Just wanna say that my first Ross was so speed blessed I was confused when he was slow in another playthough

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.

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

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.

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.

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.

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

I was doing 3H Ironman and my lysithea proc-ed 6 strength vs 3/4 magic in her first 10 levels

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 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.

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.

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.

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.

This was easier to understand than any math class I’ve ever taken

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.

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.

It's so funny to me that the more I study statistics the less it ends up mattering towards my strategy.

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.

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.

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.

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.

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.

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. :)

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

Tbh IQR would be way more helpful for this kinda thing

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.

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.

Average stats are more useful when you're trying to compare two similar units or to compare a unit to a prepromote (in theory, just read in a comment that the ones on seresnes are not accurate for that because they don't take the reroll on failed growth into account but let's ignore that for my point =p). Like "am I likely to get that unit to a point where it'll be better than that prepropromote if I train it? is a useful information to have. If the answer is "no" or "yes but barely" then might not be worth training it. And knowing what you can expect two similar units to turn out like is also useful to know where to invest. Now it's not very useful to know if the unit itself is good in a vacuum. It's more interesting to have the likelihood the unit will be "good enough" to do what you want it to do. Like, if a unit has 50% chance to turn out mediocre and 50% chance to turn out amazing because they reached the right speed threshold you might get better value on average but you might be better off going for the units that's "decent" 90% of the time and garbage the other 10%. Also why prepromotes are often great. Because they can reach like, 100% chance to be decent because they start out decent. They might be very unlikely to become amazing but you'll never end up investing in a unit that turns out to be unusuable. There's also the question "how easy is it to fix?". Like, if a unit will always be good if I give it a speedwing and only occasionnally if I don't then it's worth holding onto that speedwing, see how it turns out and give it to it if you get bad rolls but use it on another unit if that's unncessary.

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.

mmm math; reminds me of back in the day how i just never ever got a florina who turned out at all lmao

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.

Is this some sort of GBA joke I'm too EngageMaddeningFixedGrowths-pilled to understand?

BEEFBEEFBEEF

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