3434 replies to this topic

[aku chi]

Now, if I have indeed inverted the concept, why don't you show me how you think it should be done properly so I can tell you how you are wrong?

Have you stopped beating your wife?

I think you mess up oppportunity cost. Remember, best alternative forgone? It doesn't include saving it for later use unless you think Marcia isn't getting enough bexp from what you earn in chapters 8 to 11 (since she mainly needs it for chapter 12, maybe unless you are going for ridiculous turns that Cynthia isn't allowing anyway). Now, if you think saving it for Marcia instead of using 350 on Mia is the "best alternative forgone", then fine. Do you? Also, what do you mean "cannot be lower than the opportunity cost of c11 bexp?" That bexp can go to Mia or Zihark. If you dump 400 bexp on Zihark in chapter 12 (not 11, btw, as Zihark is still an enemy during the base, yes?), then you can dump 400 on Mia instead. The op. cost is whatever it is. The cost for c8 could be lower or higher or whatever depending on what you think the best use of it in chapter 8 is.

If we're comparing the opportunity cost of Mia (or anyone) getting 350 Bexp in C8 and Zihark (or anyone) getting 350 Bexp in C12, the former cannot be less than the latter. Mia's Bexp must come from Chapters 1-7. Zihark's can come from chapters 1-7 or it can come from chapters 8, 9, 10, or 11. Bexp from these later chapters is strictly less valable than Bexp from chapters 1-7 because C1-7 Bexp can be used in all of the ways C11 Bexp can be used - and more.

Concerning the opportunity cost of 350 Bexp in C8, I don't know what it precisely is. It might be giving more to Boyd or Oscar, it might be saving it to give to Marcia. It might even be giving it to Jill. Whatever the case may be, the opportunity cost of 350 Bexp in C12 must be lower, because we now have more total Bexp to give to their most valuable recipients. We've already given the Bexp to, for instance, Boyd or Oscar or Marcia, or saved it for Jill. So the next best use might be giving it to Kieran or giving more to Marcia/Jill, or saving it for Astrid/Makalov.

That's the most insane thing I've heard in a while. Higher in c8 than in c12? You are saying that it is a lower op cost to save 350 bexp from chapter 8 all the way to 12, and not use it until then, than it is to just give it to Mia? Best alternative forgone. The op. cost is the SAME. Whatever you do with that 350 bexp in chapter 8, whether you give it to Mia or save it for Zihark, the best alternative is whatever the best alternative is. It doesn't change.

I agree. But if we give Zihark 350 Bexp in C12, it can be from the less valuable C11 and/or C10 Bexp cache. Capiche?

So I'll bring up Mia and Geoffrey again. Do you think if Mia gets 1000 bexp during her life until chapter 25, that Geoffrey is entitled to 1000 bexp before you can make any comparison to Mia? I find that nuts. This "each unit gets optimal resource bundle" thing is stupid. That's all I'm trying to say.

Both units getting one or the other's optimal resource bundle is a fine approach when comparing units with similar availability and similar (enough) optimal resource bundles. It is a poor approach when comparing units with very different availability and/or very different optimal resource bundles. (I would not recommend it in a Mia vs. Geoffrey comparison. I would in a Mia vs. Zihark comparison.) No matter the comparison approach, Mia must be penalized for the resources she receives in excess of Geoffrey. Likewise with Zihark, if you so choose to compare them with different resource bundles.

Where did I ever say it's free? Granted I suggested the cost is negligible, but for those that weren't happy with it I proposed a compromise where Zihark gets a portion of Mia's bexp but not the whole thing because of the cost of saving that bexp for chapters.

You contradict yourself: "The op. cost is the SAME. Whatever you do with that 350 bexp in chapter 8, whether you give it to Mia or save it for Zihark, the best alternative is whatever the best alternative is. It doesn't change." But, as I explained above, an amount of Bexp given later is necessarily less valuable than the same amount given earlier.

And If you think I inverted PV/FV, then you need to re-read what I said. Or I'll try to reword it. Mia is the bank. You'll notice that Zihark's 500 bexp doesn't earn you interest or anything. Mia earns you interest because she uses it. This would be a completely different story if you could earn interest on bexp held from chapter to chapter. Which would be awesome, btw. I don't get how you think this is inverting when Mia is the 500 now, and Zihark is the 500 in 4 chapters. We know from PV/FV that money now is better than money in the future, and so giving Mia 500 bexp is worth the investment because she gives us 500(1+i)⁴ value for that 500, whereas Zihark gives us 500 value for that 500. The cost is the same exact number, 500. To use it early it gives bigger gains. That much is also intuitive from the playing of the game. "Mia can make contributions before Zihark joins, and those should absolutely be factored into a comparison between the two units..." So we are agreed.

All else being equal, Bexp used earlier is more valuable than Bexp used later. Don't you see: that also increases the opportunity cost of using Bexp earlier! C1-7 Bexp can make Boyd or Oscar more valuable in chapters 8-11 (and more). C11 Bexp cannot. C1-7 Bexp can be used in all of the ways C11 Bexp can be used, but the reverse is not true. Therefore, C1-7 Bexp is more valuable than C11 Bexp - it has a higher opportunity cost. If Mia takes 350 of the former and Zihark takes 350 of the latter, we pay a higher opportunity cost in the former scenario. (But, I repeat myself.)

But all else is not equal when we consider the value of Bexp when used. The recipient of the Bexp determines the value of the investment. Would you agree that it is more valuable to give Rolf X Bexp in C9 instead of saving that X Bexp to give to Marcia in C10? Of course not - that would be absurd. But that conclusion would be warranted from your naive application of PV/FV. If I'm understanding your application correctly, Bexp given earlier provides a greater investment than Bexp given later by virtue of it being given earlier. What a unit can actually do with the Bexp is not considered in your analysis.

[Tricky Dick]

You're assuming your conclusion. Mia gets Bexp and Zihark doesn't because Mia is better. Therefore, Mia is better than Zihark. If you're so confident that Mia is more valuable than Zihark, compare them when they both receive the same resources. (See this post and surrounding conversation for evidence of the rigor of this approach.)

Why should they get equal resources? The BExp on Mia in Chapter 8 goes a lot farther both in the short and long run than it does sitting in the convoy until Zihark shows up. In the now, Mia's stock rises in Chapters 8/9 due to having an immediate impact on her performance in forced chapters. And in the future, she has similar stats to Zihark but is much closer to promotion than he is, making her the more attractive option.

Even with equal resources, the only thing Zihark can do is close the level gap and take a very slight statistical advantage on Mia. Mia's existance until Zihark's appearence is still worth more.

[Narga_Rocks]

If we're comparing the opportunity cost of Mia (or anyone) getting 350 Bexp in C8 and Zihark (or anyone) getting 350 Bexp in C12, the former cannot be less than the latter. Mia's Bexp must come from Chapters 1-7. Zihark's can come from chapters 1-7 or it can come from chapters 8, 9, 10, or 11. Bexp from these later chapters is strictly less valable than Bexp from chapters 1-7 because C1-7 Bexp can be used in all of the ways C11 Bexp can be used - and more.

Um, dude, Mia can get bexp from chapters 8, 9, 10, 11, in addition to what she got from 1-7. If you want to give Zihark "Mia's optimal resource bundle", by definition it needs to be c1-7 bexp because that is where Mia's 350 came from.

Concerning the opportunity cost of 350 Bexp in C8, I don't know what it precisely is. It might be giving more to Boyd or Oscar, it might be saving it to give to Marcia. It might even be giving it to Jill. Whatever the case may be, the opportunity cost of 350 Bexp in C12 must be lower, because we now have more total Bexp to give to their most valuable recipients. We've already given the Bexp to, for instance, Boyd or Oscar or Marcia, or saved it for Jill. So the next best use might be giving it to Kieran or giving more to Marcia/Jill, or saving it for Astrid/Makalov.

Again, Mia can get that bexp, too.

I agree. But if we give Zihark 350 Bexp in C12, it can be from the less valuable C11 and/or C10 Bexp cache. Capiche?

But it can't be from c11 or c12, because Mia can take it, too. If you give Zihark 300 bexp in chapter 12, and you didn't save it from chapter 7, then giving 300 bexp to Zihark means you should give 300 more bexp to Mia.

Both units getting one or the other's optimal resource bundle is a fine approach when comparing units with similar availability and similar (enough) optimal resource bundles. It is a poor approach when comparing units with very different availability and/or very different optimal resource bundles. (I would not recommend it in a Mia vs. Geoffrey comparison. I would in a Mia vs. Zihark comparison.) No matter the comparison approach, Mia must be penalized for the resources she receives in excess of Geoffrey. Likewise with Zihark, if you so choose to compare them with different resource bundles.

If they were to show up in the exact same chapter, I wouldn't complain about giving them the same bexp and compare them then. But they don't. Mia appears earlier. Whatever you choose to do with the chapter 1 to 7 bexp is a completely separate problem from what you do with the chapter 8, 9, 10, or 11 bexp. You can't give Zihark chapter 11 bexp if you aren't willing to give Mia the same deal.

You contradict yourself: "The op. cost is the SAME. Whatever you do with that 350 bexp in chapter 8, whether you give it to Mia or save it for Zihark, the best alternative is whatever the best alternative is. It doesn't change." But, as I explained above, an amount of Bexp given later is necessarily less valuable than the same amount given earlier.

Then on that we differ. The op cost is the same because it is the same bexp. You either save it for Zihark or spend it, therefore it is the same cost. You can't give Zihark new bexp without considering giving new bexp to Mia. This is the problem with not saving bexp for a guy. New bexp, more for all your units. Not just the new ones.

All else being equal, Bexp used earlier is more valuable than Bexp used later. Don't you see: that also increases the opportunity cost of using Bexp earlier! C1-7 Bexp can make Boyd or Oscar more valuable in chapters 8-11 (and more). C11 Bexp cannot. C1-7 Bexp can be used in all of the ways C11 Bexp can be used, but the reverse is not true. Therefore, C1-7 Bexp is more valuable than C11 Bexp - it has a higher opportunity cost. If Mia takes 350 of the former and Zihark takes 350 of the latter, we pay a higher opportunity cost in the former scenario. (But, I repeat myself.)

But all else is not equal when we consider the value of Bexp when used. The recipient of the Bexp determines the value of the investment. Would you agree that it is more valuable to give Rolf X Bexp in C9 instead of saving that X Bexp to give to Marcia in C10? Of course not - that would be absurd. But that conclusion would be warranted from your naive application of PV/FV. If I'm understanding your application correctly, Bexp given earlier provides a greater investment than Bexp given later by virtue of it being given earlier. What a unit can actually do with the Bexp is not considered in your analysis.

I'm pretty sure I'd rather give Marcia 900 bexp than give Rolf 1000 bexp. Also, the interest rate is dependant on the unit. The interest rate isn't the same for each unit. Remember, the interest rate is defined by the return on investment. When you do PV/FV you go with inflation at a minimum or you can try to use what you'd earn at the bank, but this is FE. Each unit gives a different return. Rolf gives little on the investment, therefore the interest rate is small. Heck, we'd be comparing more like 990 bexp for Marcia compared to 1000 bexp for Rolf. I don't see how that's wrong. Rolf gives us something, and therefore giving him a small edge in bexp value for that 1 chapter makes sense. Except your example was bad and you should feel bad. You can't give Mist or Rolf bexp in chapter 9. They appear after you click start. A better comparison would be Rolf vs Nephenee or something. Neph gets bexp in chapter 11 base, Rolf in chapter 10 base. But would I rather give Neph 900 bexp or Rolf 1000? Obviously the former. So basically, Rolf gives us value for chapter 10, however small, and that needs to be accounted for somehow. I believe the simplest way is to give the later unit less bexp in the comparison.

[aku chi]

We seem to be doing a very bad job communicating with one another. Let's try to identify our initial point of diagreement.

Do you agree or disagree with the following:

300 Bexp earned completing chapter 7 is more valuable than 300 Bexp earned completing chapter 11.

[Narga_Rocks]

We seem to be doing a very bad job communicating with one another. Let's try to identify our initial point of diagreement.

Do you agree or disagree with the following:

300 Bexp earned completing chapter 7 is more valuable than 300 Bexp earned completing chapter 11.

I don't believe you can compare them so easily. Your point is that you can spend bexp earned in chapters 1 to 7 in anywhere from chapter 8 until final, and so it is worth more than bexp that can be spent from chapter 12 until final since there are more options. Or I think that's what you are saying. But that reasoning is flawed because the cost is defined by best alternative forgone and not the number of alternatives. If the best way to use 300 bexp is to save it until chapter 12 or later, then they have equal cost because you are saying the best use is the exact same, hence same cost.

If the best use of chapter 1-7 bexp is to spend it in chapters 8 to 11, then I can see how an argument could be made that it is more valuable. After all, you can't use chapter 11 bexp in chapter 11 base. Or 8, 9, 10. And putting 300 bexp on Marcia in chapter 10 clearly has higher returns than 300 bexp on Marcia in chapter 12 simply due to Marcia having more time to use it. But what if we aren't putting it on the same unit? 300 bexp on Marcia in chapter 10 or 300 bexp on Jill in chapter 13? You can't put that bexp on Jill any earlier, so you earned 300 bexp in chapter 9 and put it on Marcia, and earned 300 bexp in chapter 12 and put it on Jill. Now, let us further assume that those are the second best uses of that 300 bexp. So now the value of the chapter 9 bexp is 300 on Marcia, and the value of the chapter 12 bexp is 300 on Jill, provided we instead use the 600 bexp the best way possible. Now let us assume that you aren't giving that 600 bexp to Marcia and Jill because you want to place that bexp on the best possible place. Are we then to assume that the 300 bexp on Marcia is more valuable than the 300 bexp on Jill simply because Marcia came earlier? Of course not. We have to determine if 300 extra bexp for Marcia for chapters 10 to F is worth more or less than 300 bexp on Jill for chapters 13 to F. So although it is possible for chapter 7 bexp to be more valuable than chapter 11 bexp, it is also possible for this not to be the case.

[Olwen]

On what basis do you give value to bexp?

[Narga_Rocks]

On what basis do you give value to bexp?

op. cost. Everything has an opportunity cost, because if you give unit A some bexp/skill/uncommon weapon, it could've gone to unit B, C, or D. So the "value" of bexp would then be the cost of not giving it to the best option, say B. Unless you give that bexp to B, because then the value would be giving it to second best, say C.

[aku chi]

On what basis do you give value to bexp?

In this tier list: how valuable it is to completing the game efficiently. Imagine two efficient playthroughs. Suppose that in the first playthrough, we have access to some chunk of Bexp, but in the second playthrough we do not have access to that same chunk. The value of that Bexp chunk is however much the first playthrough is more efficient than the second. Opportunity cost is a related concept. While value as defined previously results from giving the Bexp chunk to the most optimal recipient(s), opportunity cost is a way to evaluate the value that we lose by giving the Bexp to certain recipients. The opportunity cost is the value we would have received had the Bexp chunk gone to its next best alternative(s).

I don't believe you can compare them so easily. Your point is that you can spend bexp earned in chapters 1 to 7 in anywhere from chapter 8 until final, and so it is worth more than bexp that can be spent from chapter 12 until final since there are more options. Or I think that's what you are saying. But that reasoning is flawed because the cost is defined by best alternative forgone and not the number of alternatives. If the best way to use 300 bexp is to save it until chapter 12 or later, then they have equal cost because you are saying the best use is the exact same, hence same cost.

I was insufficiently precise: the value of 300 C7 Bexp is at least as great as the value of 300 C11 Bexp. In almost all cases, the value will be greater.

If the best use of chapter 1-7 bexp is to spend it in chapters 8 to 11, then I can see how an argument could be made that it is more valuable. After all, you can't use chapter 11 bexp in chapter 11 base. Or 8, 9, 10. And putting 300 bexp on Marcia in chapter 10 clearly has higher returns than 300 bexp on Marcia in chapter 12 simply due to Marcia having more time to use it. But what if we aren't putting it on the same unit? 300 bexp on Marcia in chapter 10 or 300 bexp on Jill in chapter 13? You can't put that bexp on Jill any earlier, so you earned 300 bexp in chapter 9 and put it on Marcia, and earned 300 bexp in chapter 12 and put it on Jill. Now, let us further assume that those are the second best uses of that 300 bexp. So now the value of the chapter 9 bexp is 300 on Marcia, and the value of the chapter 12 bexp is 300 on Jill, provided we instead use the 600 bexp the best way possible. Now let us assume that you aren't giving that 600 bexp to Marcia and Jill because you want to place that bexp on the best possible place. Are we then to assume that the 300 bexp on Marcia is more valuable than the 300 bexp on Jill simply because Marcia came earlier? Of course not. We have to determine if 300 extra bexp for Marcia for chapters 10 to F is worth more or less than 300 bexp on Jill for chapters 13 to F. So although it is possible for chapter 7 bexp to be more valuable than chapter 11 bexp, it is also possible for this not to be the case.

I believe you have erred here. I will try to demostrate this using your example.

Suppose that the 300 C12 Bexp did not exist. The only (relevant) Bexp we have is the 300 we have in C10. If we are playing efficiently, we will use this Bexp in the way that helps us complete the game most efficiently (it's optimal use). This might be to give it immediately to Marcia. It might be to give it to Jill in C13. Assuming those are the two best options, the second best option is the opportunity cost of that 300 Bexp.

Now let's add back in the 300 C12 Bexp. Suppose, as you have, that the optimal way to distribute Bexp is to give 300 to Marcia in C10 and give 300 to Jill in C12. Let's consider the opportunity cost of those distributions. When considering the opportunity cost for giving Marcia 300 Bexp in C10, we cannot ignore the fact that we will receive another 300 Bexp in C12. Whether or not Marcia gets the C9 Bexp, that 300 C12 Bexp will exist. As per our assumption, the best use of the C12 Bexp is to give it to Jill. The opportunity cost of the C9 Bexp then, is giving 300 more Bexp to Jill, or giving it to some other unit. Likewise, when giving Jill the 300 Bexp from C12, we've already given Marcia 300 Bexp. The opportunity cost of the C12 Bexp is giving 300 more Bexp to Marcia, or giving it to some other unit. Under no circumstance can the opportunity cost of C12 Bexp be higher than the opportunity cost of C9 Bexp.

It's the marginal costs that matter when considering the opportunity cost of Bexp. I've made this mistake myself, in the past.

[Narga_Rocks]

I believe you have erred here. I will try to demostrate this using your example.

Suppose that the 300 C12 Bexp did not exist. The only (relevant) Bexp we have is the 300 we have in C10. If we are playing efficiently, we will use this Bexp in the way that helps us complete the game most efficiently (it's optimal use). This might be to give it immediately to Marcia. It might be to give it to Jill in C13. Assuming those are the two best options, the second best option is the opportunity cost of that 300 Bexp.

Now let's add back in the 300 C12 Bexp. Suppose, as you have, that the optimal way to distribute Bexp is to give 300 to Marcia in C10 and give 300 to Jill in C12. Let's consider the opportunity cost of those distributions. When considering the opportunity cost for giving Marcia 300 Bexp in C10, we cannot ignore the fact that we will receive another 300 Bexp in C12. Whether or not Marcia gets the C9 Bexp, that 300 C12 Bexp will exist. As per our assumption, the best use of the C12 Bexp is to give it to Jill. The opportunity cost of the C9 Bexp then, is giving 300 more Bexp to Jill, or giving it to some other unit. Likewise, when giving Jill the 300 Bexp from C12, we've already given Marcia 300 Bexp. The opportunity cost of the C12 Bexp is giving 300 more Bexp to Marcia, or giving it to some other unit. Under no circumstance can the opportunity cost of C12 Bexp be higher than the opportunity cost of C9 Bexp.

It's the marginal costs that matter when considering the opportunity cost of Bexp. I've made this mistake myself, in the past.

First off let me just say we are assuming Marcia and/or Jill are already getting a crapton of bexp. The assumption here is that an extra 300 bexp is still good on them, just not as good as placing 300 bexp elsewhere, specifically the best place for it. Consider them to be second best. At least, that's what I was going for.

But let's say that Marcia and Jill have been given none, to go with your example. And to keep things simple, you get precisely 300 bexp in chapter 9 and 300 bexp in chapter 12. You don't get any more. Now let's say that they are indeed the best outlets for it. Now, spending the second set of 300 is best used on Jill, for the sake of argument, even though we spent 300 bexp on Marcia already. Now let's look at giving any or all of this bexp to Boyd. Why is it impossible for the 300 on Jill to have higher value than the 300 on Marcia? Say the 300 on Marcia was mainly to improve those 3 chapters that Marcia is available and Jill is not, and Marcia doesn't do all that much good the rest of the game. But Jill takes that 300 bexp and does stuff for the entire game and gets lots and lots of use out of it. How is it then impossible for the second 300 bexp to have higher op cost?

Say we give all 600 bexp to Boyd. The op cost of the first 300 is Marcia, the op cost of the second 300 is Jill. Who is to say that the 300 on Jill isn't worth more than the 300 on Marcia?

[Olwen]

op. cost. Everything has an opportunity cost, because if you give unit A some bexp/skill/uncommon weapon, it could've gone to unit B, C, or D. So the "value" of bexp would then be the cost of not giving it to the best option, say B. Unless you give that bexp to B, because then the value would be giving it to second best, say C.

Sorry, I was wondering why bexp in Chapter 7 was more valuable than bexp in Chapter 11. Why isn't bexp just bexp? Why is one dump more valuable than the other?

[aku chi]

Sorry, I was wondering why bexp in Chapter 7 was more valuable than bexp in Chapter 11. Why isn't bexp just bexp? Why is one dump more valuable than the other?

If you're uninterested in reading the rest of the (very straight-forward) arguments, appeal to your intuition: is Bexp earned in C28 as valuable as Bexp earned in C1? Would you be indifferent between receiving all of the game's Bexp after completing chapter 28 and receiving it all before chapter 8?

Say we give all 600 bexp to Boyd. The op cost of the first 300 is Marcia, the op cost of the second 300 is Jill. Who is to say that the 300 on Jill isn't worth more than the 300 on Marcia?

Assumptions:

• There are only two (unconditional) sources of Bexp: 300 Bexp awarded after C9 and 300 Bexp awarded after C12.
• Jill getting 300 Bexp in C13 is more valuable than Marcia getting 300 Bexp in C10 is more valuable than Marcia getting 300 Bexp in C13 is more valuable than any other allocation of 300 Bexp, including giving Marcia or Jill both sets of 300 Bexp.

There are two ways to evaluate the opportunity costs of Boyd's two Bexp dumps. The first approach is to consider them in isolation and assume that the other Bexp goes to its optimal recipient. The second approach is to assume that Boyd will receive both sets of Bexp.

First approach - in isolation:
Opportunity cost for giving Boyd 300 Bexp in C10: We otherwise assume optimal allocation, so Jill will receive the C12 Bexp and giving the 300 Bexp in C10 to Marcia is the opportunity cost.
Opportunity cost for giving Boyd 300 Bexp in C13: We otherwise assume optimal allocation. As per our assumption, Jill receiving 300 Bexp in C13 is the most valuable assignment of 300 Bexp, so we assume that we reserved the C9 Bexp for this purpose. It is not possible to give Marcia the C12 Bexp in C10, so the opportunity cost is equal to giving the 300 Bexp in C13 to Marcia.

Second approach - in conjunction:
Opportunity cost for giving Boyd 300 Bexp in C10: Boyd is assumed to receive the C12 Bexp. As per our assumption, Jill receiving 300 Bexp in C13 is the most valuable assignment of 300 Bexp, so reserving the C9 Bexp for this purpose is the opportunity cost.
Opportunity cost for giving Boyd 300 Bexp in C13: Boyd is assumed to already have received the C9 Bexp. Jill receiving 300 Bexp in C13 is the opportunity cost.

In all cases, the opportunity cost for the C9 Bexp is at least as great as the opportunity cost for the C12 Bexp.

[Narga_Rocks]

Assumptions:

• There are only two (unconditional) sources of Bexp: 300 Bexp awarded after C9 and 300 Bexp awarded after C12.
• Jill getting 300 Bexp in C13 is more valuable than Marcia getting 300 Bexp in C10 is more valuable than Marcia getting 300 Bexp in C13 is more valuable than any other allocation of 300 Bexp, including giving Marcia or Jill both sets of 300 Bexp.

If we call your assumptions A > B > C > D, I'm not sure where C > D is coming from, but it probably doesn't make a difference. Technically, did I ever state that C > D? In fact, given what I said about Marcia's prospects the rest of the game (the theoretical Marcia, not the real one), it seems that D > C. But anyway, A > B > D is the main assumption here. A > B > D gives relevance to the example. Anyway, with this in mind I'll take a look.

There are two ways to evaluate the opportunity costs of Boyd's two Bexp dumps. The first approach is to consider them in isolation and assume that the other Bexp goes to its optimal recipient. The second approach is to assume that Boyd will receive both sets of Bexp.

First approach - in isolation:
Opportunity cost for giving Boyd 300 Bexp in C10: We otherwise assume optimal allocation, so Jill will receive the C12 Bexp and giving the 300 Bexp in C10 to Marcia is the opportunity cost.
Opportunity cost for giving Boyd 300 Bexp in C13: We otherwise assume optimal allocation. As per our assumption, Jill receiving 300 Bexp in C13 is the most valuable assignment of 300 Bexp, so we assume that we reserved the C9 Bexp for this purpose. It is not possible to give Marcia the C12 Bexp in C10, so the opportunity cost is equal to giving the 300 Bexp in C13 to Marcia.

Well, the op cost of the second isn't necessarily giving it to Marcia, but again it doesn't make much difference.

Second approach - in conjunction:
Opportunity cost for giving Boyd 300 Bexp in C10: Boyd is assumed to receive the C12 Bexp. As per our assumption, Jill receiving 300 Bexp in C13 is the most valuable assignment of 300 Bexp, so reserving the C9 Bexp for this purpose is the opportunity cost.
Opportunity cost for giving Boyd 300 Bexp in C13: Boyd is assumed to already have received the C9 Bexp. Jill receiving 300 Bexp in C13 is the opportunity cost.

In all cases, the opportunity cost for the C9 Bexp is at least as great as the opportunity cost for the C12 Bexp.

So let's say I'm willing to accept, for the moment, that bexp spent earlier is at least as costly as bexp spent later. But if I'm not smart enough to find the mistake, you can prove to me that 0 = 1 as well, so I say only for the moment.

How does this mean that Zihark is entitled to exactly the same amount of bexp as Mia, or more even if you want to "equate" the cost? In theory, if we can calculate the revenue and calculate the opportunity cost of giving Mia bexp in chapter 8, we don't need to give Zihark any bexp in chapter 12 and we can still make the comparison properly. Or you can give Zihark equivalent bexp and try to determine what the best use of that bexp is in chapter 12 and then subtract the op cost from his gain. Personally, I believe that neither of those calculations are easy. Maybe they aren't impossible, but certainly they are not easy. As such, it just seems simpler to reduce how much Zihark gets as a way of making it a wash. Again, how much to reduce may seem complicated, but you can just pick a range. Basically, even you'll accept that chances are there is enough bexp in a non-superltc game that Mia can make a positive economic profit from receiving some bexp in chapter 8. Like, to level 10 or something. But who is to say that giving Zihark, or even giving more to Mia, is even a net zero? Then how do you give Zihark the 500 bexp and look at their stats and say "Well, Zihark wins in stats, but he loses overall because that 500 bexp could've gone to Marcia to take out Seeker?" It just seems more difficult than my way. That is, both my original way and the compromise that never worked with anyone. The original way being, that 500 bexp was burned before Zihark showed up and it was a net gain (well, assuming it actually was a net gain. If it wasn't a net gain then this entire discussion is academic), and so we might as well consider the distribution of bexp based on their current situation and not some outdated idea of fairness. Heck, even if giving Mia that bexp and her actions from chapter 7 to 11 are a complete neutral, there's still no reason to then give Zihark bexp without giving some to Mia. She paid off her "op cost debt" by not being a worse choice for that 500 bexp than any other option.

And yes, this works even if the op cost is higher for the chapter 8 base distribution than the cost in chapter 12. With 4 extra chapters, it is easier to pay off 350 bexp in chapter 8 and 150 bexp (capping levels and whatnot) over the next 3. All a unit has to do is not be a net negative taking that bexp and they shouldn't have to be in some kind of bexp debt to a unit that we compare it with. And then when the new unit rolls around, they are looked at equally for the sake of more bexp. A unit like Rolf is obviously an inferior choice to using 700 bexp on Marcia or even Mist, the two units that appear in the base for chapter 10 with him, so when you compare Rolf to Jill there is no reason for Rolf to have an extra 700 bexp in the comparison. Now, if you are using him then it is possible for Rolf to have been given 100 or so bexp because everyone else got enough that giving Rolf 100 bexp was worth more than giving some other unit an extra 100 bexp, and then to compare to Jill there is no reason for Jill to get 100 bexp for free. You look at Rolf with 100 bexp and Jill with no bexp, then allocate bexp on each of them according to what is best on Jill, then make the comparison. Yes, Rolf has an extra 100 bexp over Jill in this comparison, whatever amount each of them is given in chapter 13, but that only makes sense because we only gave Rolf that 100 bexp in the first place because it was a net positive, or at least a net zero.

[aku chi]

So let's say I'm willing to accept, for the moment, that bexp spent earlier is at least as costly as bexp spent later. But if I'm not smart enough to find the mistake, you can prove to me that 0 = 1 as well, so I say only for the moment.

I'm not attempting anything duplicitous. Your intuition should confirm that (non-perishable) goods are more valuable (or, at least, no less valuable) when received earlier. Going through your simple example and determining opportunity costs was not trivial; I made a couple mistakes myself before correcting them. This rather highlights your point that the full and faithful way to compare Mia and Zihark (each receive their optimal resource bundle and each pay the opportunity cost associated with it) is error prone and more work than is needed. So let's discuss some alternatives that can demonstrate Mia > Zihark that are just as accurate.

One approach is the one I've already mentioned that I'm quite fond of. If Mia is better when given Zihark's optimal resource bundle than Zihark is when given Zihark's optimal resource bundle, then Mia is more valuable than Zihark. This approach can be tweaked to make agreed-upon divergances from Zihark's optimal resource bundle for Mia. For instance, if we can suppose that 300 Bexp in C9 is worth no more than 400 Bexp in C12, we might suppose that Mia gets the former instead of the latter.

I also like the approach you brought up: that if it can be shown/agreed that the cost of giving Mia X Bexp in C9 is no greater than the benefit she receives from it in chapters 9-11 alone, we can assume she receives the Bexp, ignore the costs of it and any contributions Mia makes before C12. Then, we compare Mia (+X Bexp and assumed Cexp) and Zihark's contributions from C12 on. It might not be possible to find such an amount X, so we can add another value Y, such that:

The opportunity cost of giving Mia X Bexp in C9 is no greater than the benefit in chapters 9-11 that Mia receives from X Bexp plus the opportunity cost of giving Zihark Y Bexp in C12.

Then, we assume that Mia gets X Bexp in C9, Zihark gets Y Bexp in C12 - and compare their contributions in C12 and beyond.

These comparison approaches are no less accurate than a full and faithful anaylsis, but it may be easier to reach a consensus conclusion than quibbling about different opportunity costs (which I certainly don't enjoy; I'd rather discuss how different units contribute to an efficient playthrough).

[Toothache]

There is something missing from all this - where does combat exp fit into all this? All of the focus of the discussion currently seems to be focused on BEXP, but that doesn't exist in isolation. How much combat is each unit going so see, and roughly how many levels of CEXP are we offering on average? You can't just say 'assumed cexp', you'll need to really define it for each chapter. This will mean testing, and retesting of strategies and seeing where each units are being used and therefore how much CEXP on average they are getting.

Less semantics, and more playing, methinks. Let's see some empirical evidence to back up all this wordy jargon we've seen lately

[Snowy_One]

How can you quantify that, especially on random mode? Only way to even start would be to get an identical team every time, but due to the RNG and that not every team will have the same units, you'll end up with teams at different levels each PT. Even on fixed, you won't always have enemies attack the exact same target if they have the option to attack multiple ones, not to mention random hits, misses, criticals.

Edited by Snowy_One, 25 February 2013 - 12:04 PM.