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EOR: Towards a new measure of profitability Messages in this topic - RSS

PSGarak
PSGarak
Posts: 197

8 days ago
Fallen London is a game about capitalist space-bats, the things they bought, and the people they bought them from. It is set in a cosmology where one of the protagonists is a literal marketplace. It is therefore no surprise that we, the players of Fallen London, spend much of our time thinking about the best ways for our characters to earn currency.

The most common method is EPA: Echoes per Action. I believe this method has limitations. Several others have voiced this opinion as well. I've been noodling on an idea for a replacement for a while, but after the recent discussions attempting to figure out which Expedition is the most profitable, I've finally decided to write out my thoughts. I hope that they join with other people's thoughts, and then everybody will have even better thoughts. Then a giant crab will give us money for them, or something.

First, I will illustrate a problem that I see with EPA.

A Highly Contrived Example


Imagine there is a one-time, non-repeatable choice that you are given (say, the conclusion of a one-time storyline). The two options are as follows, and are given whimsical names to make them easier to refer to later:
  • Pebble: Spend one Action to gain ten Echoes
  • Boulder: Spend ten Actions to gain fifty Echoes

Which option should you choose?


EPA would tell you that Pebble is the better option: It has an EPA of 10, compared to 5 for Boulder. But, this does not align with my intuition, and it may not align with yours. Fifty is, like, a lot of Echoes. Shouldn't that matter more? Sure, it takes more Actions to claim the reward, but isn't it still the better option?

One way of looking at this situation is that compared to Pebble, choosing Boulder will gain forty Echoes, and cost nine Actions. Should you spend nine Actions for Forty Echoes? One would think yes. So perhaps EPA has lead us astray.

Let's dig in just a little further: What is the value of nine actions? The answer depends on what you would do with those Actions if given the choice. And for most players, the answer is simple: Affair of the Box. So let's normalize the Action cost of each option by spending ten Actions on each, using Affair of the Box as the "replacement" Action when we need to, and see how much total money we make:
  • Pebble: Ten echoes plus nine plays of AotB @ 1.64 EPA, for a total of 26.4 Echoes.
  • Boulder: Fifty Echoes, straight-up.

Clearly, Boulder is the more profitable option. Given the same opportunities and the same resource expenditure, our hypothetical character comes out ahead by 23.6 Echoes.


Where EPA Goes Wrong

In short, EPA only makes sense as a metric for choices that are limited by Actions. In other words, it is useful for evaluating grinds. For something that is not limited by Actions, it doesn't make sense to use Actions as the denominator.

When presented with options that are limited by Cards, or Favors, or something similar, EPA will penalize options that require more Actions to cash in. But the true measure of profitability is actually the Opportunity Cost, i.e. "What could I have done instead?"

A New Metric: EOR


I propose a new metric named Echoes Over Replacement, abbreviated EOR, which is pronounced the same as Eeyore, the plush ungulate who is the second-best character voiced by Peter Cullen. EOR is applied to an Choice, which is enabled by an Opportunity such as a Card, or the gain of a Favor, and is used to evaluate how much money you will actually gain as a result of that Choice. EOR is calculated as:

EOR = E - (A * R)

E is the Echoes you stand to gain by taking your choice. A is the Action cost of your Choice. Either or both of these may be Expected Values, if there is probability involved.

R stands for Replacement, and is the EPA value of whatever grind you would be doing otherwise. For most end-game players, R is 1.64 from Affair of the Box. Players with access to Spirifage or the Goat-Demon grind may have higher values for R, but I will be assuming AotB for simplicity.

EOR is, very simply, the extra Echoes you make from your Choice instead of grinding Affair of the Box.


Revisiting A Highly Contrived Example



Let us use EOR to evaluate the hypothetical situation above, and see how it performs.
  • Pebble: E - (A * R) = 10 - (1 * 1.64) = 8.36
  • Boulder: E - (A * R) = 50 - (10 * 1.64) = 33.6

If we spend one Action to do Pebble, and spend the rest out of our day grinding AotB, then we will be eight Echoes and change richer than if we have simply ignored the opportunity. If we spend ten Actions to do Boulder, we will be more than thirty Echoes richer. By this metric, Boulder is around four times better. I don't know about you, but this aligns closer with my expectations.


A Real-World Example


NONE CAN ESCAPE THE OVERGOAT. Certainly not this post, which is now about Overgoats. Specifically, the Overgoat Opportunity Card. The options are actually fairly similar to the hypothetical above. We shall now calculate which of Overgoat-unlocked options is more profitable.

We start by defining the Opportunity, which is the Overgoat card. Next, we define the Choices. There are two Options on the card, but there are actually four Choices when one considers the possibility of using Second Chances or not. Following the example of the Wiki, I will evaluate a Second Chance as costing one Action to obtain it from wherever. For simplicity, I'll be using 50% and 75% as the success probabilities.
  • Ask the Goat, No second Chance: 75% chance of 2.5 Echoes, 25% chance of 1 Echo. EOR = E - (A*R) = 2.125 - (1*1.64) = 0.485.
  • Ask the Goat, Second Chance: 93.75% chance of 2.5 Echoes, 6.25% chance of 1 Echo. EOR = E - (A*R) = 2.406 - (2*1.64) = -.874
  • Use the Goat, No Second Chance: 50% chance of 25 Echoes, 50% chance of 2.5 Echoes. EOR = E - (A*R) = 13.75 - (8*1.64) = 0.63
  • Use the Goat, Second Chance: 75% chance of 25 Echoes, 25% chance of 2.5 Echoes. EOR = E- (A*R) = 19.375 - (9*1.64) = 4.615

I must say, these are not the results I was expecting. That means the science is working! I thought the numbers for using the Overgoat would be higher, but the Challenge seems to be well-tuned for its Action cost and Echo payout.


Note that technically, this is in accord with the results of the wiki, which say the EPA is similar for the two actions. It's just that the Boulder-ish option sustains that EPA over a larger number of Actions, giving a larger total payout.

Other Notes

I think that EOR is composable. By this, I mean that if we calculate (e.g.) the EOR of exchanging 15 CP of Connected: Hell for Brass, then we can plug that number straight in as an Echo value when calculating the EOR of something that gives CP Hell as a reward. I need to run through a scenario to verify, but I'm pretty sure it works out this way.

I want to eventually use this to calculate the value of Expeditions and Expedition Supplies, but it's late. That will wait for another day. In the meantime, I would appreciate any feedback, ideas, corrections, or disagreements anyone cares to make.
edited by PSGarak on 4/17/2017

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Siankan
Siankan
Posts: 168

8 days ago
Fascinating work, but you have one major flaw: Eeyore is not a horse.

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Kaijyuu
Kaijyuu
Posts: 332

8 days ago
Yeah I was thinking similarly to this recently. Personally I've just called it "profit", as an action always has the opportunity cost of your base grind's EPA. Just calling it profit would be a bit misleading though, as it'd imply your base grind has 0 profit, when it does in fact make you money.

There are probably some fancy-schmancy economics terms that could be used, too.
edited by Kaijyuu on 4/15/2017
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Guy Scrum
Guy Scrum
Posts: 197

8 days ago
This seems like a good metric. One tiny problem with your goat math though: you only use the second chance if you fail the first one, so the expected action cost (to replace the second chance) is quite a bit less. For "Ask the Goat" this comes out to EOR = 2.406 - 1.25*1.64 = 0.35, and for "Use the Goat" it is EOR = 19.375 - 8.5 * 1.64 = 5.44.

Edit: Never mind, this is totally wrong as xKiv points out below. Evidently I've been North for too long and forgot how things work back in London.
edited by Guy Scrum on 4/17/2017

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Optimatum
Optimatum
Posts: 2141

8 days ago
This seems like a useful metric, though I still feel like there's still a little something missing - I haven't quite nailed down what yet. I've been thinking about the same issue of EPA being misleading for grinds of different action lengths, ie something like 8 actions to gain 7 TC favours and cash them in on the conflict card vs 3.5 repetitions of the CoC grind. (Several similar situations have come up in a big discussion of all the ways I try to optimize my grind that I'm writing up.)

While looking at your post I also thought of a slightly different way to represent the same concept, though I haven't come up with a catchy name for it: relative EPA. In other words, EPA of the limited grind minus EPA of the base grind. (This ideally should always be provided alongside the number of actions per limiting factor, such as the 1/10 action split in your Pebble/Boulder example.) This gives basically the same information as EOR*. Mine just states the difference in EPA alongside A, instead of doing the math to combine the two variables before presenting them.

*EOR is essentially (EPAlimited * A) - (EPAbase * A) while my idea is (EPAlimited - EPAbase) * A

Edit: You mentioned this post was prompted by the recent discussions on expeditions. You also mentioned that, as with EPA, expected values may be used for measuring both the echo and action inputs to your equation. My question is, how do we actually calculate this in more complex situations? This is relevant to both EPA and EOR but it's more relevant for EOR, as far as I can tell. Just using the mode for actions instead of the mean is more of a concern when you need the exact number of actions to get the correct base profit, which is a number often on a bigger scale than EPA.

The Spirifage grind is a good example of simplicity: it's easy to calculate the average Soul gain from UB in Spite, and from there calculate the average action cost as well. But what about Expeditions, for example? The DBH typically takes one number of actions plus another number for gathering Supplies. But with optimal option order, getting A sign occasionally will save one action during the expedition phase, while even more occasionally it will save none. (Plus saving four or occasionally three Supplies that won't need to be gathered next time, the Docks Favours needed, and the Rostygold needed for some sources.)
edited by Optimatum on 4/15/2017

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dov
dov
Posts: 1433

8 days ago
The math is fine, but I don't think this is a useful or practical metric.

The main problem is that it's a subjective metric, and not an objective one. The opportunity cost is different for different players, while Actions and Echoes (which comprise the basic EPA metric) are the same for all.

Using a standard EPA allows a knowledgeable player (or the community) to give an authoritative number, and then it's up to each player to compare this to their individual alternative.

I think it's much easier to do this (just need to remember to take into account opportunity cost, which is, again, subjective), then for each player to calculate their own EOR which is situational, and some players just won't know how to do anyway.


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edited by dov on 4/15/2017

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Gillsing
Gillsing
Posts: 936

8 days ago
EOR could be renamed BTB (Better Than Box) so there's less risk of anyone confusing it with EPA. It's always been obvious to me that EPA is supposed to be compared to other, readily available EPA for the given player/character. Is it really that complicated?
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dov
dov
Posts: 1433

8 days ago
Gillsing wrote:
EOR could be renamed BTB (Better Than Box) so there's less risk of anyone confusing it with EPA.

Some people have base grinds which are better than the Affair of the Box. Some (most) players don't even have that.

But saying that some action has a 1.5 EPA is easy to understand. End game players immediately know this isn't worth their time, and low/mid level players might like it just fine.

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Pumpkinhead
Pumpkinhead
Posts: 320

7 days ago
Optimatum wrote:
(EPAlimited * A) - (EPAbase * A) while my idea is (EPAlimited - EPAbase) * A

For the record, these are exactly the same thing by the distributive property.

Honestly, I was kind of already doing this. But I do have to agree with Dov, EPA is still more useful. EOR is entirely subjective, as well as based around occasional opportunities. People are still going to make most of their money from grinds, which EPA is a fine measure for.
I think EOR could be useful, but it's certainly not a replacement for EPA as mentioned toward the top of your post.

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Optimatum
Optimatum
Posts: 2141

7 days ago
Gillsing wrote:
EOR could be renamed BTB (Better Than Box) so there's less risk of anyone confusing it with EPA. It's always been obvious to me that EPA is supposed to be compared to other, readily available EPA for the given player/character. Is it really that complicated?

Yes, it is. Among things, EPA can imply that one resource-limited sequence of actions is more profitable than another sequence limited by the same resource, when really the reverse is true.

For example, the Collections of Curiosities grind consumes one TC favour and one TC faction card per cycle. According to the wiki's estimates it has an EPA of 1.81 if done optimally. Meanwhile AotB has 1.64 EPA and Spirifage has somewhere around 1.79 EPA. The issue is that, when cashing in 7 favours, the TC/Society conflict card has 4.14 EPA. According to EPA the conflict card is unambiguously better than the CoC grind.

Doing the math, 3.5 repetitions of the CoC grind (126 actions and effectively 7 favours) is more profitable than 8 actions and 7 favours for the higher-EPA conflict card plus 118 actions for AotB. Meanwhile 3.5 cycles of the CoC grind is less profitable than 8 actions for the conflict card and 118 actions for Spirifage. Yet EPA implies the conflict card should be superior in both cases.

Pumpkinhead wrote:
Optimatum wrote:
(EPAlimited * A) - (EPAbase * A) while my idea is (EPAlimited - EPAbase) * A

For the record, these are exactly the same thing by the distributive property.


I'm fully aware of this. My point was not that the math worked out differently, but that my idea would give multiple pieces of information while PSGarak's only provides the end result.

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Kaijyuu
Kaijyuu
Posts: 332

7 days ago
Since the tomb colonies/collections thingy came up and it's relevant for the thread, I did the math for my own profitability on the matter.

For the purpose of whole numbers, I'm determining the value of 14 favors using both methods. Also I consider a collection turn-in to cost 2 favors and 2 actions, since it requires use of the Tomb Colonies card for the turn-in.

14 favors = 7 Collection turn-ins, netting 455 echoes.
Action count: 34 per collection, 2 per turn-in, totaling 252 actions
This is 1.80555... EPA, 455 echoes.

14 favors = 2 conflict cards = 66.2 echoes.
14 actions to gain favors, 2 to turn in, 16 actions total.
252 - 16 = 236 actions of base grind to be accounted for
236 * 1.73 (my base grind) = 408.28
408.28 + 66.2 = 474.48
This is 1.8828.. EPA, 474.48 echoes

Now to calculate EOR, if that's what we're calling it.
252 * 1.73 = 435.96 base EPA

Collections: 455 - 435.96 = 19.04.
19.04 / 252 = 0.0755... EOR

Conflict cards: 474.48 - 435.96 = 38.52
38.52 / 252 = 0.152857... EOR


Notes:
Using wilmont's end, there's a rare success on one of the actions to get an additional echo of compromising documents. I don't know the chances of this, but it probably bumps up the EPA by a few pence.
The conflict card has a few opportunity costs that are hard to calculate; you won't always get the conflict card when you want it, leaving you either holding in your hand for a long time or holding a Tomb Colonies card in your hand while waiting at 7 favors. Also, the Collections grind lets you get various stats up, which makes up for Nadir trips, probably letting you stay up to 9 irrigo instead of 5 without stat atrophy.
If you use Affair of the Box as your base grind, then their profitability/EOR is almost the same, meaning the above concerns probably tip it in the Collection's favor.


Ultimately, we should take a step back and ask ourselves what we're trying to do. Really, what we want to know is how much faster we are to obtaining a Cider (or other goal), and EPA is a fine measure of that. It's not so great when comparing two mutually exclusive opportunities, but pretty much any method of doing that is going to take into account big opportunity costs and be complicated to determine.
edited by Kaijyuu on 4/15/2017
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xKiv
xKiv
Posts: 620

7 days ago
Guy Scrum wrote:
This seems like a good metric. One tiny problem with your goat math though: you only use the second chance if you fail the first one, so the expected action cost (to replace the second chance) is quite a bit less. For "Ask the Goat" this comes out to EOR = 2.406 - 1.25*1.64 = 0.35, and for "Use the Goat" it is EOR = 19.375 - 8.5 * 1.64 = 5.44.


This is incorrect. You always use up the second chance.

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Gillsing
Gillsing
Posts: 936

7 days ago
Optimatum wrote:
Doing the math, 3.5 repetitions of the CoC grind (126 actions and effectively 7 favours) is more profitable than 8 actions and 7 favours for the higher-EPA conflict card plus 118 actions for AotB. Meanwhile 3.5 cycles of the CoC grind is less profitable than 8 actions for the conflict card and 118 actions for Spirifage. Yet EPA implies the conflict card should be superior in both cases.


All right, that does sound complicated. Though that's most likely because I'm not a Spirifage, so I don't really know what the numbers are for 118 actions of that. And the TC and CoC abbreviations are not native to my brain, even if I realise what they mean. For things that are complicated I prefer to stick to words that everyone can understand. When it comes to Tomb Colony favours I only trade them in when I have more than five, since that's all I need for the conflict card (Going gentle), and I get more echoes per favour if I spend the least amount necessary for the extra Favour in High Places that does not scale up with the number of favours.
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Optimatum
Optimatum
Posts: 2141

7 days ago
Gillsing wrote:
When it comes to Tomb Colony favours I only trade them in when I have more than five, since that's all I need for the conflict card (Going gentle), and I get more echoes per favour if I spend the least amount necessary for the extra Favour in High Places that does not scale up with the number of favours.

That's actually backwards: Going gentle is the one conflict card where spending seven favours is better than spending five. Each favour above three gives 5 echoes in wine, so spending seven favours is an extra 10 echoes for only two actions. As such spending five favours on the card is 3.85 EPA while spending seven is 4.14 EPA.

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dov
dov
Posts: 1433

7 days ago
Optimatum
That's actually backwards: Going gentle is the one conflict card where spending seven favours is better than spending five.[/quote
wrote:

As far as I know, this is true for all conflict cards, except for Constables/Criminals, where the reward from the Constables is the same whether you use 5, 6, or 7 Criminal Favours. In all other cases, the reward scales with the number of Favours used.

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Gillsing
Gillsing
Posts: 936

7 days ago
Optimatum wrote:
That's actually backwards: Going gentle is the one conflict card where spending seven favours is better than spending five. Each favour above three gives 5 echoes in wine, so spending seven favours is an extra 10 echoes for only two actions. As such spending five favours on the card is 3.85 EPA while spending seven is 4.14 EPA.

Oh, I think I failed to consider that the 250 bottles of extra wine were 2 pence a piece rather than 1 penny each. Shows how little I care about the game nowadays I guess. But my regular grind is worse than Collections of Curiosities, so if I can spend 35 actions doing that instead of my regular grind, that's 4.85 Echoes for each favour. And I need the stats I get from War of Assassins to cover for my weekly visits to the cave. 4 extra cards of Nadir for 2-3 trade-ins that are 15 pence lower per favour still sounds like a good deal. So I guess I'll still keep doing what I'm doing. In case I get back to caring again.
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Kaijyuu
Kaijyuu
Posts: 332

6 days ago
dov wrote:
As far as I know, this is true for all conflict cards, except for Constables/Criminals, where the reward from the Constables is the same whether you use 5, 6, or 7 Criminal Favours. In all other cases, the reward scales with the number of Favours used.

It's true that they scale, but Going Gentle is the only one that really gets better with more favors spent. The rest, ideally, should be played at 5 favors, though the difference is often marginal.

If you're waiting on drawing a conflict card, it's still better to gain favors than keep favor cards in your hand (except crime and punishment of course). This is because you're more likely to draw that favor generating card again than draw the conflict card, so it's a waste to keep it around and not use it. Your overall EPA will go down, but the number of actions used will go up, so your total profit will go up.
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 Saklad
Saklad
Posts: 290

6 days ago
PSGarak wrote:
Then a giant crab will give us money for them, or something.



  • I don’t think Temtum gives cash rewards for innovative thinkers.

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    PSGarak
    PSGarak
    Posts: 197

    5 days ago
    Thanks to all of you for your feedback, especially Siankan for Eeyore's proper taxonomic classification.

    Pumpkinhead wrote:
    EOR is entirely subjective, as well as based around occasional opportunities. People are still going to make most of their money from grinds, which EPA is a fine measure for.

    I'm replying to several people here, but Pumpkinhead stated it the most succinctly.

    First, EOR is relative but it is not subjective. Different players will have different values for EOR, but any one player's EOR is a completely objective calculation. While it complicates things, EOR being relative is not strictly a bad thing. It reflects the reality that some actions have different values to different players, and this may impact which choice is the best. In practice, it's not such a big burden: Most players deep enough in the game to spend time calculating this stuff will mostly have one of maybe three EOR values.

    Second, I think we're all in agreement when EPA should be used and when EOR should be used. EPA reflects grinds (i.e. action-limited choices), and EOR is intended for otherwise-limited choices. Pumpkinhead has a valid point that players probably make the bulk of their cash from grinds. But grinds are easy to understand, and we spend more time and effort on this forum trying to crunch numbers of non-grinds.

    As an aside, EPA still has a use for non-grind actions: It tells you whether something is worth doing or not, compared to your best grind available. EOR takes more work if that's the only answer you want. As Optimatum said, where EOR gives more accurate answer than EPA is when evaluating one opportunity which may have different available uses.

    The more that I think about it, the more I'm of the opinion that the real value of EOR is something that I stated in the footnote down at the very bottom of the post: It's composable. By that, I mean that you can calculate the EOR of complicated set of actions by simply adding together the EOR of its individual pieces. That is difficult to do with EPA because ratios don't combine easily. But EOR represents net-profit consider effort of turn-ins. This should allow us to calculate the profitability of bighuge action sets (like expeditions) by breaking it down into smaller parts.

    I'm going to demonstrate what I mean by this by showing two different ways to calculate the EOR of a three-step process, and showing that they're equal. The process will be grinding casing, selling information to hell, and selling hell connections for brass. This is not actually profitable (EPA is around 1.03), but my point is that both methods produce the same result.

    Method 1: All at Once
    Spend 5 actions to generate 18 cp Casing. Spend 3 actions to convert 18 cp Casing to 90 cp Connected: Hell. Spend 6 actions to convert 90 cp Connected: Hell into 6x240=14.4 Echoes of Brass.
    EOR = E-(A*R) = 14.4 - (14 * 1.64) = -8.56.

    Method 2: In Pieces
    Part A: EOR of Connected: Hell
    Spend 1 action to convert 15cp Hell to 2.4 Echoes of Brass
    EOR = E-(A*R) = 2.4 - (1*1.64) = 0.76 EOR for 15cp Hell.

    Part B: EOR of Casing
    Spend 1 action to convert 6cp Casing to 30cp Hell. Echoes valued at 2 * 0.76, from Part A.
    EOR = E-(A*R) = 1.52 - (1*1.64) = -0.12 EOR per 6cp Casing.

    Part C: EOR of Gang of Hoodlums
    Spend 5 actions to generate 18cp Casing. Echoes valued at 3 * -0.12, from Part B.
    EOR = E-(A*R) = -0.36 - (5*1.64) = -8.56.

    Both calculation methods produce the same result! It's more work, but Method 2 provides us with two important advantages. First, the intermediate steps are re-usable. This is actually a concrete value Echo value for Connected: Hell. It can be used as part of evaluating any other action that generates Connected: Hell. For example, the option on the Faction card: one action for 0.51 Echoes. Boom, done. Another example: Consideration for Services Rendered. The cost is 10.1 pennies of Connected: Hell for 30 pence of brass and some cp of Someone is Coming. As soon as we calculate the value of SiC, those values can simply be summed. Because these pieces are re-usable, the community can more easily converge towards agreed-upon valuations for common resources like Favors and Souls and Collections of Curiosities, which will make valuing difficult things like Expeditions easier.

    Secondly, it makes it easier to review and revise the calculation. The assumptions and the values of different resources are immediately apparent. If there's a better way to spend Connected: Hell (say, by a conflict card), updating all of the calculations is simple. If some players place a different value on SiC (because they have different options available), it's easier to see what impact that has. By comparison, EPA calculations tend to be monolithic and they're difficult to update when two players disagree on assumptions.

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    Optimatum
    Optimatum
    Posts: 2141

    5 days ago
    A suggestion, to limit the issue raised of numbers varying by player. How about when EOR is presented outside of math, it's given as the Echoes value alongside an example EOR for AotB? That way:
    • The majority of players will have a number relevant for themselves
    • Players using more profitable grinds like the Soul Trade can approximate whether the action in question will be profitable personally, based on whether the EOR is significant or only slightly above zero
    • Players who want the exact numbers for other grinds with have the Echoes value immediately available for calculations
    PSGarak wrote:
    Second, I think we're all in agreement when EPA should be used and when EOR should be used.

    I suspect this was a case of miscommunication due to poor phrasing: "I've been noodling on an idea for a replacement for a while".

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