Map Management Resource

"

Flapdrol wrote:

These numbers seem right to me:
- 17% for Champions
- 15% for Commanders
From this also follows that:
- 10% for Twinned is a good assumption (since you get 10% of your items from bosses)
- 90% for Maze may be a better estimate (it doubles the map, but not the boss).

You need to use your modifiers properly. It's not 17% for Champions; it's 14% more and 3% increased. You need to keep the two modifiers separate. Twinned is 10% more with a 6% increase. Maze is tricky because it effects certain maps more than others; for example, it nearly triples size on Temple, and if we consider "nearly tripling" to be a 2.7 multiplier, but not on the boss so it's only a 2.7 multiplier for 90% of the loot, then it's equivalent to about 153% more in that instance. In the case of Shipyard, I agree that 90% more seems more accurate.

We may want to more accurately measure loot-from-which-monster-type (especially bosses, 10% more seems generous) and the effect of Maze on Shipyard.

"

Flapdrol wrote:

I think that we starting to hit on something much more useful than the case "Is there a pathological case where Exalting a map would be good?": a general model for when to reroll a map.

That's correct. It might be worth getting more precise experimental data than even that link you gave me; having thoroughly accurate affix percentages, combined with knowledge of the market value of each map type, would allow us to measure with mathematical precision the exact "good enough" state for every level of map.

"

Flapdrol wrote:

I propose we conclude the following on this particular issue:
Exalting Guideline for Maps In general, Exalting any map is a bad idea.
Exceptions:
- exalting a Shipyard with a specific combination of mods may be of minor benefit.
- if map prices rise over 3 exalted, there may be more cases.

I think Shrine could also qualify, but regarding any map 76 and lower... I haven't done the math yet, but I'd be utterly dumbfounded if there was even one instance where it would be appropriate. Even with 77s, my sample map was showing a niche case; your sample was showing what happens the other 95+% of the time, and Exalting is clearly wrong there.

"

Flapdrol wrote:

And that we devote our brainpower to a more general map-rolling model, since we seem to have most of the building blocks:
- we need to add some assumed values for Chaining and Chilled Ground and neatly list our assumptions and values
- we can compute the expected value of an Affix/Suffix
- we can compute the expected value of a reroll (and its standard deviation)
and if a map costs X chaos, you should reroll as long as your current map roll is below the expected value of the highest of X rerolls

Is the above correct (especially the last step)?

Actually, you've got your f(x) where your x should be; we don't want to compute the expected value of a reroll (because Chaos don't work like Exalts), we want to compute the expected number of rerolls for each value (that is, each effective quantity). This allows us to say "maintaining this standard for this map will cost you, on average, X Chaos, which is justified because of the market value of the white map." It's standards that matter here, not currency spent. If someone meets the standard with their Alch roll, and thus doesn't need to spend a single Chaos, more power to them; if someone has crappy luck and goes over the expected Chaos cost, they shouldn't just stop rerolling, they should continue until they meet the standard; over a long enough period of time, all of that good and bad luck will cancel each other out.

It's worth noting that, if our findings turn out to be significantly outside the conventional wisdom, it may lead to a shift in market prices; this, ironically, could turn all of our math on its head and force us to redo it for the new conditions. I plan on using a very ornate, self-designed Excel spreadsheet to allow rapid recalculation in the event of market changes.

"

27/08/2013: Shrine potential moved from tier 3 to tier 5 in light of something that has now been confirmed.

Thought I'd link it into the present discussion.

To the last point made: not all your math would be turned on its head. Your numbers for rerolling don't change, therefore adjusting for market value of maps is simple arithmetic.

In other words, I reckon the math is probably worth doing. So let's talk methodology. Two assumptions are made.

Firstly, exact numbers on affix chances. Suggestion: someone (you, me, random unfortunate volunteer) starts recording all affixes per alc/chaos on each map. Would probably need to redo the data to include chaining and chilled anyway.

Secondly, relative values of white/blue/yellow/boss mobs and their drops. This one's going to be a lot trickier, particularly since...what's the interaction between map IIQ, party IIQ and personal IIQ again? Anyway, suggestion: run multiple white 66s on a zero MF character. Instead of recording # of mobs, record # of packs which spawned as blue/white. I think you'll find that while # of packs per map varies, the ratio of blue to white packs should be fairly constant.

Also while you're at it, record # of rare mobs. While here, do a count-up of # items dropped of each rarity, per pack of course, with a separate table for rares and the boss. (Yeah, good luck with that. Told you it was going to be trickier.) You can also probably get this data from non-map zones, if you are so inclined, but I'd do it in 66 white maps anyway because that's where you get actual bosses and who knows whether Piety and Kole have different drop rate modifiers.

I would request that you post enough of the math that it can be followed and a general guideline can be found. I can write it up in matlab or something, or someone can, then when the numbers for the above two points are found, it would be a simple matter of changing the assumed values to actual ones, and running the script again would return the new value of "how many rerolls would it take to equal or better this quantity, on average".

"

Kirielis wrote:

"

27/08/2013: Shrine potential moved from tier 3 to tier 5 in light of something that has now been confirmed.

Thought I'd link it into the present discussion.

I think Shrine is a 4; it's gone from being underrated before to being overrated now. There is a clear distinction between Shrine and Shipyard that should put them on separate tiers; the upgrade was an overreaction.

Note: I have personally not run either. I'm good at math, and thus I believe I can contribute in some ways to this thread despite a lack of experience, but I shouldn't mislead anyone. I'm basing my opinions on Shrine and Shipyard entirely off of Twitch and YouTube, which is something I guess, but I know it's not as good as the real thing.

"

Kirielis wrote:

what's the interaction between map IIQ, party IIQ and personal IIQ again?

Maps use the local increase system. You know how when your weapon gets 100% increased physical damage, it's a lot more effective than 100% increased physical damage on the passive tree? That's because one all the other local increases are rounded up, the effect of the increases is finalized, and then global increases are tacked on multiplicatively. It ends up feeling a lot like a more bonus.

Party IIQ is a more bonus.

Personal IIQ is a global increase system.

"

Kirielis wrote:

Anyway, suggestion: run multiple white 66s on a zero MF character. Instead of recording # of mobs, record # of packs which spawned as blue/white.

First off, we don't care about how many white or blue monsters there are, we care about how much stuff they drop. This makes it even harder to calculate, because item rarity is a factor. Ideal testing would accelerate the process with lots of IIQ (both map and personal), IIR, Labyrinthine/Massive, Pack Size, Commanders, and Twinned (although that's asking a lot — less than ideal will have to be accepted sometimes); Commanders and Twinned are to increase frequency of relatively uncommon events, and would be factored out in the final math (vitally important to record Commanders values and yes/no on Twinned). Although group would be ideal in theory, unless we got an entire group of like-minded volunteers, it's more likely that extra people would just contaminate results or lose data, so solo is far more likely. It's very likely that rare/magic density increases as map level increases, and thus testing would probably have to be done within the maps themselves (no Docks runs) and separated by map level (at least until the preceding hypothesis is confirmed or refuted).

"

ScrotieMcB wrote:

First off, we don't care about how many white or blue monsters there are, we care about how much stuff they drop. This makes it even harder to calculate, because item rarity is a factor.

One more thing. Different packs may have different 'expected number of items', i.e. a white pack of zombies on average drops more items than a white pack of goats.

Another desireble data is the expected number of maps dropped. This information is something many 'mapping logs' contain thus it can be accumulated and processed given someone is dedicated enough to go through all that logs. It requires a lot (how many exactly?) of sample data because of low EV and high variance. The good thing is that map drops are not affected by player IIR/IIQ and party bonuses.

High tier maps are among the most desirable drops, blue mobs can drop +1 tier, rares and bosses +2. '50% more rare monsters' mod on Bazaar may add, say, 10% to total rares dropped, but 40% to 77 tier maps dropped.

An easy thing to track is experience gain per map. Are there any useful conclusions that can be made gived this data (exp gain, player level, map level, pack and size improvement affixes)? Just throwing in an adea. Counting rare drops from packs requires some time, counting magic drops seems impossible unless some not-that-legal software is implemented.

Friend of mine tracked experience gain per map once. Or tried to. It didn't work out all that well for him, due to the intrinsic randomness of spawned packs.

"

Kirielis wrote:

In other words, I reckon the math is probably worth doing. So let's talk methodology. Two assumptions are made.

Firstly, exact numbers on affix chances. Suggestion: someone (you, me, random unfortunate volunteer) starts recording all affixes per alc/chaos on each map. Would probably need to redo the data to include chaining and chilled anyway.
Secondly, relative values of white/blue/yellow/boss mobs and their drops. This one's going to be a lot trickier, particularly since...what's the interaction between map IIQ, party IIQ and personal IIQ again? Anyway, suggestion: run multiple white 66s on a zero MF character. Instead of recording # of mobs, record # of packs which spawned as blue/white. I think you'll find that while # of packs per map varies, the ratio of blue to white packs should be fairly constant.
Also while you're at it, record # of rare mobs. While here, do a count-up of # items dropped of each rarity, per pack of course, with a separate table for rares and the boss. (Yeah, good luck with that. Told you it was going to be trickier.) You can also probably get this data from non-map zones, if you are so inclined, but I'd do it in 66 white maps anyway because that's where you get actual bosses and who knows whether Piety and Kole have different drop rate modifiers.

My suggestion would be to not do all of the above (I'm a CS guy and not a methodologist, and this will show). Data gathering to the point where it becomes accurate will be a tremendous amount of work.

1) Work with estimates. Take the spreadsheet, guesstimate values for chaining and chill, round everything and use this
2) Use the remaining guesstimates that were discussed above
3) Do the math (in the elaborate spreadsheet) and see what comes out
4) Now vary some of your guesstimates and see how the outcomes change in the spreadsheet. This will show that some guesstimates urgently need refining as small changes in the guesstimate give dramatic changes in the output, while other guesstimates do not.
5) Now you can work on gathering data until you can show that your model is fairly robust.

"

ScrotieMcB wrote:

You need to use your modifiers properly. It's not 17% for Champions; it's 14% more and 3% increased. You need to keep the two modifiers separate. Twinned is 10% more with a 6% increase. Maze is tricky because it effects certain maps more than others; for example, it nearly triples size on Temple, and if we consider "nearly tripling" to be a 2.7 multiplier, but not on the boss so it's only a 2.7 multiplier for 90% of the loot, then it's equivalent to about 153% more in that instance. In the case of Shipyard, I agree that 90% more seems more accurate.

I stand corrected.

"

ScrotieMcB wrote:

I think Shrine could also qualify, but regarding any map 76 and lower... I haven't done the math yet, but I'd be utterly dumbfounded if there was even one instance where it would be appropriate. Even with 77s, my sample map was showing a niche case; your sample was showing what happens the other 95+% of the time, and Exalting is clearly wrong there.

Once we do the work described above, solving this case would be trivial. I retreat to "Never exalt maps of 76 and lower. There may be some cases where exalting a 77 is beneficial"

"

ScrotieMcB wrote:

Actually, you've got your f(x) where your x should be; we don't want to compute the expected value of a reroll (because Chaos don't work like Exalts), we want to compute the expected number of rerolls for each value (that is, each effective quantity). This allows us to say "maintaining this standard for this map will cost you, on average, X Chaos, which is justified because of the market value of the white map." It's standards that matter here, not currency spent. If someone meets the standard with their Alch roll, and thus doesn't need to spend a single Chaos, more power to them; if someone has crappy luck and goes over the expected Chaos cost, they shouldn't just stop rerolling, they should continue until they meet the standard; over a long enough period of time, all of that good and bad luck will cancel each other out.

I stand corrected again. Nothing goes above working with smart people.

"

ScrotieMcB wrote:

It's worth noting that, if our findings turn out to be significantly outside the conventional wisdom, it may lead to a shift in market prices; this, ironically, could turn all of our math on its head and force us to redo it for the new conditions. I plan on using a very ornate, self-designed Excel spreadsheet to allow rapid recalculation in the event of market changes.

Or we could keep it secret and make out like bandits :)

save for later reading

Hmm, I don't think Excel will be able to handle it; there are 80,621,568 different rare map affix possibilities (4-, 5-, and 6-affix rares all added together), and there are max 1,048,575 rows per sheet, which would mean 77 sheets for that task alone. Excel would probably break under the stress.

Does anyone know a program that can handle that kind of statistical volume?

"

ScrotieMcB wrote:

I think Shrine is a 4; it's gone from being underrated before to being overrated now.

Nope. We've known it to be a five for a long time. I chose not to change it until I had conclusive proof of what I wanted to know. Shrine may not be as big as a Shipyard, but it natively has large packs because of its signature monster type.

There may be the odd case here and there though.