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This was initially posted to reddit on and the official Path of Exile forums on Mar 2, 2015.

References 4,5,6,7 to externally hosted images were changed to inline images.

https://www.reddit.com/r/pathofexile/comments/2xn0xq/analysis_on_the_effectiveness_of_increased_item/
http://www.pathofexile.com/forum/view-thread/1210745

Analysis on the Effectiveness of Increased Item Quantity and Rarity in Path of Exile

Mar 2, 2015

Abstract

Hillock was killed 2500 times in sets of 100 with increased item quantity values of 0/20/40/60/80 and increased item rarity values of 0/100/200/300/400. Diminishing returns for IIQ and IIR are estimated, and an estimate is given for the drop rates of non-rarity and unique items. Data summaries are included as appendices.

1. Introduction

There is limited information available on the effectiveness of increased item quantity (IIQ) and increased item rarity (IIR). Chuca79 has a brief summary of 1000 Dominus kills [1], but details are scant. GGG staff has commented on IIQ and IIR, but without offering much detail [2]. This post seeks to offer insight into the mechanics of IIQ and IIR, and how that might affect drop rates of items without rarity.

2. Methodology

Two characters were used to gather data, a 73-74 crit tornado shot ranger and a 79-80 blood magic dual flame totem marauder (dedicated magic find character). The tornado shot character was used as movement speed bonuses from the skill tree were quite beneficial. Data were gathered over several weeks, and occasionally the characters were used for other purposes, hence the level changes. Character experience gained from the runs was negligible.

Hillock was killed on standard in sets of 100 with a given value of IIQ and IIR. Target IIQ was 0/20/40/60/80 and target IIR was 0/100/200/300/400, for a total of 2500 kills. Both maximum IIQ and IIR values should be achievable exclusively during a temporary league, but high values of both IIQ and IIR are only achievable on standard using legacy gear (IIQ gem and helmet and amulet with IIQ). Actual IIQ values and IIR values used to gather data vary from targeted values by +/- 2 IIQ and +/- 2 IIR with one exception (0 IIQ 409 IIR).

Hillock was chosen as a target, as opposed to Dominus, for several reasons: it is easier to count a small number of drops, strand is one of the most linear zones (saving on time searching for the correct path forward), stopping to vendor or place items in stash is convenient, and time for a complete run is short. [3]

3. Analysis

The following analysis is valid for Hillock on standard. Caution should be used when applying these results to other mobs in game. Additionally, a large amount of variance is shown in the data, so conclusions are only weakly drawn.

3.1 IIQ Effectiveness

As stated by GGG, IIQ suffers from diminishing returns. A baseline of 517 drops per 100 Hillock kills is established by averaging the number of drops with no IIQ. The expected number of items dropped by increasing IIQ can be predicted by multiplying the baseline by 1.2/1.4/1.6/1.8, and this can be compared to the average number of drops for each amount of IIQ (Chart 1 [4]). This shows that after the first 20 IIQ, the effective IIQ decreases non-linearly by about 5% per 20 IIQ. The results are summarized in Table 1.

Chart 1
[4] Chart 1

Table 1

IIQaverageexpectedeffective IIQ
05175170
20603.8620.416.79%
40672.8723.830.14%
60722.2827.239.69%
80761.8930.647.35%

3.2 IIR Effectiveness

The number of normal items which drop falls off sharply as IIR increases (Chart 2 [5]) while the number of magic items increases in a non-linear fashion (Chart 3 [6]). This seems to indicate nothing has changed since what GGG poster Rhys has stated [2]:

It currently rolls for Unique first, then if that fails, it rolls for Rare, then Magic, etc. +IIR is applied to every roll (with diminishing returns).
Chart 2
[5] Chart 2

Chart 3
[6] Chart 3

Due to the nature of how item rarity works (rolling a non-rarity base and/or then rolling each rarity [2]), establishing IIR effectiveness is slightly more complex. Here, only the effectiveness on the number of rare item drops will be evaluated.

Ignoring the large amount of variance, there is a definite upward trend for the number of rare items dropped as IIR increases to 400 (Chart 4 [7]).To establish effectiveness, the number of rare drops is normalized per IIQ (percent of total drops is used) and averaged for each tier of IIR. As IIR is not as simple an attribute as IIQ, no baseline is given to establish effectiveness, but a summary of effectiveness is given in Table 2. Chart 4
[7] Chart 4

Table 2

rare IIRaverage % rare items
06.66
1009.30
20012.56
30014.13
40015.57

Table 2 shows that the most benefit is given by the first 200 IIR with severe penalties applied afterwards. This roughly confirms Chuca79's results.

3.3 Non-rarity droprates

With such a large amount of variance, no meaningful conclusion can be drawn from how IIQ and IIR affects drop rates of items without rarity, although it does appear IIQ increases the number of non-rarity items. However, an estimate for drop rates of items without rarity should be possible from the amount of data collected, assuming IIR and IIQ has no affect on the drop rate of items without rarity (which may be incorrect). Below is a summary of the drop rates for non-rarity items. Note: according to the wiki [8] there will be a 36.4% drop rate penalty for currency items, which may or may not apply to scrolls, skill gems and other crafting items.

Table 3

item# drops% of non-rarity% of total
scroll of wisdom19441.72%7.76%
portal scroll9520.43%3.80%
skill gem326.88%1.28%
armourer's scrap286.02%1.12%
orb of transmutation255.38%1.00%
orb of augmentation143.01%0.56%
orb of alteration143.01%0.56%
blacksmith's whetstone112.37%0.44%
orb of chance81.72%0.32%
orb of alchemy81.72%0.32%
cartographer's chisel71.51%0.28%
chromatic orb71.51%0.28%
chaos orb71.51%0.28%
jeweler's orb61.29%0.24%
orb of fusing30.65%0.12%
orb of scouring30.65%0.12%
vaal orb10.22%0.04%
blessed orb10.22%0.04%
glassblower's bauble10.22%0.04%

Ratio's of one item to another approximately align with previously posted values with some notable differences [9]. This could be due to the large amount of variance, or because the previously posted values were wrong or because drop rates have been changed since originally posting.

3.4 Unique droprates

Due to the large amount of variance, no significant conclusions can be drawn to how IIQ and IIR affect unique drop rates. Summing total results and ignoring IIQ and IIR, unique drop rate is estimated to be around 0.207%.

4.0 Conclusion

Data seems to align with Chuca79's results, although it appears an ideal balance of IIQ and IIR to other stats is achieved at a lower value than the "C=8" value.

Currency drop rates are shown to be disproportionate to the currency upgrade path offered by vendors. Orbs of chance and alchemy are much more common as drops than other "lower" currencies.

Appendix A

Data summary
IIQ IIR unique rare magic normal non-rarity sum unique % rare % magic % normal % non-rarity % # runs char level
0 0 2 35 187 285 10 519 0.39 6.74 36.03 54.91 1.93 100
0 100 1 48 266 191 9 515 0.19 9.32 51.65 37.09 1.75 100
0 203 3 69 349 81 13 515 0.58 13.40 67.77 15.73 2.52 100
0 301 2 76 410 22 13 523 0.38 14.53 78.39 4.21 2.49 100
0 409 2 81 415 0 15 513 0.39 15.79 80.90 0.00 2.92 100
20 0 1 38 209 348 11 607 0.16 6.26 34.43 57.33 1.81 100
20 102 1 53 344 192 14 604 0.17 8.77 56.95 31.79 2.32 100
20 202 2 85 398 103 16 604 0.33 14.07 65.89 17.05 2.65 100
20 302 2 83 465 30 23 603 0.33 13.76 77.11 4.98 3.81 100
20 402 1 99 482 0 19 601 0.17 16.47 80.20 0.00 3.16 100 79
40 0 0 41 200 415 21 677 0.00 6.06 29.54 61.30 3.10 100 73
40 101 0 66 368 218 23 675 0.00 9.78 54.52 32.30 3.41 100 73
40 202 3 84 438 123 21 669 0.45 12.56 65.47 18.39 3.14 100 73
40 300 2 91 518 37 20 668 0.30 13.62 77.54 5.54 2.99 100 73
40 399 0 108 542 0 25 675 0.00 16.00 80.30 0.00 3.70 100 80
62 0 0 53 208 440 19 720 0.00 7.36 28.89 61.11 2.64 100 74
61 99 1 67 369 256 27 720 0.14 9.31 51.25 35.56 3.75 100 80
61 200 3 84 489 132 14 722 0.42 11.63 67.73 18.28 1.94 100 80
61 300 1 109 536 61 18 725 0.14 15.03 73.93 8.41 2.48 100 80
60 399 2 119 586 0 17 724 0.28 16.44 80.94 0.00 2.35 100 80
81 0 0 52 238 444 22 756 0.00 6.88 31.48 58.73 2.91 100 80
81 99 1 71 392 277 20 761 0.13 9.33 51.51 36.40 2.63 100 80
81 200 1 85 505 142 30 763 0.13 11.14 66.19 18.61 3.93 100 80
80 299 1 105 585 50 27 768 0.13 13.67 76.17 6.51 3.52 100 80
81 399 2 100 641 0 18 761 0.26 13.14 84.23 0.00 2.37 100 80

Appendix B

Non-rarity summary part 1
IIQ IIR scroll of wisdom portal scroll augmentation transmutation alteration jeweler's chromatic fuse chance alchemy
0 0 5 2 1
0 100 4 3 2
0 203 8 1
0 301 6 5 1 1
0 409 6 1
20 0 4 2 1 1
20 102 4 3 1 1 1
20 202 5 4 1 1 1 1
20 302 9 6 1 4 1
20 402 7 3 3 1
40 0 14 3 1 1 1
40 101 6 4 2 1 1 1 1 1
40 202 10 3 2 2 1
40 300 6 6 2 1 1 1
40 399 10 3 1 1 2 1 1 1
62 0 9 5 2 1
61 99 13 7 1 1
61 200 9 2 1 1
61 300 3 6 2 1 1 1
60 399 4 5 2 1 2 2 1
81 0 11 6
81 99 6 3 1 1
81 200 12 4 2 2 2
80 299 14 8 1 1
81 399 9 1 1 1 1
a sum 194 95 14 25 14 6 7 3 8 8
a % of non-rarity 41.72% 20.43% 3.01% 5.38% 3.01% 1.29% 1.51% 0.65% 1.72% 1.72%
a % of total 7.76% 3.80% 0.56% 1.00% 0.56% 0.24% 0.28% 0.12% 0.32% 0.32%
Non-rarity summary part 2
IIQ IIR scouring chaos vaal blessed skill gem whetstone armourer's cartographer's bauble sum
0 0 1 1 10
0 100 9
0 203 1 1 2 13
0 301 13
0 409 2 6 15
20 0 2 1 11
20 102 1 2 1 14
20 202 1 1 1 16
20 302 1 1 23
20 402 1 1 2 1 19
40 0 1 21
40 101 1 1 2 1 1 23
40 202 1 1 1 21
40 300 1 1 1 20
40 399 3 1 1 25
62 0 1 1 19
61 99 2 2 1 27
61 200 1 14
61 300 4 18
60 399 17
81 0 3 1 1 22
81 99 2 2 4 1 20
81 200 4 1 2 1 30
80 299 2 1 27
81 399 3 1 1 18
a sum 3 7 1 1 32 11 28 7 1 465
a % of non-rarity 0.65% 1.51% 0.22% 0.22% 6.88% 2.37% 6.02% 1.51% 0.22% 2500
a % of total 0.12% 0.28% 0.04% 0.04% 1.28% 0.44% 1.12% 0.28% 0.04%

Appendix C

List of skill gems dropped, in order.

ground slam
reave
flame surge
tempest shield
fireball
fire penetration
generosity
static strike
chance to flee
frost wall
poacher's mark
sweep
lightning arrow
spark
animate guardian
lightning strike
added chaos damage
molten strike
knockback
ethereal knives
detonate dead
chain
convocation
lightning warp
superior raise zombie
frostbite
melee damage on full life
bear trap
fire trap
spectral throw
frenzy
assassin's mark

Appendix D

List of unique items dropped, in order.

wurm's molt
honourhome
carnage heart
prismatic eclipse
the covenant
geofri's baptism
bramblejack
chalice of horrors
blackgleam
slitherpinch
titucius' span
aurumvorax
hrimnor's hymn
wanderlust
pyre
bronn's lithe
asphyxia's wrath
ondar's flight
mokou's embrace
shiversting
ondar's flight
perandus blazon
nomic's storm
ungil's gauche
forbidden taste
ambu's charge
shackles of the wretched
wideswing
hyrri's bite
lochtonal caress
ezomyte peak
goldrim
geofri's baptism
tabula rasa

References

[1] http://www.pathofexile.com/forum/view-thread/725812
[2] http://www.pathofexile.com/forum/view-thread/531619/filter-account-type/staff
[3] Of course, one of the disadvantages of strand is the lack of masters and corrupted zones.
[4] http://i.imgur.com/MQF0gBF.jpg
[5] http://i.imgur.com/WPVfuou.jpg
[6] http://i.imgur.com/4hwTpho.jpg
[7] http://i.imgur.com/iabIBI0.jpg
[8] http://pathofexile.gamepedia.com/Drop_Rate
[9] http://www.reddit.com/r/pathofexile/comments/2dvjol/drop_rate_of_currency_in_poetw_wiki/