Mechanics that you want

[Kngt_Of_Titania]

The impact of Luck mostly occurs at the extreme ends of the stat. Characters on the low end(Kent,Knoll) face critical percentages very often and have poor evade, characters like Priscilla or Ninian almost never face criticals and have very good evade. It's especially useful due to the double RNG determining hit as an extra X amount of luck can lower true hit by more than 1% per point.

Knoll/Kent: Mediocre SPD is as much as a culprit as poor LUK for low evasion. It's not like Sain is dodging much more noticeably than Kent, and he has double the LUK.

Prissy-Poo/Nin-Nin: High SPD inflates the value of LUK. Much bigger difference between 50 and 70 avo than, say, 30 and 50 avo.

Now, true hit is a sigmoidal curve, so it can actually either deflate or inflate the value of avoid more than displayed hit would suggest. Now, this is probably a pretty crazy complicated formula (and honestly, I don't remember how to represent a sigmoidal curve as an equation), so I don't know the exact point where it breaks even. Typically, however, true hit tends to devalue the value of avoid at extremes (90%+ or 10%-) and super-value it at "average" values (40-60% range). Anyways, enough of my rambling, let me get to another point.

Each point of avoidance is typically worth more than the last. To make an extreme and obvious point, I'm going to borrow a "time to live" mechanic often used in WoW tank theorycrafting (I know, I know, leave me be...I don't play it anymore). If 5 avoidance reduces your chance to be hit from 10% to 5%, your time to live essentially doubles (200% of its original value), but if it only brings your chance to be hit from 100% to 95%, your time to live only increases to 105.23% of its original value. So, for characters that already are reaching 40-60% hit rates from enemies due to SPD alone, an extra 15-25 avoid from LUK means a hell of a lot more than it would to a low SPD character (say Dorcas, who might have 70%+ hit rates from enemies). And since 40-60% range actually is the region where true hit that most inflates each point of avoid, LUK is boosted even more.

Now, following this reason, we can conjecture a couple of points:

1. Hard modes will devalue avoid, simply because enemy hit rates will increase; an enemy who might have a 40-60% chance to hit on NM will then have a 55-75% chance to hit on HM, which essentially decrease the time to live each point of avoid gives. This point alone will make SPD/LUK less valuable. However, some characters might value SPD more (think Bartre in HHM needing SPD not to be doubled) or less (think Edward in FE10), and LUK may be worth more depending on if HM noticeably increases enemy crit rates and/or gives more enemies killers.

2. FE11 and FE12, which I've noticed decrease the amount of hit/avoid given per stat of SPD/LUK/SKL, heavily decreases the value of avoid in general, for much the same reason as #1. I know IS was trying to stabilize hit rates, but it really took a bat to LUK's value of a stat, relegating it to near worthless unless crit evade is necessary.

Hard modes in FE11/FE12 combine points #1 and #2 into one giant shitstorm, and the enemy hit bonus in Lunatic mode FE12 pisses in LUK's face.

[Vorena]

Luck could be used to effect more things that are normally trivial, but are minor boons all the same. Luck could effect the ability of randomly picking up 100 gold anyway on the ground during a map. Perhaps luck was on your side and saved you a usage in durability. You might even get a random discount when buying items or an increase in a selling rate.

None of these are broken mechanics, but are certainly useful for certain moments.

[Momo]

I don't feel like Luck makes no difference in the game. There is a significant difference between the characters that have it and those that don't, such as say, Clarine and Saul.

I think there's a gray area between "absolutely equal" and "is so insignificant that it shouldn't exist".

Comepare that to FE11/12 though, in which it's cut in half for Avoid. That's what I was referring to, why did they even bother making it a stat if it makes no real difference?

[Anouleth]

Knoll/Kent: Mediocre SPD is as much as a culprit as poor LUK for low evasion. It's not like Sain is dodging much more noticeably than Kent, and he has double the LUK.

Prissy-Poo/Nin-Nin: High SPD inflates the value of LUK. Much bigger difference between 50 and 70 avo than, say, 30 and 50 avo.

Now, true hit is a sigmoidal curve, so it can actually either deflate or inflate the value of avoid more than displayed hit would suggest. Now, this is probably a pretty crazy complicated formula (and honestly, I don't remember how to represent a sigmoidal curve as an equation), so I don't know the exact point where it breaks even. Typically, however, true hit tends to devalue the value of avoid at extremes (90%+ or 10%-) and super-value it at "average" values (40-60% range). Anyways, enough of my rambling, let me get to another point.

Each point of avoidance is typically worth more than the last. To make an extreme and obvious point, I'm going to borrow a "time to live" mechanic often used in WoW tank theorycrafting (I know, I know, leave me be...I don't play it anymore). If 5 avoidance reduces your chance to be hit from 10% to 5%, your time to live essentially doubles (200% of its original value), but if it only brings your chance to be hit from 100% to 95%, your time to live only increases to 105.23% of its original value. So, for characters that already are reaching 40-60% hit rates from enemies due to SPD alone, an extra 15-25 avoid from LUK means a hell of a lot more than it would to a low SPD character (say Dorcas, who might have 70%+ hit rates from enemies). And since 40-60% range actually is the region where true hit that most inflates each point of avoid, LUK is boosted even more.

Now, following this reason, we can conjecture a couple of points:

1. Hard modes will devalue avoid, simply because enemy hit rates will increase; an enemy who might have a 40-60% chance to hit on NM will then have a 55-75% chance to hit on HM, which essentially decrease the time to live each point of avoid gives. This point alone will make SPD/LUK less valuable. However, some characters might value SPD more (think Bartre in HHM needing SPD not to be doubled) or less (think Edward in FE10), and LUK may be worth more depending on if HM noticeably increases enemy crit rates and/or gives more enemies killers.

2. FE11 and FE12, which I've noticed decrease the amount of hit/avoid given per stat of SPD/LUK/SKL, heavily decreases the value of avoid in general, for much the same reason as #1. I know IS was trying to stabilize hit rates, but it really took a bat to LUK's value of a stat, relegating it to near worthless unless crit evade is necessary.

Hard modes in FE11/FE12 combine points #1 and #2 into one giant shitstorm, and the enemy hit bonus in Lunatic mode FE12 pisses in LUK's face.

Luck was still valuable to avoid criticals from enemies, as people have mentioned. Low luck characters like Sirius do have issues, and someone like Michalis is almost unusable since he has a 15% chance to die in any given round of combat. Certainly, the lower difficulties have no value for luck or skill any more than the higher difficulties: if anything, skill and luck are even less important, since landing and avoiding criticals is no longer as necessary.

[Paperblade]

Due to the way crit is calculated in FE12, Ice Dragons, Berserkers, and Snipers regularly had crit rates high enough that you want a double digit amount of Luck, which some characters have a bit of trouble reaching.

Seriously guys. Ch. 13 Ice Dragons have 14-15 crit, and Ch. 14 ones have 16-17.

Late game Berserkers and Snipers have 20+ crit, going up to about 24 in Ch. 22. Michalis (who has 2 Luck) faces ~15 crit from the LOWER end of enemy crit

And this is not an insignificant amount of enemies

Edited November 27, 2011 by Paperblade

[Dark Sage]

Comepare that to FE11/12 though, in which it's cut in half for Avoid. That's what I was referring to, why did they even bother making it a stat if it makes no real difference?

That's not true at all. Recently I tried to argue Ellerean out of Free Silvers tier on the grounds that he can take an Arms Scroll to get Excalibur and then OHKO all the Flying Dragons on the desert at base, just like Merric. The reason why he was kept in Free Silvers was not just because he needed an Arms Scroll to compare to a mediocre unit, but also because he had crappy luck and thus faced crit against everything which if you combine with his crappy enough durability, means that he has a substantial chance of dying against anything.

[eclipse]

FE11 - Medeus has 13 crit on Normal. Snipers exist, and I can think of at least one with a Killer Bow. Some characters have problems reaching that, which sucks, because low-percentage criticals aren't unheard of. Sure, Roger-like luck might not be absolutely necessary, but Luck as a whole isn't unnecessary, either.

[Kngt_Of_Titania]

Luck was still valuable to avoid criticals from enemies, as people have mentioned. Low luck characters like Sirius do have issues, and someone like Michalis is almost unusable since he has a 15% chance to die in any given round of combat. Certainly, the lower difficulties have no value for luck or skill any more than the higher difficulties: if anything, skill and luck are even less important, since landing and avoiding criticals is no longer as necessary.

Relegating it to near useless unless crit evade is necessary

So we agree, for the most part. Like I've said in another thread at least, it is my first time running FE12,and I'm just wrapping up the prologue. I had no idea what crit rates are in later FE12, so I didn't speak to them, merely stating that they'd have to be quite high compared to most other FE games I've played for LUK to be useful. However, my point that, in FE11/FE12 (and especially in their hard modes), that the avoidance portion of LUK becomes more of a hidden, useless function than actually important in any capacity. Enemy hit rates are so high that both the mechanics of true hit and avoidance itself work against it.

I'm currently working on graphing true hit versus displayed hit, as well as how true hit works in favor/against avoidance's value. I solved it, but I suck at modeling and Excel sucks at solving series.

[Paperblade]

the FE12 board has a stickied topic with enemy stats from every chapter except 20x

[Kngt_Of_Titania]

the FE12 board has a stickied topic with enemy stats from every chapter except 20x

Alright, good to know. Anyways, on to the promised post:

[spoiler=Solving for True Hit, 0-50% Hit Chance]

Alright, so this is the basic gist. Instead of one roll from 0-99 determining what your chance to hit is as displayed hit would suggest, true hit uses two -- if the average of the two rolls is less than the hit percentage displayed on screen, the hit will land. To write this as a formula:

(Random[0-99] + Random[0-99]) < Displayed hit chance*2

Since there are 100 possibilities per roll and 2 rolls, there are (100^2) = 10,000 total combinations. To figure out the true hit for each displayed hit chance, find the number of combinations where the sum of the rolls is less than (Displayed Hit Chance)*2 and divide it by 10,000. For example, at 1% displayed hit, the sum of both rolls must be < 2. There are only three rolls that satisfy this condition -- 00 00, 01 00, and 00 01. This means that the true odds of hitting are 3 in 10,000, or 0.03%.

So how do we solve this? First, let's find a pattern:

Sum=0: 00 00 (1 combination)

Sum=1: 00 01, 01 00 (2 combinations)

Sum=2: 00 02, 02 00, 01 01 (3 combinations)

Sum=3: 00 03, 03 00, 02 01, 01 02 (4 combinations)

Notice that the number of combinations is exactly one more than the sum. As a note, this pattern doesn't seem to stop, so let's run with it. This would mean that the total number of combinations with a sum less than or equal to S would be Σ(N+1), N: 0->S (0 is below the Σ, S is above). When the displayed hit is 1%, S is 1...when displayed hit is 2%, S is 3...when displayed hit is 3%, S is 5...and so on. We can express this as an equation:

# of combinations = Σ(N+1), N: 0->(2*D-1), where D is the displayed hit on your screen (in %).

And thus:

True hit (in %) = [(Σ(N+1), N: 0->(2*D-1) / 10,000] * 100%

This equation works for 0-50% hit chance at least, and then it seems to break down (I'm not entirely sure why)...however, we can employ a similar method to solve 50-100%, working backwards.

[spoiler='Solving for True Hit, >50% Hit Chance]

So, when hit chance > 50%, we simply try a slightly different technique...we find the number of combinations where the sum is greater than or equal to (Displayed Hit Chance)*2 and then subtract that number from 10,000 to find the number of combinations where the sum is less than (Displayed Hit Chance)*2. We then take this value and divide it by 10,000 to find the true hit. So let's follow the same technique as in the last section:

Sum=200: No combinations, as each RN<=99.

Sum=199: No combinations, as each RN<=99.

Sum=198: 99 99 (1 combination)

Sum=197: 99 98, 98 99 (2 combinations)

Sum=196: 99 97, 97 99, 98 98 (3 combinations)

Sum=195: 99 96, 96 99, 98 97, 97 98 (4 combinations)

I'm seeing a pattern come up...are you? The total number of combinations with a sum greater than or equal to S is Σ(199-N), N: S->198. Following the exact same procedure as our last section, this means that:

True hit (in %) = ([10,000 - Σ(199-N), N: S->198]/10,000)*100%

This equation holds for all values where hit chance > 50%. Yeah, adding a second roll to this complicates shit way more than you'd think.

Anyways, on to the "Great, so what the fuck does this all mean?" section of my post.

[spoiler=Graphs and Useful Math Shit]

So first, let me show you what true hit actually does. The X axis is the displayed hit on screen, while the Y axis is the true hit. Notice the distinctly sigmoidal pattern that emerges, and how it stabilizes extremely high and extremely low true hit rates, especially those above 90% and those below 10% (no, I can't find out how to shrink it, HELP!):

Second, let me show you a graph that shows how a person's survivability increases as enemy hit chance decreases (loosely read as, "As your avoid increases faster than the enemy's hit"):

Essentially, this shows us that true hit tends to decrease survivability in general until hit rates start dipping below 50% -- now, while this is more common in earlier FEs, hit rates dropping below 50% is much rarer in FE11 and FE12. Notice how the slope of the true hit curve starts out lower and soon becomes larger than that of the non-true hit curve; this means that true hit is initially devaluing avoid at high hit rates but, at when enemies tend to miss frequently enough, making it more valuable than it normally would be.

My last graph, which shows the relative value of avoid for each enemy hit rate, will show at what hit rates devaluing/super-valuing of avoid occurs:

What the graph tells us is that, when the enemy hits you more than roughly 70% of the time, true hit actually decreases the value of each point of avoid; when enemy hit chance drops below 70%, true hit actually works in avoid's favor.

All of this information, of course, verifies my original hypotheses:

1) Low enemy hit rates drastically increase the value of avoid, especially when true hit is present. A single point of avoid at 65% enemy hit rate effectively increases your time to live to about 102% of its previous value. However, 1 avoid at 20% enemy hit rate increases your time to live to about 112% of its previous value. 1 avoid at 100% enemy hit rate? Barely registers. Under a true hit system, it looks like it takes until an enemy hit rate of 75% until 1 avoid actually means a 1% increase in time to live. LUK, which gives avoid, is similarly inflated/deflated as a stat by these same mechanics.

2) Hard modes and FE11/FE12, which tend to favor high hit rates, thus devalues avoid as a whole, and thus LUK. Unless you can drop below a critical value of maybe 75-80% enemy hit, avoid is extremely lackluster and RNG fickle. So the only reason you'd want LUK is if enemy crit rates are high enough to warrant it.

P.S. Should I make my own seperate thread posting this information? I'm not sure if anybody has actually analyzed true hit this deeply before.

Edited November 27, 2011 by Kngt_Of_Titania

[Dark Sage]

Seems like a tl;dr version of shit we already knew to me. Thus, I doubt it warrants a new thread.

[Kngt_Of_Titania]

Seems like a tl;dr version of shit we already knew to me. Thus, I doubt it warrants a new thread.

Ah, and it had a shiny new equation to calculate true hit for any displayed hit too.

[grandjackal]

That's not true at all. Recently I tried to argue Ellerean out of Free Silvers tier on the grounds that he can take an Arms Scroll to get Excalibur and then OHKO all the Flying Dragons on the desert at base, just like Merric. The reason why he was kept in Free Silvers was not just because he needed an Arms Scroll to compare to a mediocre unit, but also because he had crappy luck and thus faced crit against everything which if you combine with his crappy enough durability, means that he has a substantial chance of dying against anything.

Just jumping in to say a bit here, but I'm positive Luck does not mean a thing since both he and Maric are so slow and so pathetic in durability they're more often than not just simply ORKOd.

[arvilino]

Just jumping in to say a bit here, but I'm positive Luck does not mean a thing since both he and Maric are so slow and so pathetic in durability they're more often than not just simply ORKOd.

If I remember correctly both Promoted!Merric and Arms Scroll!Ellerean can survive one Flying Dragon attack on chapter 11 on H3 and can then OHKO with Excalibur. So they can from full HP kill a Flying Dragon on the enemy phase, but Ellerean has a larger chance take a critical hit than Merric.

Ellerean has 2 Luck(with 30% growth), Merric has 6 or 7(if he procs his 70% growth from a level from the prologue). The flying dragons have 15/16 skill and thus 7 and 8 crit. so Ellerean is facing 5-6% crit rates and Merric is facing 1-2% at worst but gets out of that range after a few levels.

[Snowy_One]

I, personally, subscribe to the 'Murphy's law' RNG. If you have 99% hit and NEED to kill that one boss on that strike, you will miss. If your unit has even a 1% chance of being critted, it will happen at the one moment when you can't recover from it.

[General Banzai]

If you want another reason for why luck is fine as is, there's the fact that it's not influenced by class in any way, either in bases, growths, or promotions gains. It is the only stat that is like this and whether or not a character has high/low luck is solely determined by the individual character. Therefore, it is nearly random who has high/low luck. If you want a character with high speed, then you can typically pick one based on class (a myrmidon, etc). Or if you want a character with high defense, it's easy by basic knowledge of classes which one you should pick. But if we were to buff luck to make it equal to other stats, then having a character with specifically high luck would be desirable, even at the cost of other stats. But who would you pick for a "high luck" character? Since most characters have roughly equivalent luck bases, it's not always possible to tell who will have high luck just from base stats, and it's impossible to tell who would have high luck by their class, something completely unlike every other stat.

Luck is a stat completely independent of any common factor. Any type of unit could have massively high luck or massively low luck, unrelated to their class or bases. Thus it should remain a secondary stat to speed and skill.

Even beyond that: What luck does is not explained in the game. It is a kind of "mystery stat", where having it does good things but you're not exactly sure what. It's supposed to play off exactly like, well, luck: A character with high luck has a slightly higher evade chance than one with low luck, perhaps undetectable to one not in constant surveillance of their combat stats, leading to a slight increase in the amount of attacks dodged, amount of criticals avoided, amount of hits landed. Buffing it and making luck's relation to combat stats obvious would eliminate the entire point of luck.

Sometimes I'm glad the developers don't listen to you guys at all.

[Rothene]

The problem with that example it that it is assuming an environment where a character would have 0 growths in two stats, which doesn't happen. I might be much more convinced if you re-ran that with a 10 in the two stats that you had at 0 there.

Alrighty...

Character A 20Skill, 10Spd, 10 Luck.

Character B 10Skill, 20Spd, 10 Luck.

Character C 10Skill, 10Spd, 20 Luck.

Same 50Hit weapon...

Character A has 70% chance to Hit Character A, 50% chance to hit Character B, 60% chance to hit Character C

Character B has 50% chance to Hit Character A, 30% chance to hit Character B, 40% chance to hit Character C

Character C has 60% chance to Hit Character A, 40% chance to hit Character B, 50% chance to hit Character C

...I don't really see much difference between leaving them as 0 or placing a value there. Notice the one with high luck seems to have the least extreme hit/avo rates(as expected)?

PS: ROUTER LIVES!!!

[grandjackal]

If I remember correctly both Promoted!Merric and Arms Scroll!Ellerean can survive one Flying Dragon attack on chapter 11 on H3 and can then OHKO with Excalibur. So they can from full HP kill a Flying Dragon on the enemy phase, but Ellerean has a larger chance take a critical hit than Merric.

Ellerean has 2 Luck(with 30% growth), Merric has 6 or 7(if he procs his 70% growth from a level from the prologue). The flying dragons have 15/16 skill and thus 7 and 8 crit. so Ellerean is facing 5-6% crit rates and Merric is facing 1-2% at worst but gets out of that range after a few levels.

Only thing I can really say against it is that no one wants the Aries or Libra shards, but that's still 2-3% vs...Well, zero. Well, that and I imagine a lot of people are squabbling over a crest at this point in time (as a lot of characters are usually wanting to promote around that time), and if Elleraen can wait while Maric can't (on account of being OHKOd)...

Ehh, probably still hopeless. I hate arguing FE12, simply because there's almost no room for deviation.

[Snowy_One]

If you want another reason for why luck is fine as is, there's the fact that it's not influenced by class in any way, either in bases, growths, or promotions gains. It is the only stat that is like this and whether or not a character has high/low luck is solely determined by the individual character. Therefore, it is nearly random who has high/low luck. If you want a character with high speed, then you can typically pick one based on class (a myrmidon, etc). Or if you want a character with high defense, it's easy by basic knowledge of classes which one you should pick. But if we were to buff luck to make it equal to other stats, then having a character with specifically high luck would be desirable, even at the cost of other stats. But who would you pick for a "high luck" character? Since most characters have roughly equivalent luck bases, it's not always possible to tell who will have high luck just from base stats, and it's impossible to tell who would have high luck by their class, something completely unlike every other stat.

Luck is a stat completely independent of any common factor. Any type of unit could have massively high luck or massively low luck, unrelated to their class or bases. Thus it should remain a secondary stat to speed and skill.

Even beyond that: What luck does is not explained in the game. It is a kind of "mystery stat", where having it does good things but you're not exactly sure what. It's supposed to play off exactly like, well, luck: A character with high luck has a slightly higher evade chance than one with low luck, perhaps undetectable to one not in constant surveillance of their combat stats, leading to a slight increase in the amount of attacks dodged, amount of criticals avoided, amount of hits landed. Buffing it and making luck's relation to combat stats obvious would eliminate the entire point of luck.

Sometimes I'm glad the developers don't listen to you guys at all.

Sooo... That it's perfectly fine to pick a character with low luck and consider other stats far more important is now a GOOD thing?

[bottlegnomes]

Sooo... That it's perfectly fine to pick a character with low luck and consider other stats far more important is now a GOOD thing?

He's saying it's generally pretty easy to tell what stats a character will specialize in besides luck, eg SM for speed, general for def, etc. If luck became the most important stat, it'd be harder to tell who is worth using. Not the best argument, but whatever.

How about keep the avoid system in FE12, along with the critical system, since provided the enemies actually have competent stats, it'd mean a boost to enemy critical rates, but make luck boost avoid and hit by say .75 per point, rounded up. Or if you want to go to the 1 speed = 2 avo, just boost lucks contribution again, say 1.5 hit and avo for each point. But I do think they should keep the critical system from FE12. Makes enemy criticals actually existant, so characters like Sirius are in danger, and the slight boost for your units is nice, too.

[Anouleth]

It might also be nice to have more skills that operate off luck. Miracle in FE9 and FE10 was really only good to reduce the chance of surprise crits, so ironically it ended up being only good for low-luck units. Or maybe add a small portion of Luck to all skill activation rates in a similar way to how Biorhythm affects all skills.

[Snowy_One]

It might also be nice to have more skills that operate off luck. Miracle in FE9 and FE10 was really only good to reduce the chance of surprise crits, so ironically it ended up being only good for low-luck units. Or maybe add a small portion of Luck to all skill activation rates in a similar way to how Biorhythm affects all skills.

I... Cannot... believe this but...

HOLY CRAP I HAVE AGREED WITH ANNY TWICE IN LESS THAN SEVEN DAYS!

[Anouleth]

I... Cannot... believe this but...

HOLY CRAP I HAVE AGREED WITH ANNY TWICE IN LESS THAN SEVEN DAYS!

Don't worry, I'm sure you'll go back to being wrong on basically every subject soon enough.

[Dark Sage]

I... Cannot... believe this but...

HOLY CRAP I HAVE AGREED WITH ANNY TWICE IN LESS THAN SEVEN DAYS!

Even a broken clock is right twice a day.

[CrashGordon94]

Actually, I don;t like Luck being a "mystery stat", its uses should be listed just like the other seven primary stats.

Also, the "who has good Luck?" issue would be solved by doing something IS should've done from day one: DISPLAYING THE GROWTH RATES!