[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:
	plus		totalMaps
	probit		negative
			binomial
	(1)	(2)	(3)	(4)	(5)
Quantity	0.007***	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)
magicInfo	0.002			0.001
	(0.002)			(0.001)
rareInfo	0.003*			0.002
	(0.002)			(0.001)
packInfo	0.004**			0.002*
	(0.002)			(0.001)
creatormapsProj1	0.059			0.067
	(0.123)			(0.081)
creatormapsProj2	-0.023			-0.007
	(0.147)			(0.093)
creatormyth	-0.027			0.056
	(0.134)			(0.087)
magicD		0.068			0.026
		(0.066)			(0.038)
rareD		0.097			0.036
		(0.066)			(0.039)
packD		0.141**			0.052
		(0.065)			(0.038)
Constant	6.150***	6.286***	0.496	0.425	0.748**
	(0.773)	(0.635)	(0.314)	(0.439)	(0.362)
Observations	3,040	3,040	3,040	3,040	3,040
Log Likelihood	-1,817.311	-1,818.414	-4,917.319	-4,914.001	-4,916.216
theta			44.604 (31.901)	47.676 (36.319)	45.631 (33.348)
Akaike Inf. Crit.	3,652.623	3,648.828	9,840.637	9,846.002	9,844.433

[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.

	level	overall	neither mod	has one mod
	66	66.6	66.6	66.5
	67	67.1	67.2	67
	68	67.8	67.8	67.9
	69	68.4	68.5	68.3
	70	69.1	69.1	69.2
	71	70.1	69.9	70.3
	72	70.5	70.6	70.3
	73	71.4	71.6	71.3
	74	72.2	72.4	72
	75	72.8	72.8	72.8
	76	73.5	73.5	73.5
	77	74.2	73.9	74.5
	78	74.7	74.9	74.5

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

	Dependent variable:
	plus		totalMaps
	probit		negative
			binomial
	(1)	(2)	(3)	(4)	(5)
Quantity	0.005***	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)
magicInfo	0.001			0.001
	(0.001)			(0.001)
rareInfo	0.003**			0.002*
	(0.001)			(0.001)
packInfo	0.002			0.002***
	(0.001)			(0.001)
creatorjddogg	0.012			-0.079
	(0.089)			(0.051)
creatormapsProj1	0.052			-0.014
	(0.065)			(0.040)
creatormapsProj2	-0.010			-0.088*
	(0.088)			(0.051)
creatorpyrodan2	-0.003			-0.058
	(0.131)			(0.086)
magicD		0.056			0.037
		(0.052)			(0.030)
rareD		0.120**			0.035
		(0.052)			(0.031)
packD		0.092*			0.069**
		(0.051)			(0.030)
Constant	5.308***	5.565***	0.262	0.283	0.603*
	(0.621)	(0.535)	(0.270)	(0.355)	(0.309)
Observations	4,777	4,782	4,782	4,777	4,782
Log Likelihood	-2,838.709	-2,841.432	-7,760.944	-7,743.295	-7,758.142
theta			41.345* (21.765)	46.303* (27.188)	42.855* (23.340)
Akaike Inf. Crit.	5,697.418	5,694.863	15,527.890	15,506.590	15,528.280