The LIE of Average Stats
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- เผยแพร่เมื่อ 1 มี.ค. 2024
- Just use a binomial distribution instead. So much easier to talk about.
Average Stats are used in Fire Emblem discussion because they represent the supposed "most likely" outcome for a unit, mathematically calculated via adding their growth rates in a linear fashion. While this is useful in a vacuum, the real performance of a unit in a game with randomized growths like most FEs is more akin to a roulette wheel, where you could go hot and hit even a rare number every time, or go cold and never hit even a super high rate, but you will never get partial credit and nothing is guaranteed.
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Just wanna say that my first Ross was so speed blessed I was confused when he was slow in another playthough
Exactly. My first Ross was really RNG screwed, while Garcia got some lucky level ups, so I benched Ross and used Garcia. When I played the game again, Ross got very lucky, especially in speed, so I used him. Fire Emblem, especially the old ones, are very based on the luck you get with the level ups, so you should be at least somewhat adaptable
I know I had this exact same experience, that when I saw Mekkah's video on Ross I was like "what are this idiot talking about, WHEN ROSS HAD PROBLEMS WITH SPEED?"
Then on my next playthrough of Sacred Stones my Ross was extremely strength blessed, but didn't get a single level in speed during his training with only the +1 speed of the pirate promotion to show for it.
Average stats are just what the expected value would be if you had 10,000 people train a unit and then took the mean of their actual stats at each level. The calculated average stats should be almost perfectly linear provided there’s a large enough sample size.
The “expected values” provided by average stat charts aren’t what you should confidently expect your individual unit’s stats to be, but rather what you should expect those calculated averages to be. Tbh that’s how I’ve always seen average stats being used and interpreted, but approximately 5 out of every 4 people don’t understand statistics, so misinterpretations are probably far more common than I realize.
"Approximately 5 out of every 4 people don't understand statistics" is my new favorite phrase!
I do appreciate the existence of the linear average stats though, because of the whole "in a vacuum" state -- it does help if you want to get an idea like, "which archer given to you is likely to suck the least?" or "which of Ogma's fighter boys is likely going to see more use as they level because of potential level ups?"... it's not perfect, as you outlined in the video, but sometimes it's what you need to decide between Gordon and Ryan in New Mystery for early game archer, or between Barst/Bord/Cord.
Really nice to see the binomial distributions and it's great to reaffirm how statistics work but I don't know what propped this up because I thought we all agreed averages were just a convenient way we established for the sake of unit discussions and were definitely not a fixed or definitive description of what a unit will look at x point. But still good stuff
My biggest point was trying to figure how to describe units that are low level units that rely on having good growths to get going. Average stats rarely show these units favorably, or can sometimes give a very skewed vision of their effectiveness, as in the case of Ross and Franz on opposites sides of the scale (Franz's average make him look better than a lot of players' experiences and Ross's make him look worse).
@@MythrilZenith I hate to be that guy but if your argument is in conflict with the numbers you might just be wrong, and Franz is statistically better
I'm only about half way through the video so I don't know if this gets brought up, but the linear averages on serenes also doesn't take in to account that if you get a 0 stat level the game rerolls, and it does this twice if you get 2 0 stat levels, so you can get up to 3 chances, so level ups are theoretically always on average better than growth rates would suggest.
This only applies to the gba games to my knowledge.
For three houses, the game always rolls until you get at least 2 stats for byleth and the students, but people like shamir and Catherine can get 0 stat levels. This also makes units slightly better than their growths would suggest on average.
Another, not exactly intutive fact about the randomness of growth is that the variance in stats is the highest if the growth rate is exactly 50%. That means that units with 20% growth or 80% growth are more likely to adhere to their averages than a unit with a 50% growth. It also means that units with average growths are more likely to be either screwed or blessed.
Like the non-Christmas cav in Sacred Stones.
The one time I tried to use him he didn't level well AT ALL
A much better way of looking at a unit is to look at the probability they hit the benchmark for a given map.
You look at the *enemy* stats and find the doubling and one rounding benchmarks for the weapon you think they should use, assume how many level's they'll get by that map and then calculate the chance of hitting those benchmarks. maybe do it a few times for the various weapons (though honestly there's typically only 1 maybe 2 weapons for a given unit against a given group). This method is actually pretty easy to do, and with the exception of say RD BEXP (which I have a python script for if you need) is a much simpler and more productive way of looking at growths.
For example one key benchmark for SOV Boey is killing the brigands in 2-2, he has a 50% strength growth and with 1 strength and 2 speed wells he needs 1 str proc to ORKO all of them, so if your boey gained strength on map 1 you think he's an ORKOing machine that just keeps on going (since EXP snowball) but if he doesn't you think he's the most disappointing thing since your son. (what I do is I rig the first STR proc on 2-2 by getting boey to 1.99 to give you an idea of how big the gap is)
The virgin "average" stats vs. the chad thresholds
Once had a mozu that only got like 1-2 HP level ups throughout like 35ish levels absolutely wild how the rng in these games be sometimes
I was doing 3H Ironman and my lysithea proc-ed 6 strength vs 3/4 magic in her first 10 levels
Same to me, but 3h uses minimums. As soon as she got in the magic focused classes all the screw ups didn't mattered
Part of what makes fire emblem an RPG is that characters will have different stats from playthrough to playthrough, so your decision-making on who to use should be contextual to that playthrough. Expected value charts let you see if your character is over or underperforming in a given stat, which can help guide that decision.
I use average stats solely to inform me if it's time for me to promote a unit or not.
It's interesting you bring up Franz since I'm doing a Sacred Stones playthrough now and at level 10 Cavalier, Franz has either at or below average in every stat. I planned to use him, but despite having good growths, he's not getting good level-ups. This is one of the things that makes Fire Emblem interesting, each playthrough your luck will be different, so you'll have to adapt. Like in my Sacred Stones playthrough, most of my bulky units aren't turning out good, so I'll need to rely on the later units more.
That does depend. If you use units often enough they will eventually be good enough. Just like growths, stat boosters, exp distribution etc are not strictly bound to a meta. But as you said, sometimes units turn bad while other times they turn out good which makes the games so fun and replayable.
I've also felt like "Average stats" are often taken a bit too literally.
It's much like how I've genuinely never had a situation where the Trainee units in sacred stones ended up bad in any of the supposed stats they should.
My Ross (without enhance items) usually ended up with around 12 to 15 res. Which according to this, really shouldn't happen at all.
Or, how in Valentia, I was super blessed in that Kliff was able to get super high Def despite being turned into a Mage.
Average stats however are treated almost like gospel. Making some units go completely ignored.
I like seeing average stats so that I can know how bad my units are, because so many times, the "good" units end up increasing 1 stat each level up. And it's HP.
As a math person I do look at distributions over just average, but in general the number of rolls you get is pretty low statistically speaking to look at averages, especially when a point or 2 of speed can kill or make a unit.
In just sacred stones I have rolled an unpromoted 16 speed gilliam, a vanessa that capped strength and defence by level 5 promoted, and various amelias that have capped any specific stat stupid early. Heck the last time I attempted to use syrene she got 4 straight strength levels.
And Syrene was STILL trash :P
This just made me remember one of my Awakening playthroughs where I reclassed Miriel at like level 14 or something to a dark mage and as a level 17 dark mage she had 14 magic but hey at least she had 16 def. (I have a screenshot but it has been years since then) She stayed on the team cause I thought it was funny.
In my first RD play through my Jill got 2 points of strength over 15 levels (50% strength growth) 😭
I think it’s also important to note it would be really lucky for a given unit to get average or higher stats in every stat. If there is a 50% chance a unit gets their average stats or better, then the odds of getting average or above in every stat would be (0.5)^8 or 9 depending if they have both magic and strength, which comes out to about a 0.4% chance.
Yeah this was just one stat at a time, when you take all the stats on a unit the odds get truly insane, hence the sense that low level units are basically the lottery.
Through using the Bonus exp and accidentally I managed to max out my 20/20/20 Jill during my first playthrough. A fun memory for sure xD
One thing to add to this is that with any given unit, you're rolling the dice on a bunch of different stats and you're rolling for each of those stats on a dozen or more characters. Some of those aren't overly important but pretty much every unit has multiple very important stats they're hoping for (strength/magic, speed, defense, etc.) so the odds that things go very far from averages on some of your characters end up even higher considering how many chances you have.
This was easier to understand than any math class I’ve ever taken
I'm no math expert so I can only talk from a position of "stumbling around until I figure it out" but if that works for you then great! I hope I didn't horribly mess anything up lol
Shining Force Growth rates > Fire Emblem Growth rates for this very reason in my opinion.
The big difference is that there is a system in place that makes so your stats will always be close to the average. If you are expected to have 10 str at level 6, you may have 12, you may have 8, but you wouldn't jave the str you started with at level 1 nor you will ever get perfect levels across the board.
It retain randomness but it also doesn't ceeate a system where levelling up is a russin roulette.
One system sounds more fun then the other though
@@Silberlangbogen personally i found every system better than FE.
The game can't risk a softlock so it actually is designe around you not getting them so FE growths are basically just set dressing that only feel like it matter because the game put a lot of bell and whistle to it.
berwick saga's got this in the form of stat bracketing
@@noukan42 first, if the game literally was made impossible to beat because of stats, that'd be a hard lock, for not even resetting can save you.
Second, FE is nowhere near as tight to screw the player that much. The worst it has ever done is the thracian door hell and that isn't because of growths
Thanks for addressing one of the biggest beefs I have with the Fire Emblem community. Too many people (especially in the "efficiency" discussions) act like the average will always happen, and don't take into account variability.
There's value in the law of averages but not as much value as people like to claim, especially when you are accounting for specific breakpoints or necessary stat bumps.
Average stats are more like a forecast than a guarantee, and you can only really rate a unit on the average + consideration for deviation. Hence why prepromotes are often so good. They're rng proof.
Getting 3 points of Strength and Speed in the first 3 level ups is the difference between a unit like Nephenee in RD struggling and snowballing.
Average stats are great until units you play with don't meet them, I don't care about how godly Nolan and Jill are in FE10 if in my current run, they've gained jack and shit for their level ups due to bad RNG. I know they are good units on average but I'm not so inflexible that I'll force myself to use the same units every run because of the law of averages.
The above example actually happened to a Cousin of mine which was highly amusing to watch how she had to improvise with her unit selection and leveling up.
I've never had a Nolan with good strength or a Jill with good speed but I have had the most blessed Edward and Aran on the same run. Was real cool.
In games without fixed growths, I think average stats are (at least intended to) communicate a lot of the same points as a binomial distribution in a vacuum. Binomial distributions, to me, are most useful specifically when seeing the odds a unit crosses a key threshold (speed, damage, bulk). Totally agree that taking average stats at face value in a variable growth game (Unit X will have Y outcome) isn't going to be super productive.
Personally, I think variable growths are part of the fun of replaying Fire Emblem. To me, that's part of the in-game storytelling that Fire Emblem is so great at providing. Will Ross end up worse than Garcia on average? Well, yea. But you never know until you open the mystery box. :)
I was recently playing fe8 lunatic mod and every single cav of mine got strength screwed except for forde whose strength was so bad that it was still somehow the worst of the bunch. I early promoted kyle just to get SOME increase in effectiveness so I could have a non seth mounted unit that could get something done and then franz got exclusively strength on every level up for the next few chapters and surpassed kyle in every stat without even promoting. Franz was still pretty far below average in strength.
I always use a fixed growths patch in GBA and would in every game if it existed.
Fixed mode gang
This is all for a single stat on a single unit. Now look at the distribution of all a units stats and then all the units in an army, and you are bound to get some anomalous results somewhere
The binomial distribution thing is interesting to talk about, but not useful either.
I feel what this video is saying, and put simply, average stats are pre-gameplay expectations. Once you start using a unit, those expected averages aren't valuable in assessing the continued use of them.
Really to keep it as short as possible, anyone that's telling you not to use a unit that's already looking pretty blessed doesn't understand on a deeper level how much that immediately raises unit viability. And people that don't understand/know thresholds aren't accurately judging things regardless of stats.
The only thing that I like to add into the mix of this is that rate of growth also heavily effects this stuff too. If I take two units on different ends of a spectrum, like let's say Seth and Ross, can I talk about how well they would perform in the early game, of course Seth is going to perform better. But it's pretty realistic to expect Ross after he joins to be able to gain roughly a point of speed every chapter if you chose to use him, well it would be more likely for Seth to gain a point of speed every several chapters instead, despite his higher growths. In different ways this is an advantage in each characters estimations. Seth is still going to be above thresholds that you need to hit for a significant portion of the game, and you can completely neglect or not even care about his growth for quite a few chapters without really any consequence. Meanwhile Ross, despite his weak start, can see many opportunities to improve. Thinking about the averages as you do this isn't exactly the most valuable thing to focus on. Well it's useful to think in the manner that Ross during the first few chapters after recruitment is likely to see multiple levels of the minimum combat you should care about those early levels. If he breaks ahead immediately, there's a pretty good potential to see a unit snowball considerably as a unit that gets ahead is pretty likely to stay ahead. And because of the units growth rate being faster, a single overall bad level up isn't as damning to him as a unit like Seth.
Still if you give Ross 3 levels and he gets no speed, that's when you should start think if it's better to bench him.
My Kyle has even more defense, 😊.
Average stats are for the 50% of the time you"ll get that. It isn't much but we're not going to argue with 75% chances growths.
Some people do talk about 100% chances as that is essentially 0% growths.
But it's not 50% of the time, it's like 1/8th of the time. The rest of the time you'll be over or under it.
@@MythrilZenith
I'm Speaking with accumulated probablility. The idea is explain what you could do with *at least* those stats.
Tbh IQR would be way more helpful for this kinda thing
The first time I played FE7 - my first time playing any FE - my Sain hit 20 strength at level 14. He starts with 8 str at level 1, so he missed 1 str in 13 levels. Crazy. (60% growth).
Also, one thing you don't really explicitly call out about growth vs averages is that if a unit gains 3 str in 3 levels their actual average result after another 10 levels isn't the same as if they gained 0. You sorta hit on it with calling them growth units lottery units, tho.
Averages over time are course-correcting mathematical functions, this is strictly the math at work. Because growth rates are fixed, they don't care about what you gained when - the math cares only as far as it calculates the likelihood of a total set, but if you keep shifting it up or down based on the actual growths you receive, then the possibility space narrows and gets pushed linearly up or down with your given results.
@@MythrilZenith that's all only true if you haven't gained the levels. Nothing in FE results in course correction over the span of levels you gain. If a character joins at level 1 with 6 str, then hits 3 STR levels, it's like they joined at level 4 with 9 STR.
One thing that I keep thinking about because of this is: If base stats are a much better indication of a unit's value and growth rates have so little impact in most games, why did Kaga bother to put random growth rates in the first place?
For example, Shiida has awful growth rates in every stats except skill and speed, the two stats she is already close to cap. It makes me question why put 90% growth to the stat that she would have more than likely maxed out anyway if it was below 30% instead of the stats that are below everyone else average and would have found much more benefit from those 90% like her 10/20% strength.
In FE1 specifically, it is because promotion doesn't work on promotion gains, rather, it uses promotion "minimums".
Like SoV or 3h.
Palla will cap skill early, Catria and Caeda the same with speed. Palla and Catria are likely to not gain Strength on promotion, while Caeda is almost guaranteed to get a huge surge.
Maybe by the end they'll be the same unit, but on the road they'll have meningful differences.
Granted, I still preffer class base stats as promo gains and most FEs do it like that.
To keep units and playthroughs different. You had very little ability to differentiate units of the same class back then. They didn't want to give units massive bases across the board, so they gave them different growths to project the most likely course of units while still letting them be more random and unique.
Though FE1 in particular is a unique example which I will probably be making a video on in the future.
The question always is - can a unit perform at base? If yes then averages are a good indicator where they might end up at various points of the game. If no then averages are kinda useless. Unit like FE12 Minerva gets worse with bad level ups, but she's never unusable - in 0% growths she's useful for a good portion of the game. Meanwhile unit like Donnel on Lunatic has really hard time to even get a single level up and if it's a bad one, then his averages don't matter, he will most likely hit the bench.
mmm math; reminds me of back in the day how i just never ever got a florina who turned out at all lmao
Is this some sort of GBA joke I'm too EngageMaddeningFixedGrowths-pilled to understand?
Kinda and not really at the same time.
Core fire emblem is random growth rates. So removing that aspect takes away some of the continuous management and judgement the strategy game wants you to make. But pure fire emblem would also expect you to not know the actual unit growth rates as well. The skill it wants to test is your judgement of the random improvement, not your ability to know 50% is higher than 25% because you can see that listed.
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Bro if mekah see this he would had a Seizure. LOL
people really do b playing baby mode SRPGs with graphs like it's a competitive game