Determining Roy and Lilina's real mothers using MATH! A (not so deep) analysis

[indigoasis]

Probably a somewhat lukewarmly debated topic of the Fire Emblem shipping wars is the question of who Roy and Lilina's "canon" mothers are. While the shipping wars of Genealogy/Awakening/Fates are far more hotly contested thanks to having two generations in the same game, Roy and Lilina have the benefit of being in another game entirely, not to mention that their parents' outings are in a prequel that had the benefit of hindsight.

Similarly to another thread I've done, I'm going to be compiling the growth rates and inheritance of Roy and Lilina's prospective parents together to determine who, mathematically speaking, is the most likely candidate for their "canon" mothers. However, the only real stats I'll be able to use are growth rates and affinities, so my findings are going to be inherently less complex (and less thematically interesting) than what I might be able to figure out from a game like FE4. Also, since I doubt that any of the calculations are going to be one-to-one the same, our goal instead will simply be to determine which pairing has the closest match to Roy and Lilina's growth rates.

Quick Disclaimer: This thread is purely for speculative fun. The information provided is not meant to prove or disprove anyone's personal biases, so please do not take this like I'm spreading gospel.

~ ~ ~

For the calculations to determine growth rates, I'll be using a slightly modified formula of Awakening's equation: (Father’s growth rates + Mother’s growth rates)/2. It's simply just an averaging equation. If I were to use FE4's formula, Roy and Lilina's growth rates would have been absolutely cracked, and quite frankly, they'd be way off the mark.

It should also be noted that, at least from my understanding (and feel free to correct me if I'm wrong here), Strength and Magic in FE6/7 are essentially treated as the same stat and share the same growth rate, but there aren't any classes in these games that would use both stats anyway. For the sake of the following calculations, Strength and Magic will be considered as one stat, but will conform to the character's classes as such (so since Lilina is a mage, she will have Magic; as for Roy, since he's a Lord, he uses Strength).

I would also like to point out that Eliwood and Hector actually have two different sets of growth rates for FE6 and FE7 respectively. To keep things consistent, I'll only be using their growths from FE7.

The possible candidates, as well as their personal affinities are as follows:

• For Eliwood (Anima)
  • Lyn (Wind)
  • Ninian (Ice)
  • Fiora (Wind)
• For Hector (Thunder)
  • Lyn (Wind)
  • Florina (Light)
  • Farina (Anima)

Also, for reference, here are Roy and Lilina's growth rates and affinities (the latter of which probably isn't going to come into play... like, at all, but I figured I'd include it anyway):

Spoiler

Roy

HP - 80%  STR - 40%  SKL - 50%  SPD - 40%  LCK - 60%  DEF - 25%  RES - 30%

Total Growths: 325%

Affinity: Fire

Lilina

HP - 45%  MAG - 75%  SKL - 20%  SPD - 35%  LCK - 50%  DEF - 10%  RES - 35%

Total Growths: 270%

Affinity: Light

Now then, starting with Roy, here are his possible growth rates:

Spoiler

Eliwood+Lyn

HP - 75%  STR - 42.5%  SKL - 55%  SPD - 50%  LCK - 50%  DEF - 25%  RES - 32.5%

Total Growths: 330%

Eliwood+Ninian

HP - 82.5%  STR - 25%  SKL - 27.5%  SPD - 55%  LCK - 62.5%  DEF - 30%  RES - 52.5%

Total Growths: 335%

Eliwood+Fiora

HP - 75%  STR - 40%  SKL - 55%  SPD - 45%  LCK - 37.5%  DEF - 25%  RES - 42.5%

Total Growths: 320%

As for Lilina, here are her possible growth rates:

Spoiler

Hector+Lyn

HP - 80%  MAG - 50%  SKL - 52.5%  SPD - 47.5%  LCK - 42.5%  DEF - 35%  RES - 27.5%

Total Growths: 335%

Hector+Florina

HP - 75%  MAG - 50%  SKL - 47.5%  SPD - 45%  LCK - 40%  DEF - 32.5%  RES - 30%

Total Growths: 320%

Hector+Farina

HP - 82.5%  MAG - 55%  SKL - 42.5%  SPD - 40%  LCK - 37.5%  DEF - 37.5%  RES - 27.5%

Total Growths:  322.5%

~ ~ ~

So, based on the results, who are the most likely to have been Roy and Lilina's mothers? Well... none of them, really. As it turns out, trying to mathematically figure out a character's growth rates based on their parents' growth rates from an entirely different game doesn't work out as well as I thought it would, and is a fundamentally flawed experiment. Lilina is a totally different kind of unit from Hector, and Roy actually shares more in common with his father than anything else; the only difference between Roy and Eliwood is that the latter takes a 15% dip in Luck to give 5% to his Strength, Defense, and Resistance respectively.

However, that answer is a total cop-out and not what I'm looking for, even if it's the truth. So, among the characters that provide the least radical changes and are the most consistent with Roy and Lilina's growths, it would be Eliwood+Lyn and Hector+Florina.

~ ~ ~

And there you have it folks! Quite frankly, unless my math is messed up somewhere, which I sincerely hope it is, I can't say that an Eliwood+Ninian shipper such as myself is all too thrilled with this outcome. When it comes to affinities, only Florina and Lilina share a Light affinity, and unless an Anima affinity can flip Ice into Fire, it seems I've only been able to confirm one of own personal biases today. How tragic.

Edited February 17, 2023 by indigoasis

[ping]

Counterproposition:

• Eliwood x Village Girl
• Hector x Other Village Girl
• Lyn x Florina

However, your method does help us figuring out the general nature of those two mysterious women by looking at their growth rates:

• Roy's mum: [ HP 80 | Str 35 | Skl 50 | Spd 40 | Lck 75 | Def 20 | Res 25 ]
• Lilina's mum: [HP 0 | Str 90 | Skl -5 | Spd 35 | Lck 70 | Def -30 | Res 45 ]

Starting with Eliwood's bride - none of her growths are particularly strange individually, but I have to point out that this specific combination (high HP and Lck growths, low to decent everything else) really isn't all that common. My educated guess: Roy's mum was a Trainee - which makes sense, given that the SacSto trainees are clearly inspired by the Gaiden villagers, and the three of them tend to have quite respectable Luck stats, but mediocre growths in the more "solid" stats. If I had to narrow it down further, I'd assume a sword- or bow-wielding trainee variant - high Skl and (to a lesser degree) decent Res is something that wouldn't be out of place on a Myrmidon or Archer.

Now, Hector's bride... oof. I hate to say it, but those growths seem to be those of a joke character. Zero HP growth? Negative Skl, let alone Def growths?! Even if we assume that the latter two only express themselves ingame as 0% - that's a weird set of growths. If the growths were all terrible, it would've been plausible for Hector to have wooed the Gotoh archetype of some adventure taking place shortly after the events of BlaBla, but that excellent Str/Mag growth in particular makes me believe that Lilina's mum was still expected to gain some extra levels. Now, this guess is obviously far less educated, but I'll go ahead anyway and say that Hector ended up marrying a Scribe, which is a class concept I just made up. Instead of actually fighting, the Scribe just sits there and scribbles magic runes to either attack enemies from afar or provide passive bonuses to nearby allies. Because of the lack of exercise, her physical growths (HP/Skl/Def) are all literal zeros, while her existing Spd growth represents faster writing.

[Original Alear]

Affinity could arguably be based on birth month: that's how the tacticians' affinity is determined, isn't it? So a differing affinity between a parent and child may not be very meaningful. Of course, one can argue based on unit personalities that a certain affinity fits one unit or another. Just an attempt at some food for thought.

[indigoasis]

51 minutes ago, ping said:

Counterproposition:

• Eliwood x Village Girl
• Hector x Other Village Girl
• Lyn x Florina

However, your method does help us figuring out the general nature of those two mysterious women by looking at their growth rates:

• Roy's mum: [ HP 80 | Str 35 | Skl 50 | Spd 40 | Lck 75 | Def 20 | Res 25 ]
• Lilina's mum: [HP 0 | Str 90 | Skl -5 | Spd 35 | Lck 70 | Def -30 | Res 45 ]

Starting with Eliwood's bride - none of her growths are particularly strange individually, but I have to point out that this specific combination (high HP and Lck growths, low to decent everything else) really isn't all that common. My educated guess: Roy's mum was a Trainee - which makes sense, given that the SacSto trainees are clearly inspired by the Gaiden villagers, and the three of them tend to have quite respectable Luck stats, but mediocre growths in the more "solid" stats. If I had to narrow it down further, I'd assume a sword- or bow-wielding trainee variant - high Skl and (to a lesser degree) decent Res is something that wouldn't be out of place on a Myrmidon or Archer.

Now, Hector's bride... oof. I hate to say it, but those growths seem to be those of a joke character. Zero HP growth? Negative Skl, let alone Def growths?! Even if we assume that the latter two only express themselves ingame as 0% - that's a weird set of growths. If the growths were all terrible, it would've been plausible for Hector to have wooed the Gotoh archetype of some adventure taking place shortly after the events of BlaBla, but that excellent Str/Mag growth in particular makes me believe that Lilina's mum was still expected to gain some extra levels. Now, this guess is obviously far less educated, but I'll go ahead anyway and say that Hector ended up marrying a Scribe, which is a class concept I just made up. Instead of actually fighting, the Scribe just sits there and scribbles magic runes to either attack enemies from afar or provide passive bonuses to nearby allies. Because of the lack of exercise, her physical growths (HP/Skl/Def) are all literal zeros, while her existing Spd growth represents faster writing.

I did consider what the Village Girl(s) might bring to the table (but figured nahhh), and I gotta say, the Scribe is legitimately funny. Nice work coming up with a story for those, too! It'd be a neat novelty to see a unit with negative growths in a future game (outside of negative growths runs).

44 minutes ago, Original Alear said:

Affinity could arguably be based on birth month: that's how the tacticians' affinity is determined, isn't it? So a differing affinity between a parent and child may not be very meaningful. Of course, one can argue based on unit personalities that a certain affinity fits one unit or another. Just an attempt at some food for thought.

If you wanna go the extra step, there are blood types too!... but only in Japan.

[Shanty Pete's 1st Mate]

6 hours ago, indigoasis said:

It should also be noted that, at least from my understanding (and feel free to correct me if I'm wrong here), Strength and Magic in FE6/7 are essentially treated as the same stat and share the same growth rate, but there aren't any classes in these games that would use both stats anyway.

The Energy Ring can boost either stat, as opposed to the "Energy Drop"/"Spirit Dust" dichotomy we saw later on. So it's fair to call them the same stat, with two different names.

6 hours ago, indigoasis said:

However, that answer is a total cop-out and not what I'm looking for, even if it's the truth. So, among the characters that provide the least radical changes and are the most consistent with Roy and Lilina's growths, it would be Eliwood+Lyn and Hector+Florina.

Huh. That roughly matches my most common (although not necessarily my favorite) pairings of these units. Guess I was on to something.

[AnonymousSpeed]

On 2/17/2023 at 1:51 PM, indigoasis said:

For the calculations to determine growth rates, I'll be using a slightly modified formula of Awakening's equation: (Father’s growth rates + Mother’s growth rates)/2.

Wouldn't it make more sense to derive an Elibe-specific formula using characters who actually have canonically known parents, like Clarine or Fir?

On 2/17/2023 at 5:12 PM, Original Alear said:

Affinity could arguably be based on birth month: that's how the tacticians' affinity is determined, isn't it? So a differing affinity between a parent and child may not be very meaningful. Of course, one can argue based on unit personalities that a certain affinity fits one unit or another. Just an attempt at some food for thought.

Yeah, I'm not if there's a support conversation that contradicts that somewhere, but it could just be a weirdo Zodiac sign. The Japanese version also relates it to blood-type, so in that sense it may also be semi-inheritable, but I don't think they have any clear direct relation like "O negative tends to be Fire affinity" or anything like that.

[indigoasis]

3 hours ago, AnonymousSpeed said:

Wouldn't it make more sense to derive an Elibe-specific formula using characters who actually have canonically known parents, like Clarine or Fir?

Y'know, I didn't even think to do that. I think you've definitely got the right idea, but I'm not sure how well reverse engineering a growth formula would go. I'm don't know if finding a formula for one character will translate over to another.

I'll give it a shot and see what I can do, though!

[ping]

6 hours ago, indigoasis said:

Y'know, I didn't even think to do that. I think you've definitely got the right idea, but I'm not sure how well reverse engineering a growth formula would go. I'm don't know if finding a formula for one character will translate over to another.

I don't believe a formula for one stat will translate over to another, to be honest. For example, while Fir's HP is near the average of Karla and Bartre's (60+85 --> 75), her Str and Spd are the same as Karla's, while her Skl and Lck are higher than that of both of her parents. Maybe if you subtract the class growth rates you can go somewhere, but I wouldn't bet on it.

[indigoasis]

9 hours ago, ping said:

I don't believe a formula for one stat will translate over to another, to be honest. For example, while Fir's HP is near the average of Karla and Bartre's (60+85 --> 75), her Str and Spd are the same as Karla's, while her Skl and Lck are higher than that of both of her parents. Maybe if you subtract the class growth rates you can go somewhere, but I wouldn't bet on it.

This was something I noticed after looking into it a bit. Just the fact that they share certain growths tells me it may not be possible in the first place.

I'm no mathematician, either. I'll try to come up with something, but like I mentioned, the formula for one character won't necessarily translate over to another.

[indigoasis]

Apologies for the double post, but I've added something to the original formula that I think is worth warranting an additional post. Now, it's definitely not perfect, and there's probably a better equation that can be used that yields the exact results, but I'm too lazy/not smart enough to figure it out, so for the sake of my own time and sanity, I'll post what I've got this time around. I think it's a tad more consistent than the original formula, at least.

Using the class growth rates that @ping mentioned, I took the difference between Roy and Lilina's growth rates and their class growth rates to yield a "growth modifier," so to speak.

Spoiler

Roy

HP (-10)  STR (-5)  SKL (+10)  SPD (-5)  LCK (+20)  DEF (+10)  RES (+18)

Lilina

HP (-10)  MAG (+20)  SKL (-20)  SPD (0)  LCK (+30)  DEF (+5)  RES (0)

I then combined these modifiers with the growth rates I previously found, making the new formula [(Father's Growth Rates + Mother's Growth Rates)/2 + Child's Growth Modifiers]. I've also gone ahead and bolded exact matches and italicized+underlined the closest matches to their original growth rates.

Spoiler

Eliwood+Lyn

HP - 65%  STR - 37.5%  SKL - 65%  SPD - 45%  LCK - 70%  DEF - 35%  RES - 50.5%

Eliwood+Ninian

HP - 72.5%  STR - 20%  SKL - 37.5%  SPD - 50%  LCK - 82.5%  DEF - 40%  RES - 70.5%

Eliwood+Fiora

HP - 65%  STR - 35%  SKL - 65%  SPD - 40%  LCK - 57.5%  DEF - 35%  RES - 60.5%

~ ~ ~

Hector+Lyn

HP - 70%  MAG - 70%  SKL - 32.5%  SPD - 47.5%  LCK - 72.5%  DEF - 40%  RES - 27.5%

Hector+Florina

HP - 65%  MAG - 70%  SKL - 27.5%  SPD - 45%  LCK - 70%  DEF - 37.5%  RES - 30%

Hector+Farina

HP - 72.5%  MAG - 75%  SKL - 22.5%  SPD - 40%  LCK - 67.5%  DEF - 42.5%  RES - 27.5%

With that, the new closest matches are Eliwood+Fiora and Hector+Farina.

...I'll get it the way I want one of these days.