What's the big deal with turn-shaving arguments in tier lists?

[Redwall]

I have seen several LTC players critical of turns saved as a tiering criterion, which puzzles me. I'll try to communicate some of my thoughts on tiering this way.

Let's establish some definitions to make sure we're all on the same page. Unit X saves n turns in a particular team composition A={X,B} containing Unit X and a subset B of deployed units (and reclasses, stat-booster assignments, etc.) if the elements of subset B, operating on their own without Unit X, require a minimum of n additional turns to clear the level. We define B to contain only units (and their reclasses etc.) that are actually deployed. In general we can define other team compositions A' and corresponding subsets B'.

(Reliability can be self-consistently accounted for in this framework by computing expected turn-counts, and while I think it is preferable to think in terms of expected turn-counts [without necessarily computing them accurately], in this post I will mostly speak in terms of raw turn-counts for various argumentatively irrelevant reasons, unless otherwise stated.)

I'll list some examples of how I think the definitions can be applied.

1) (disclaimer: I've never played FE8, so I'll discuss a hypothetical game FE80) Consider Sath, a high-availability Paladin who is good enough to be banned from most FE80 drafts, yet whose absence from an all-out LTC of FE80 results in a minimum slowdown of only three turns. Suppose there also exists a Pegasus Knight named Venassa, whose combat stats are inferior to Sath's in every way but whose absence results in a slowdown of five turns even when Sath remains on the team. (I took the three-turn thing from Espinosa, though it should be obvious [in the actual FE8] that the increase in expected turn-count for this one context is much greater than three; because drafts and tier lists expect some reliability, I think it's preferable to consider expected turn-counts over raw turn-counts) There are those who suggest that this invalidates saved turns as a tiering criterion; after all, Sath is supposed to be better than Venassa, right?

This is not a problem; to avoid restricting discussion to only the One True Team, tier lists have traditionally considered a large ensemble of non-specific team compositions:

"Reality" [as pertains to tier lists] is what happens over an infinite number of imaginary playthroughs with a hypothetical tier player, the specifics of which are defined as closely as possible by the actual people participating in the discussion.

Consider the ensemble of non-specific team compositions containing Sath. If, on average, Sath's removal from each of these compositions increases the minimum expected turn-count across the ensemble to a lesser extent than does Venassa's removal from the ensemble of contexts containing Venassa, then Sath would be ranked above Venassa. For this reason, even in a tier list structured around minimizing the expected turn-count, the three-turn slowdown caused by Sath's removal from an otherwise full team is not by itself sufficient to remove him from the top-tier position.

2) Now consider the addition of some hypothetical characters S*th, all of whom have the exact same parameters and availability as Sath, with the caveat that it is impossible to deploy more than one of the S*ths (including Sath himself) in any stage. Going by Celes' definition of "saving a turn," each S*th would save zero turns in a context permitting any one S*th to be deployed and leaving all the others on the bench; the reason is that deleting (say) Sath from the game results in no increase in turn-counts when a S*th from the bench can be deployed. The definition presented here avoids this problem by considering only deployed units; all S*ths remain at the same position as they would if there were only one S*th. This is not an ad hoc fix since we can consider a large number of team compositions.

3) A problem to consider, one related to uniqueness, is the following: suppose in a hypothetical game FE60, there exists a Myrmidon (Rutger) who is great for boss-killing, and a Pegasus Knight (Thany) who can quickly transport Rutger to the boss. Suppose that in Rutger's absence, a clear with Thany takes 50 turns longer (because Thany can't fight well, nor can her non-Rutger teammates); that in Thany's absence, a clear with Rutger takes 50 turns longer (because Rutger's Mov is even lower than that of her non-Thany teammates); and that in the absence of both Thany and Rutger, the clear still takes 50 turns longer than it does in the presence of both Thany and Rutger. In other words, having either Thany or Rutger without the other makes no difference, whereas having both speeds up a clear by 50 turns. We can look at the problem like so:

The set {B,R,T} results in +0 turns.
The set {B,R} results in +50 turns.
The set {B,T} results in +50 turns.
The set {B} results in +50 turns.

where B is a supporting set of deployed units, R is Rutger, and T is Thany.

We see that there are two sets (the first and third) that contain Thany. Assuming the sets are weighted equally, removing Thany results in an average increase of 25 turns: one results in a set corresponding to no change from +50, while the other results in a set corresponding to a 50-turn slowdown from +0. Likewise for Rutger. Hence, across the ensemble, Thany and Rutger each receive credit in killing the boss. (I'm just using these numbers to convey the point more clearly; I realize that, for example, you won't have three +50s in practice.)

4) An issue arises when considering Edward, who shaves many turns in a trivial chapter but who only rarely (from what I'm told) does much else of note in subsequent parts of FE10. The objection seems to be that Edward is intuitively a bad unit since, with perhaps a few exceptions, he can't fight that well outside of 1-P, a stage in which he is simply the least bad option. Whether this is bothersome or not to a given person is dependent on how he or she perceives the goals of the tier list: are we using combat prowess/utility as a proxy for how many turns this unit cuts (across varying contexts blah blah), or are we using turn-shaving as a proxy for combat prowess/utility? I personally would agree with the former, so it's not a problem to me.

Finally, there are things like Lyn's first Prologue chapter, but I think people settled this type of thing long ago: there's no value in tiering mandatory actions, just as there's no value in tiering the A button above the L button.

tl;dr: I don't see a problem with using turn-shaving arguments in efficient-play tier lists, as long as we understand that we need to consider contexts beyond the one optimal combination of characters; that although no one's actually going to do all the math (which includes figuring out how to weight different outcomes in the ensemble), we can still get a rough feeling for how many turns a character is responsible for cutting in a given context; and that while "unique" contributions can be small, they should still be recognized.

Edited September 13, 2013 by Redwall

[Klokinator]

Why did you write this and who in their write mind (haha) would read this and not get a headache.

[dondon151]

tl;dr i don't know what you're trying to say.

most units save 0 turns if they join late enough in the game regardless of what arbitrary "contexts" you put them in. this is considering the gross definition rather than the net definition (i.e., you're comparing team + unit to team + empty slot). the turn shaving argument still breaks down there. i also disagree with your proposal that we shouldn't assume the best auxiliary team because that violates the concept of opportunity cost.

[General Horace]

this is long and confusing but from what I understand, what you're trying to say is something like Rath firing the Brave Bow at walls in Genesis is higher valued than anything Pent does, since he's replaceable as a lategame warper but Rath saves a turn or something by breaking walls and doing nothing else of value, but Pent is pretty much always deployed when he exists, and has very good combat, but probably doesn't save any turns directly like Rath?

ha, that was the best run-on sentance ever, and I'm too lazy to edit it but I think you get my drift.

[Redwall]

tl;dr i don't know what you're trying to say.

I cleaned the post up a bit. The gist of it is to examples of how turn-shaving arguments make conclusions similar to what we accept in existing tier lists (except for the Edward thing).

most units save 0 turns if they join late enough in the game regardless of what arbitrary "contexts" you put them in. this is considering the gross definition rather than the net definition (i.e., you're comparing team + unit to team + empty slot). the turn shaving argument still breaks down there.

As you suggest, these late joiners save 0 turns in a variety of contexts, so the turn-shaving argument seems to hold, albeit in a trivial way.

I wrote my post with the gross definition in mind to account for inferior units like Cecille having the potential to (more or less) replicate Luke's contributions, assuming only one Altean Cav is fielded long-term; if a variety of team compositions are considered, then we can still look at Cecille's gross turn-shaving (assume it's reasonably high gross turn-shaving) in the Cecille teams and find that it isn't as valuable on average as Luke's contributions to the Luke teams, justifying not just Luke > Cecille but also the placement of both in high tier. The net definition is appropriately applied.

i also disagree with your proposal that we shouldn't assume the best auxiliary team because that violates the concept of opportunity cost.

Let's consider only one team, then, the one that achieves the lowest TC. I have the feeling you would still object to the definitions presented here (well, the net definition would be enforced in a slightly different way, but yeah) in the case of, say, FE8, in which Seth's absence costs only three turns. Yet when you value the end goal of tier lists as minimizing turns:

certainly, there are some facts that are more objective, so to speak, than others. one is that everything is a means to an end, and that end is turncounts.

it makes more sense to use turns shaved as the main tiering criterion, no?

this is long and confusing but from what I understand, what you're trying to say is something like Rath firing the Brave Bow at walls in Genesis is higher valued than anything Pent does, since he's replaceable as a lategame warper but Rath saves a turn or something by breaking walls and doing nothing else of value, but Pent is pretty much always deployed when he exists, and has very good combat, but probably doesn't save any turns directly like Rath?

I haven't played FE7 in years, so I can't be sure if what I'm saying here is accurate. But I guess I would say that Pent would receive some credit as a lategame warper once suboptimal auxiliary teams are considered; if we restrict ourselves to only the optimal team, then Pent's Warping means basically nothing. Rath's wall-breaking is only a small plus, but it is one that holds in more contexts.

Edited September 13, 2013 by Redwall

[General Banzai]

Okay I dunno about the math or the philosophy behind it but your argument and your evidence seem to have at most a tangential relation to each other; I read the entire post and had absolutely zero idea what you were trying to say until I got to the tl;dr, which struck me as not actually connected to the post itself. dondon and Horace said much the same.

On top of that, I think becoming slaves to pure numbers is ridiculous and getting away from the actual played experience even in LTC. As I said in the other thread, a tier list in which Vanessa is above Seth no longer means anything to anyone but the mathematician that put the numbers together

Edited September 13, 2013 by General Banzai

[dondon151]

it makes more sense to use turns shaved as the main tiering criterion, no?

of course it does, but the very significant problem of using turns shaved as the criterion is that so many units don't shave any turns because they join too late for their contributions to be unique. FE6 provides better examples because it has a larger and more redundant cast. so long as you can claim that a decent unit like noah doesn't actually save any turns (even though early promoting him is definitely helpful), then he's on the same level as dumb units like barth and dorothy. actually, you can also claim that barth > noah because barth breaks down the wall for ogier to trade his armorslayer to marcus or zealot, which may-or-may-not shave a turn.

in the end, it's just not intuitive at all. for a unit to have saved any turns, you have to conclusively prove that there are no viable alternatives. this is easy in some cases (fliers, jagens, warp/rescue users, dancers) and difficult in others. earlygame units will necessarily have positive net benefits because there's no one to compete with them. one could make a case for merlinus > dayan because merlinus goes shopping in chapter 2, for instance.

Edited September 13, 2013 by dondon151

[XeKr]

Personally I think those who understand the underlying principles should find this mostly intuitive (all 5 of us), but this is still very useful for clarification and reference.

Why did you write this and who in their write mind (haha) would read this and not get a headache.

I don’t understand, so no u.

What’s with the wave of anti-intellectualism SF is experiencing recently? Just don’t post in these threads if you don’t care and have no relevant/useful contribution. Or ask for clarification if you’re interested. Same as any other topic.

At any rate, these formal definitions offer a suggested method of dealing with the arbitrariness that has plagued FE tier lists across gamefaqs and SF for 1000s of posts. Whether that’s good or not is each one’s own opinion. Whether it’s worth discussion or not merely depends on player interest.

most units save 0 turns if they join late enough in the game regardless of what arbitrary "contexts" you put them in.

Unless I’m misunderstanding you, I think you should read the definition again.

In addition, I don’t think this is true in general if considering reliability. Sure there will be many contexts that identically reach a certain turncount, but they won’t do so at the same reliability. This also follows from the intuition people have in arguments like “this unit is “better” at combat" (assuming same move, etc).

Many common counterarguments to the turns-centric tiering method fail if considering expected turncount. Such as optimal tier vs. non-optimal tier silliness. It’s possible to consider a gradient, which orders the characters nicely (somewhat).

this is long and confusing but from what I understand, what you're trying to say is something like Rath firing the Brave Bow at walls in Genesis is higher valued than anything Pent does, since he's replaceable as a lategame warper but Rath saves a turn or something by breaking walls and doing nothing else of value, but Pent is pretty much always deployed when he exists, and has very good combat, but probably doesn't save any turns directly like Rath?

ha, that was the best run-on sentance ever, and I'm too lazy to edit it but I think you get my drift.

tl;dr is basically: Compare expected turncount of Unit A + non-specific team vs. non-specific team. “Expected” and “non-specific” are very key.

In your example, suppose Rath saves 1 turn in nearly all contexts with no investment. That’s fairly good if it’s truly unique to him.

Pent (as the best warpskipper, if only because of needing no/little exp investment and also good combat) on most teams will save lots of turns.

Pent on a team with a trained Erk or whatever specifically designed to obsolete him might not really save turns but that’s a fairly specific group in the ensemble.

You might also then imagine a very similar argument for Erk (as Pent). However, he also took up exp, meaning at the very least reliability was sacrificed earlier. His contribution is still less (cost more).

It’s then certainly possible to imagine that averaged over the ensemble, Pent is still better over the others. Erk vs. Rath would depend on how good is warpskipping vs. the exp investment compared to Rath’s turnshave. I’m inclined to think warpskipping is that good but w/e who knows in theory FE land.

The “weighting” issue of the subsets/contexts could still be quite bothersome but that’s for another day…

Edited September 13, 2013 by XeKr

[Espinosa]

one could make a case for merlinus > dayan because merlinus goes shopping in chapter 2, for instance.

I think you could make that case on the basis of Dayan existing only on the most annoying route of the game and Merlinus letting you go shopping in the desert plus passing around Warp/Rescue in Zephiel's map. Then again, with max manipulation, isn't it preferred to go to Sacae?

You might also then imagine a very similar argument for Erk (as Pent). However, he also took up exp, meaning reliability was sacrificed earlier. His contribution is still less (cost more).

Reliability only shows here insofar as Erk needs to be blessed in magic to surpass Pent's staff range (which doesn't even need to be all that high anyway; iirc he needs 2 extra points over base for chapter 28x, then 4 extra for chapter 30 which is admittedly harder to obtain). The opportunity cost is levelling Erk all the way up and getting his staff rank all the way from the very bottom to the very top, which is not just costly but really annoying (he has to begin with Heal staves).

[XeKr]

It also shows up in that the exp Erk took could go to other units which makes meeting their stat benchmarks more robust, no? Plus funds maybe? Or instead of staff-spamming (which may rely on certain units getting hit and such), he (or someone else in that deployment spot) could be chipping to help out. Or it would result in more flexibility in movement/positionings. I'm just throwing out ideas, but there's tons of little things to be considered.

EDIT: Err...you basically alluded to this in your post, lol. >_>

Edited September 13, 2013 by XeKr

[General Banzai]

Personally I think those who understand the underlying principles should find this mostly intuitive (all 5 of us), but this is still very useful for clarification and reference.

"People who understand it will find it intuitive"

That statement is inherently contradictory/meaningless (intuitive means you don't need to understand the underlying principles in order to get it), and it certainly isn't helped by your half-joking "all 5 of us" which is not much of an exaggeration

Edited September 13, 2013 by General Banzai

[Espinosa]

It's actually probably more of an understatement because it might mean "whichever one of us 5 will decide to do an LTC run some time during this decade".

[XeKr]

"People who understand it will find it intuitive"

That statement is inherently contradictory/meaningless (intuitive means you don't need to understand the underlying principles in order to get it), and it certainly isn't helped by your half-joking "all 5 of us" which is not much of an exaggeration

I notice you took out the relevant wording. >_>

There are things we understand intuitively that we do not understand or think about formally/rigorously.

I'm curious though, why are you so aggressive about this issue?

EDIT: As a matter of clarity, I do see your point as I often have sentences with awkward syntax/word choice (especially this late, plus technically not my first language, plus laziness). As a matter of semantics...I'll let you discuss with Celes or whoever likes talking about that.

Edited September 13, 2013 by XeKr

[dondon151]

In addition, I don’t think this is true in general if considering reliability. Sure there will be many contexts that identically reach a certain turncount, but they won’t do so at the same reliability. This also follows from the intuition people have in arguments like “this unit is “better” at combat" (assuming same move, etc).

Many common counterarguments to the turns-centric tiering method fail if considering expected turncount. Such as optimal tier vs. non-optimal tier silliness. It’s possible to consider a gradient, which orders the characters nicely (somewhat).

reliability is prohibitively difficult to calculate properly for auxiliary units (where these calculations would matter the most) and most of the time the difference in reliability is hardly noticeable.

[MacLovin]

You plaugerized this from Mekkah.

[XeKr]

@dondon:

While you’re right in your objections, I’m just pointing out the methodology directly addresses your concern. The performance of these “redundant” units can be resolved, even if (very?) difficult to do so. In most cases, we’re settling for estimates of their potential contributions in these fringe cases.

Still, the point of considering varying contexts and an ensemble is that these contributions don’t have to be unique. They just have to (sometimes) exist. The more often they exist (less specific the team needs to be) and bigger the contribution (turns shaved) the better. What remains is deciding what contexts and contributions are more important.

I do think there is some messiness in how the varying contexts are weighted (equally or weighted toward “higher tier” compositions, etc), but this treatment still feels better (or at least not worse) than other tiering criterion. Surely if this standard does not resolve differences, then a more lenient/arbitrary one won’t also.

There is obviously some dissonance in that an somewhat “objective” tiering standard is proposed here but there also remain tons of proposed rough estimates and subjective factors. But it’s unnecessary (and inappropriate) to consider this as the magical silver bullet solution for tiering: that’s an overly ambitious and impossible expectation. Rather, I think this sort of thing has always been presented simply as an useful framework to consider and discuss efficiency (and rank characters).

Edited September 13, 2013 by XeKr

[Baldrick]

Well, what is the purpose of the tier list?

If it's to determine who is objectively the best, stuff like expected turncount, varying teams and shared credit is muddying the waters. If it's as a framework for discussion, whether the criterion is rigorous or arbitary doesn't really matter; it's how interesting the discussion it generates.

If it's as a reference for the SF community in general, I think the main issue is may be accurate, but it's not useful. Edward might be at the top of the tier list because of his 1-P performance, but that doesn't mean he's the best unit to bring to endgame.

If it's as a reference for those interested in LTC, that's well and good. You don't need to worry about how it's viewed. It'll either interest you or it won't, and if you fall in the latter category you can safely ignore the tier list.

[Chiki]

I agree with the OP. You have prodigies like Espinosa who is an LTC player and who also thinks Mia shaving a turn from FE9 is "stupid" even though LTC tier lists are based on cutting turns and reliability. We have to start ignoring certain people at some point.

I'm not sure why an argument not being intuitive is a point against it. Ex: incest is intuitively disgusting even though there's no objective basis to find it disgusting.

A lot of arguments that aren't intuitive are widely accepted.

Speaking of LTC tier lists, I don't think anyone really cares anymore about them. I really do think it's meaningless now because there are some people who, very understandably, don't care; there are people who are just not sharp enough to understand the concepts and contradict themselves as a result; and there are people who come on the tier lists to just spout ignorant stuff.

I think maybe we should start making tiers based on making the game easy. This is very subjective and meaningless, but there's not much of a choice since no one really cares.

A tier based on the subjectivity of making the game easy may get people interested.

Or maybe, more objectively, two things: reliability and combat potential. Intuitively, it's obvious that a unit with high reliability and combat potential will make the game easy. Though earlier I said intuitive doesn't mean correct, we kinda have to rely on intuitions to get people interested.

Would people be interested in me making an FE13 tier list based on reliability and combat?

Edited September 13, 2013 by Celes

[Elieson]

So a basic, "Welcome to Fire Emblem, novice FE player! This Tier list will help you gauge the worth of X under general circumstances" Tier list? Yea go for it. I'd join the cause.

Though that's pretty much what I started Rate the Unit for, and I'm pretty sure all the FE games bar TS/BS have one made for them.

Edited September 13, 2013 by Elieson

[JSND Alter Dragon Boner]

DDSOL did not have an RTU

Although frankly the RTU for that game would be

Marth - Best Bosskiller and most efficient Warp Target 9.5/10

Jeigan - Jeigan 8/10

CaBel - Amazing 9/10

Warper - Warp/10

or something like that because the game is poorly balanced >_>

[Chiki]

It's not an RTU. But I guess it's similar.

[Elieson]

Well in this tier list, people will be arguing/counter-arguing appropriate positioning and unit placement among the other units, so it'll eventually break down to a RTU [excluding extreme LTC] discussion anyway.

Would you propose that said list excludes drafting too?

[Chiki]

Why would my tier list have drafting included? Turns aren't even important.

[PKL]

I want a forum section just for LTC

Also, something Ive learned: dont make tier lists accurate if youre good at making tier lists. It kills discussion if the tier list is already agreed upon. Like my FE13 tier list that got 0 discussion and all it received was posts saying I agree bla bla (barring Miriel/Ricken's placement). Having a few controversial/questionable tier placements could spark discussion.

Edited September 13, 2013 by PKL

[Rehab]

I'm in danger both of coming off like a combative asshole and preaching to a lot of the choir here, and neither is my intention, but seriously

This topic seems like the perfect example of why tier lists for Fire Emblem games need to state a specific purpose for which they're considering certain units better than others; i.e., they're games that are going to have multiple tier lists each, if the tier lists are to have a use to every player. Assuming the tier lists must be made at all.

You can just slap LTC on one list's title, Draft on another, 0% growths on another, and, I dunno, "units that will get you through the game most reliably, without you even needing to know what you're doing," on another.

Not every game lends itself well to having one tier list. IMO that's mostly the preserve of 1v1 fighting games where the only objective measure by which characters (options) are measured is tournament results. Even the communities based around those sometimes have a hard time distinguishing what to do when, say, the character generally agreed to have the best matchups isn't technically winning the most tournaments.

Other strategy game communities, though I would hazard a guess not always rarely exist in complete harmony themselves, have learned this lesson. For example, in Civilization 5 (at least up to Gods & Kings), people have been able to agree that based on the evidence, the best (or at least most successfully used in aggregate) civilizations in multiplayer are not necessarily the best civilizations with which to win reliably against the AI on the hardest difficulty (which is a remarkably different challenge, because the AI gets bonuses out the eyeballs), which may not be the best civilizations to get the highest "score" on any possible difficulty, which might not be the best civilizations in any of the given on certain map types. Beating the game in as few turns as possible is actually seen as a very important measure of capability in that community, as well, but, despite ongoing arguments and evidence continually being presented to fuel them, it's accepted that it's not the only appropriate yardstick by which to measure options. Indeed, the game is exceedingly difficult to try measuring by a single standard, and might not even lend itself to that approach at all.

I think you guys can do the same, because this is a similar situation where the game is played to multiple ends, many of which have been constructed not by the game itself, but by some of the players. I can't imagine how hard it'd be for a totally new player to make sense of it all, at least not without some friendlier introductions than seem to be available.

Edited September 13, 2013 by Rehab