Thursday, April 17, 2014

[POE] Maps, Levels, and Quantity

I love maps in Path of Exile. But I've always been curious about the details of the map drop system. Does it get harder to get higher level maps? Exactly what does quantity do?  What about the desirable mods (pack size, more magic monsters, more rare monsters) - how much quantity are they worth?

As usual, the forums have an abundance of speculation about these answers. But I wanted math.

So I started to collect data on the maps that I've been running in PoE. Unfortunately, this kind of data gathering takes time, so I was only able to gather data on around 500 maps. Which just isn't enough data to study processes that are based on rare events.

To take this further, I combined my data with a few other projects that had collected data from maps into one, larger, spreadsheet of doom. (Note: all of these sources were gathered since 1.0, which substantially changed the mapping system.)
  • My data - link
  • /u/dansenMONSEN - link
  • /u/jddogg - link
  • /u/IcyRespawn - link
  • /u/Shadowclaimer- link
  • /u/pyrodan2 - link
  • /u/Skyl3lazer - link
This gave a total 4076 map runs, covering a wide range of map levels and map quantity.

From this data, I can take a look at the basics of map drops.

Map Level
One finding is painfully apparent for anyone that runs maps in PoE: it gets harder to progress your map pool on higher level maps.  For every increase in map level, the average level of maps dropped increases by 0.71. For 66 maps, the average drop is an increase in map levels (66.5).  By level 70, the average drop is only 69.1, and by 78 maps the average drop is down to 74.6. Maintaining a high level map pool gets harder with each level.

Map Quantity
Declining average drop level makes getting high quantity critically important for maps (since higher quantity means more maps, which increases the odds of getting equal-or-higher level maps).
On average, I estimate that every 100% quantity increases the number of maps dropped by 0.85 maps. (Results from a negative binomial regression - full table after the break.) This, in turn, improves the chance of getting a higher level map.  The same 100% quantity increases the chance of getting a higher level map by around 20%.

Pack Size / Magic Monsters / Rare Monsters
But what about the desirable mods (pack size, magic monsters, rare monsters) - what effect do they have on map drops?
  • Pack Size: aids in getting both more and higher level maps. However, the data suggests that pack size isn't as game-breaking as others suggest. From the models, every 2% pack size is worth about 1% quantity. So a 20% pack size roll is worth only about 10% quantity - less than the other available suffixes that could roll on a map.
  • Magic / Rare monsters: have no effect on the number of maps (or, whatever effect is there is lost to noise / too small to estimate). Rare monsters increases the likelihood of getting a higher level map (it is likely that magic monsters does too, just that the effect is fairly small).  Again, the mod is about half as valuable as quantity.  So a low rare monsters roll is equivalent to about 13% quantity.

Thoughts
These results are... surprising.

While I've always been told to roll for the desirable affixes, these results suggest that they may be overrated. Of course, there is one caveat: some maps - like tunnel - don't have much room for large packs to spawn, diminishing the effect of the mod. I'll try and gather more data to evaluate this claim.

I'm really surprised that the magic monsters mod didn't show any statistical significance, no matter how I looked at the data. I'm thinking this might have to do with selection effects. The problem is how highly the mod is rated: if players immediately run a map with +magic monsters regardless of the other mods, this would result in +magic monsters being associated with worse maps and fewer drops. I'll try some quasi-experimental methods out to get around this problem.

I'm also surprised that 1% quantity doesn't equate to another 1% chance to get a map... this makes me think something else may be going on with the models, so I'll take another pass at the topic soon.

So very excited to have data to play with!




For the stats nerds:  full table after the break.



Dependent variable:
plustotalMaps
probitnegative
binomial
(1)(2)(3)(4)(5)
Quantity0.007***0.006***0.005***0.005***0.005***
(0.001)(0.001)(0.001)(0.001)(0.001)
Level-0.100***-0.101***-0.003-0.004-0.008
(0.012)(0.010)(0.005)(0.007)(0.006)
magicInfo0.0020.001
(0.002)(0.001)
rareInfo0.003*0.002
(0.002)(0.001)
packInfo0.004**0.002*
(0.002)(0.001)
creatormapsProj10.0590.067
(0.123)(0.081)
creatormapsProj2-0.023-0.007
(0.147)(0.093)
creatormyth-0.0270.056
(0.134)(0.087)
magicD0.0680.026
(0.066)(0.038)
rareD0.0970.036
(0.066)(0.039)
packD0.141**0.052
(0.065)(0.038)
Constant6.150***6.286***0.4960.4250.748**
(0.773)(0.635)(0.314)(0.439)(0.362)
Observations3,0403,0403,0403,0403,040
Log Likelihood-1,817.311-1,818.414-4,917.319-4,914.001-4,916.216
theta44.604 (31.901)47.676 (36.319)45.631 (33.348)
Akaike Inf. Crit.3,652.6233,648.8289,840.6379,846.0029,844.433

[UPDATE]  Anonymous wanted to know the average map drop by level, then for maps without the rare / magic mod, and then for maps with one of those mods.  This excludes maps that dropped no map.

leveloverallneither modhas one mod

6666.666.666.5

6767.167.267

6867.867.867.9

6968.468.568.3

7069.169.169.2

7170.169.970.3

7270.570.670.3

7371.471.671.3

7472.272.472

7572.872.872.8

7673.573.573.5

7774.273.974.5

7874.774.974.5

[UPDATE2]
Another run of the results, for jddogg and the redditors.


Dependent variable:
plustotalMaps
probitnegative
binomial
(1)(2)(3)(4)(5)
Quantity0.005***0.005***0.005***0.005***0.005***
(0.001)(0.001)(0.0005)(0.001)(0.001)
Level-0.087***-0.090***-0.0001-0.001-0.006
(0.009)(0.008)(0.004)(0.005)(0.005)
magicInfo0.0010.001
(0.001)(0.001)
rareInfo0.003**0.002*
(0.001)(0.001)
packInfo0.0020.002***
(0.001)(0.001)
creatorjddogg0.012-0.079
(0.089)(0.051)
creatormapsProj10.052-0.014
(0.065)(0.040)
creatormapsProj2-0.010-0.088*
(0.088)(0.051)
creatorpyrodan2-0.003-0.058
(0.131)(0.086)
magicD0.0560.037
(0.052)(0.030)
rareD0.120**0.035
(0.052)(0.031)
packD0.092*0.069**
(0.051)(0.030)
Constant5.308***5.565***0.2620.2830.603*
(0.621)(0.535)(0.270)(0.355)(0.309)
Observations4,7774,7824,7824,7774,782
Log Likelihood-2,838.709-2,841.432-7,760.944-7,743.295-7,758.142
theta41.345* (21.765)46.303* (27.188)42.855* (23.340)
Akaike Inf. Crit.5,697.4185,694.86315,527.89015,506.59015,528.280

4 comments:

  1. Hey, you have done great work and I will definitely be changing the way I reroll maps because of it. What I would be interested in is the breakpoint in quantity necessary to sustain a map pool.

    ReplyDelete
  2. "For every increase in map level, the average level of maps dropped increases by 0.71. For 66 maps, the average drop is an increase in map levels (66.5). By level 70, the average drop is only 69.1, and by 78 maps the average drop is down to 74.6. Maintaining a high level map pool gets harder with each level."

    Can you give the average map level dropped by level 76 maps? Jumping from 70 to 78 is too much, because 78's cannot drop maps +1 or +2 levels from them. From the numbers you gave, 66->70 is average of .65 levels per level of map run, and 66->78 is .675 levels per level. Also, is that the aggregate statistic across all maps run, or singling out magic\rare or non magic\rare?

    Thanks!

    ReplyDelete
    Replies
    1. I tried to reply as a comment, but the blogger formatting was... bad. So I added it to the post.

      Delete
  3. The main reason the mod's are desirable are because maps are so largely rng based, getting like 4-5 maps out of a white mirrored and 0 from a 100 quant, people just roll packsize/magic monsters because they are the biggest increase to XP gained from the map and just wait on rng/carto boxes to keep the map pool going.

    ReplyDelete