Some general thoughts on whether or not this will happen:
If we're going to be getting a first-party character for this wave it will probably be someone from Three Houses. Love or hate Fire Emblem, it's one of Nintendo's biggest series as of now especially with
Fire Emblem Heroes being a massive hit for them. The game was first publicly shown off during E3 of last year and Sakurai has sometimes went off of concept art alone to design a character. He did this in SSB4,
creating a whole moveset for Greninja in May 2012 when X/Y was first publicly revealed in early 2013. If Nintendo intended to promote one of their big upcoming games then time wouldn't have been much of an issue in this case. Three Houses is also the third most digitally purchased Switch game as of this writing (the first two being Minecraft and Mario Maker 2) so a promotional rep could definitely happen if we get a season 2.
On the downside though, Fire Emblem fatigue in Smash is a thing that
even Sakurai is aware of (hence why he was hesitant to add Corrin into SSB4). Yes we did get Chrom in Ultimate, but only as an echo and after immense fan demand (not to mention that he was originally planned for SSB4 anyway). Also Sakurai has said that he usually doesn't add characters unless their game is out,
which is why he didn't decide on Incineroar until he got his hands on Ultra Sun/Moon. Granted this shouldn't be too much of an issue since Three Houses is already out, but Sakurai may have wanted to try it out personally before deciding on whether to add someone. As for personal beliefs, I'm still a believer that most - if not all - of the characters for this wave will be third-party.
So in short while I don't think this is impossible I also don't think we are likely to get a Three Houses character for this wave. Ok now for the individual chance/wants...
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Edelgard
Chance: 10%
Edelgard was definitely the most popular character when the game was first shown off and seems to be the most significant of the house leaders. The worldwide ingame statistics also show that she is the most popular house leader as well as the most popular unit in the game overall. Claude and Dimitri are the 2nd and 3rd most popular house leaders respectively. Because of this I think Edelgard is easily the most likely of the individual house leaders especially if we get a season 2 wave of DLC. That said though, there is a chance that she could get Azura'd and be ignored over the actual main character of her game.
Want: 80%
Edelgard is without a doubt my favorite of the three leaders and I chose Black Eagles as soon as I got the game. Her design is cool and the fact that she can use axes would make her stand out from all of the current FE characters who use swords. Only reason this isn't higher is because there are still a few other FE characters I'd want over her, specifically Celica and Lyn.
Byleth
Chance: 10%
I think it could go either way with Byleth or Edelgard. Whereas Edelgard seems to be more popular, Byleth benefits from being the actual main character of the game.
Want: 70%
I initially didn't care about Byleth at all, but over time I've grown to them (well except the female design of them which I'm still not a fan of). Having a character with a whip sword in Smash would be awesome.
Dimitri
Chance: 1%
I don't see us getting a Three Houses character that isn't Edelgard or Byleth. They have a lot more going for them that it'd feel odd for Dimitri to make it in over the two.
Want: 5%
Dimitri is my least favorite of the house leaders and I'm not a fan of the people in his house. While I wouldn't mind a lance fighter, I definitely would not want him to make it in over Edelgard.
Claude
Chance: 1%
Like I said with Dimitri, I think it's Edelgard/Byleth or bust. I just don't see Claude making it in as the sole Three Houses rep.
Want: 15%
I'm more interested in Claude/Golden Deer than Dimitri. A character whose moveset revolves around their bow would be pretty cool.
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SNK rep chance prediction: 18.68% (with only 2 slots left and no new writeup from me, this will definitely be lower than last time)
Tekken rep chance prediction: 21.72% (if my ramblings in the newcomer discussion thread are anything to go by this rating will be higher than Heihachi's last chance score)
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Nominations:
Concept: Rockstar Games rep x5