X of 40*(200+160), or 14,440. Plug 14,440 into the step function of ((14,440-444)/2211)+21, and get 6.33+21, or 27% when rounded down. They will see offers randing from 17% to 37%.

If using Spec Finesse, let's hypothesize the modified Charisma is 40+8, so it would be 48*(200+160), or 17,280. The results of the step function would be 7.61+21, or 28% when rounded down. However, the Trader adds 4% directly to the bonus for being 40th Circle, and so the final bonus is 32%. Whatever they're having an NPC make an offer on, it can range from 22% to 42%.

Miscellaneous Information

Gem pouches can start to be sold at X = 2100 or higher. For most Traders, this is probably basically 20 Charisma and a total of 105 ranks between Trading and Appraisal.
Below this, the Trader gets told they don't have enough standing to sell gems in bulk. Doesn't affect bundles of course, since anyone can sell those, and Traders just get the extra income.

NPC buyers subject a flat cap of 60% to selling, no matter how high the bonus may be.

The Trader bonus itself appears to be capped at 50%. However, the direct bonus from Finesse bypasses this cap.
For illustration, Naniaki has been seeing 40%-60% standard offers for almost 6 years despite ever increasing Trading and Appraisal ranks.
However, when using Finesse, he NEVER sees an offer below 56% (currently 165th circle).
Therefore, he's at an apparent 50% cap under normal circumstance, but under Finesse conditions he's effectively getting 50%+16%=66%+/-10%, which yields 56% to the 60% cutoff.

Tables

While no longer necessary, these are included for completeness. Contact Naniaki if you want a copy of the Calc worksheets with all the hard data, formulas, and notes.

Bonus	Known Minimum Points	Known Maximum Points	Error (Min-previous Max)
0		200
1	210	418	10
2	420	629	2
3	630	830	1
4	840	1040	10
5	1060	1240	20
6	1260	1460	20
7	1470	1659	10
8	1680	1880	21
9	1890	2079	10
10	2100		21

Bonus	Known Minimum Points	Known Maximum Points	Error (Min-previous Max)
7	2101	2449	1
8	2450	2794	1
9	2800	3146	6
10	3150	3475	4
11	3510	3753	35
12	3850	4158	97
13	4200	4536	42
14	4550	4899	14
15	4900	5075	1
16	5250	5425	175
17	5600	5775	175
18	5950	6125	175
19	6300	6475	175
20	6650	6825	175
21	7000	7320	175
22	7350	7945	30
23	8022	8041	77
24	8066	8399	25
25	8400	10582	1
26	10619	12789	37
27	13356	15028	567
28	15062	17238	34
29	17306	19448	68
30	19480	21201	32
31	21774	23875	573
32	23900	25893	25
33	26352	28077	459
34	28304	30369	227
35	30688	32606	319
36	32850	34524	244
37	35055	37140	531
38	37170	39300	30
39	39360	41548	30
40	41580	43757	32
41	43778	45780	21
42	46013	48060	233
43	48909	50160	849
44	50827	51940	667
45	52920	54824	980
46	54880	56840	56
47	57240	58800	400
48	59280	60600	480
49	61620	62975	1020
50	63840		865