Redwall

Joint-multinomial distributions, son.

I think just below Luke is fine. Draug has terrible bases, so-so growths outside of Spd, bad weapon ranks, and wants a Seraph Robe just like Sirius does.

Sirius has a decent chance of getting stat-cursed since his EXP growth is so low (also recall that s.d divided by mean for gained stats scales as n^-0.5, with n being the number of levels gained [which is, for Sirius, much smaller than one would like]). His low personal bases don't really help. I can see him somewhere in high tier since he can be OK with some boosters, but he definitely needs more boosters than the other top-tier units.

The topic offers a definition of saving a turn, in a slightly different way from how most users define the phrase, and presents thought experiments demonstrating the use of turn-shaving as a tier list criterion. I see no need to merge this with the general-philosophy thread since this topic focuses exclusively on the logical consequences of enforcing turn-shaving criteria, whereas the general thread is intended for a wider range of tiering discussion.

RBY demands a lot of hustle and is fun for this reason, but the hax gets a bit too ridiculous for my liking. In a game from a few hours ago, I was initially outplaying this guy on the ladder, with me getting an early sleep and predicting his Chansey moves perfectly and baiting him into paralyzing my own Chansey, but then I later missed a Stun Spore and suffered two FPed Explosion attempts and had a complete meltdown. GSC looks potentially interesting, but the only people I can find on the ladder aren't really familiar with the GSC metagame at all. RSE is fun, though I do wonder how it would look if Magneton (and possibly Dugtrio) were gone. I didn't really like the heavy-offense teams in DPP, but other than that it was okay. Never really got into BW for various reasons, including the weather wars.

Which do you like the most? My favorite is probably RSE, though ideally I would want a metagame with just slightly less offense. I'd like to learn GSC, but it's rare to find good players on the ladder.

I can't really answer this, since I haven't played FE7 in a while (nor have I played it at a very high level). That's why it's preferable to me to measure their worth in turns instead of combat vs. utility. In practice no one's actually going to go all-out and get exact numbers, but we don't necessarily need to do too much math to get a rough feel of whether one unit cuts more turns (not just unique ones) than another. I don't disagree that it's a place for that topic to be discussed. That doesn't mean that it should be the only place for it to be discussed. This thread considers only one method of tiering, whereas the tiering philosophy thread discusses other things as well. I looked through the Code of Conduct and found nothing that would recommend a merge of the two topics.

That's what I'm doing. The framework allows you to look at the gross benefits to start, and the consideration of which character confers the highest amount of gross benefits allows us to determine net benefits, exposing the problems you suggest: some characters are less good than others. Cecille is, for the most part, less good than Luke, for example. I'm not neglecting the opportunity cost as you suggest.

It's made for discussing tiering philosophy, but there is no evidence to suggest that it is intended to be the only outlet for doing so. Narga has stated that his purpose in creating that thread was to prevent people from derailing tier lists: Also, Narga was reading this very topic at some point and evidently felt no need to merge the threads. Finally, since it seems that my definitions aren't clear, let me reiterate that units can save turns that aren't unique turns precisely because we can consider an ensemble of team compositions (at least in principle) and subsequently compare the results obtained from removing characters from said compositions. If only considering a single composition, then yes, the proper application of the so-called net definition would only look at unique turns, but it's for this reason that we're not restricting ourselves to one single composition.

My second post in the thread addressed this concern: Units are appropriately rewarded for having potential to do things across the ensemble; the only difference between that and a "unique" contribution is that the unique contribution occurs more frequently in the ensemble. For this reason, going by some of the arguments you and others have made in other threads, Alance would receive some late-game credit for being a so-so Paladin (although they're not as likely to meet certain stat benchmarks for low-turning, they still are rewarded for their potential due to the gross turns saved in teams without Percival); not as much credit as would Percival, but some credit nonetheless. Similar arguments for Noah. And as XeKr said, I'm not suggesting that turn-shaving arguments are perfectly objective, that we actually go out and do all the math, assigning weights to different team compositions and such. It is simply a slightly less arbitrary framework IMO than what is commonly accepted. Not necessarily. I suspect many would object to having Vanessa above Seth, but for the wrong reasons: namely, that they have committed themselves to valuing combat above utility in all cases. Certainly I would suspect that Seth should be above Vanessa due to Seth's contributions across the ensemble cutting more turns (not just "unique" ones) than Vanessa's contributions, but like I said, I haven't played FE8. Celes has made a tier list like this, with blackjack and hookers. I acknowledged in my first post that some people simply don't like tiering according to LTC; if you don't, that's fine, but it's not relevant to this topic, which discusses the logical consistency (not necessarily the appeal) of turn-shaving as a tiering metric. I see no reason for that. The tiering-philosophy thread, in Narga's words, was created to avoid having people derail existing tier lists. That doesn't preclude the existence of other "unofficial" tiering-philosophy threads.

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

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: 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.

Just keep all the Clerics alive. For what profit is it to a man who gains 72 EXP, but loses his soul?

I thought Mormons weren't supposed to gamble?

Anyone else think Celes has a crush on Anacybele?

In the parlance of FE tier lists, oranges have high availability. They go with all sorts of dishes (salads, soups, etc.), and, unlike lemons, you can just slice them and eat. A high-tier fruit if I ever saw one.

Post your fruit tier lists here. Top Cherries Watermelons Mangoes High Oranges Plums Raspberries Blueberries Kiwis Pineapples Mid Bananas Apples Cantaloupes Grapes Strawberries Low Persimmons

Wasp hives are only bug-type, not both bug- and flying-type (x4 effectiveness), so I don't see how a large rock would be more effective than fire.

I'm just saying that because an extra point of Def is equivalent to n effective points of HP (where n is the # of hits you'll sustain), it's more correct to treat a level-up as having four branches of possibilities (+HP and +Def; +HP only; +Def only; neither Def or HP) using the multinomial distribution and establishing some minimum value of HP + n*Def, as opposed to using the binomial distribution to find a minimum value of Def and a minimum value of HP and computing a joint probability.

That just tells me there is a durability threshold you haven't bothered to determine, albeit possibly (since you haven't done the math on all the possibilities) a somewhat lenient one. OK then.

I've never played RD and don't plan to so I have to ask: what are the bare minimum defensive parameters for doing 3-6 with Jill? XeKr's calculations assume that 42-Atk Tigers are negligible, and the probability calculations he made are also not quite exact (though they're probably close) since he didn't use a multinomial distribution.

These turn-counts are too low. I want to see some lame turn-counts. PKL, I'm waiting for you respond to my argument in the other thread. never mind

Tiering discussion is relevant to the topic, in my opinion. The thread is intended to discuss outdated concepts of what's good and what isn't; the discussion has shifted to whether Jill, once perceived as mediocre, is as good as advertised when she is dependent on rational favoritism. Given his most recent posts here, Espinosa seems not to have any problem with discussing this.

That also works. Either way, we are getting off topic.

Oh, forgot about doubling. I think Catria is preferable as the face-tanking Sniper since she can double and has better durability. Wo Dao is best on Marth, I think. But yeah, that's more or less what I figured out independently.