TheNuttyOne

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I'm here to help out at least until SSB5 is released. So yeah, hi.

I'm picky with grammar, formatting, and consistency and can be pretty stubborn about them in a one-on-one debate (though I'll generally relent when I'm clearly outnumbered). I think it is very important as an encyclopedia that we present ourselves in a professional manner and these three aspects are some of the best ways to accomplish (or ruin) that image.

Also, the Oxford comma is always right. Sorry.

Things I'd like to see in Ultimate

Fighters

Given Ultimate's focus on veterans and Sakurai himself stating that there will be fewer newcomers than usual, it takes a different point of view to give a reasonable wishlist/prediction than a typical Smash game. Usually, Sakurai emphasizes other aspects (such as moveset potential, representation of Nintendo as a whole, and his personal like for them) over popularity; however, much like the DLC for Smash 4, he is more likely to focus on popularity in order to make more fans happy since there will be overall fewer newcomers. The three newcomers already confirmed (as well as some deconfirmed characters) give an indication as to what he is focusing on:

Shoe-Ins: Characters that the roster seems empty without, a la Inkling. These characters aren't necessarily highly requested -- but it's because everyone just expects them to be automatically included.
Wow Factor: Characters that have the fans shrieking -- some in joy, some in terror -- a la Ridley. These characters have caused quite a bit of debate in the past as to whether or not they are reasonable, or perhaps they haven't even been requested because everyone is too afraid of being disappointed.
Easy: AKA clones, a la Daisy. These characters don't require much effort at all and could be added at the last second just to buff up the roster. It helps if they come with some popularity -- like Daisy -- but they may beat out other, more popular characters -- like Waluigi.

We also now know that the game was being planned during development of Smash 4's DLC (I believe Sakurai said sometime in mid-to-late 2015?). Because the roster is one of the first things decided, this likely rules out:

ARMS. Even if ARMS was already in development, it would be too risky as a new IP for Sakurai to put effort into.
Xenoblade Chronicles 2. Similarly, Xenoblade Chronicles was a relatively lesser-known game prior to Smash 4, so it would be hard to predict how successful its sequel would be.
Super Mario Odyssey. Not that there are a lot of fighter options anyway, but we already know it hasn't impacted Mario's moveset significantly, indicating Sakurai did not consider it during early planning.
And potentially Breath of the Wild. However, Breath of the Wild has been in development for so long and Zelda is popular enough that I wouldn't completely rule it out. It did, after all, heavily influence Link, so Sakurai was pretty aware of it.

I feel like several potential newcomers can be taken from the Assist Trophies shown off -- or rather, not shown off. There seemed to be a lot of emphasis on demonstrating popular fighter choices (Waluigi was a particular punch to the gut, but we also saw Bomberman, Midna, Ghirahim, Krystal, Lyn, and Takamaru, who have all had their spotlights in the prediction games before), but several were conspicuously absent:

Shadow the Hedgehog: Honestly, this is the one I'm most suspicious of, and that's coming from someone who absolutely does not want to see Shadow -- or any other secondary Sonic characters -- as a fighter. However, not only was Shadow absent from E3, but they also have been showing off Knuckles, a new Sonic Assist Trophy, quite a bit. While it's possible we could see two Sonic Assist Trophies, it would be a first (granted, having two playable Sonic characters would be, too) and I see no reason to keep Shadow a secret. Even if he wasn't ready to be seen in gameplay, it seems to me that he would be shown in some of Sonic's screenshots. Additionally, as one of the most popular Sonic characters, Shadow would bring a huge amount of "Wow Factor" and, although I would be very shocked if he were a clone, his attributes are similar enough to Sonic that he may even count as "Easy" compared to other characters.
Ashley: I've never really understood her popularity, but hey, it exists. She'd also be a nice representative of the surprisingly lacking "magic users" category. I'm not convinced she carries enough "Wow Factor" to actually stand a chance, but she deserves a mention.
Dark Samus: I think Ridley has probably stolen any chances Dark Samus had, but again, she deserves a mention. Like Shadow, she probably would not be a clone, but she may be similar enough to qualify as "Easy" and carries a bit of "Wow Factor".
Dillon: Dillon was considered a "Shoe-In" for Smash 4, but does that still carry now? I'm not convinced, but again, he deserves a mention.
Isaac: This one is the easiest to explain away since he wasn't an Assist Trophy in Smash 4, but he has reached almost memetic standards of popularity much like Ridley. That carries quite a bit of "Wow Factor".
Isabelle: This one is more my personal hope than anything, but come on -- how in the world do you justify saying she wasn't ready to be shown off or is being kept a secret? She's probably one of the easiest Assist Trophies to program and is hardly a surprise. And she could be an "Easy" clone of Villager.
Phosphora: Another one I don't quite understand, but she's apparently a really popular Kid Icarus character. And unlike Viridi, she comes with a moveset. Her "Wow Factor" isn't great, but we know Sakurai favors his own series, so that might give her an edge.
Skull Kid: I'd definitely like to see him get in, but I'm wary. It seems like Sakurai would be more likely to favor Midna or Ghirahim. Not to mention Skull Kid doesn't have much moveset potential -- in fact, his Assist Trophy role was pretty arbitrary, so it honestly wouldn't surprise me if they're keeping him a secret because he'll have a new function (dropping the Moon on us like a Peach's Castle Banzai Bill?) or are cutting him entirely.
Tingle: Okay, um... no. He comes with a "Wow Factor" but I think it's the wrong kind, tbh. Also, he's probably only absent because of Great Bay. But I felt obliged to mention him.

As for other characters that may be possible:

Simon Belmont: I'm a little influenced by all of the leaks, but I do think he has a pretty good chance. I feel like we would have gotten Bomberman if they weren't considering Simon at all. But Simon definitely has the "Wow Factor".
Crash Bandicoot, Banjo & Kazooie, and Steve: These are also incredibly likely third-party characters with a good amount of "Wow Factor". I'm leaning towards Crash or Banjo, but there are the leaks that say Steve is coming. I don't know how I'd feel about that yet.
Shovel Knight and Shantae: Probably the most likely indie characters as well as the ones with the most "Wow Factor". I think Shovel Knight is more of a "Shoe-In" while Shantae is more wow.
A new Pokemon: This is probably the next most "Shoe-In" after Inkling. We've had a Pokemon from the newest generation in every game, I think the roster would feel incomplete without one. I think Decidueye has an advantage over my previous choice of Mimikyu due to its popularity, but I'm still crossing my fingers for Mimikyu to finally share the spotlight with Pikachu. And as for the development starting well before Sun & Moon was released -- they did the same thing with Greninja in Smash 4.
Bandana Waddle Dee and Viridi: These balance "Shoe-In" status with Sakurai's personal favoritism. Bandana Waddle Dee has the advantage of having an easy moveset, while Viridi was actually created by Sakurai. Which means both will probably lose to someone like Phosphora, or maybe Medusa or Hades, who have both aspects. Ah well.
Celica: Look, I'm not giving up on this. Sakurai previously broke from his solely-popular character mold during Smash 4 DLC by including Corrin, which was pretty risky, and Celica has already proven to be pretty popular. And like the Pokemon character, the development time doesn't matter as much because Sakurai took both Roy and Corrin pre-launch. And also like Pokemon, we've gotten a new Fire Emblem character in every game since Melee. I think Celica -- at least slightly -- qualifies for "Shoe-In" status. Also, she would still have quite a bit in common with Robin even if she's not a clone, so she gets the "Easy" tag as well.
King K. Rool, Geno, and Rayman: These characters are borderline memetically requested, just like Ridley, which qualifies them for a pretty strong "Wow Factor". Geno and Rayman probably stand a better chance than K. Rool, and I think Sakurai has even stated that he considered Geno once, so I'm kind of hyped for that possibility. Square, please play nice.
Mipha: She's borderline "Shoe-In" status thanks to her popularity, but her lack of moveset still bugs me.
Blood Falcon, Urbosa, and Dixie Kong: I'd say these are the next three most likely clones, after Alph who's already confirmed to be a costume (which kind of confuses me but oh well), making them "Easy" choices. Dixie and Urbosa come with a bit more popularity while Blood Falcon would get some wow because of F-Zero's newfound obscurity, so I'm not comfortable making a prediction on which are the most likely.

My personal prediction/wishlist based on this is:

Geno
Decidueye
Celica
Phosphora
Shadow the Hedgehog
Simon Belmont
Dixie Kong^ε
Blood Falcon^ε
Isabelle^ε

...which would give us 12 newcomers, four of which are clones. I don't think that's an unreasonable number -- it also comes with the benefit of being equal to the Original 12 and giving a sense of coming full circle, just saying -- and I feel as though most people would be more-or-less satisfied with a roster that looks something like this.

Stages

New Donk City: A traveling stage a la (and likely replacing) Delfino Plaza. It would start on the festival stage, where Pauline and the New Donk Players are. If the current music track is Jump Up, Super Star!, Pauline will be singing along; otherwise, she'll just be standing in the background and watching. Some landmarks it could stop at are in front of town hall, the helipad where the Odyssey lands, the pool on the ceiling, and Mayor Pauline Commemorative Park (where the remains of Mecha-Wiggler could be found and bounced on), among others.
Bowser's Airship: Finally, a home stage for Bowser! This could either be a side-scrolling stage, or a simple stage similar to Pirate Ship. Either way, Rocky Wrenches, Bullet Bills, and/or Flamethrowers could appear as hazards. If stage bosses come back, Boom Boom could be one.
Hyrule Castle: Based on the version from Breath of the Wild, of course. Another traveling stage. Guardians could appear as hazards, while briefly stopping in one of the guard towers to fight a Lynel would be a neat touch.
SR388: The surface of SR388. Rocky terrain resembling the mouth of a cave on the left side of the screen, with a pool of purple liquid on the right side that will damage players. Alternatively, it could function like a classic Metroid stage and have the purple liquid rise and lower to damage players.
Aether Paradise: Fighters battle on the Aether Paradise dock, with water beneath them. Occasionally, Professor Kukui's boat will arrive to give another platform, but it will eventually leave. Various Pokemon and Aether employees appear in the background.
Divine Terminus: Lord Hyness's battlefield, but shrunken down to give it bottom blast lines. The red spikes in the background appear along the edge and will damage fighters who touch them. Hyness can be seen conducting his ceremony to rebuild the Jamba Heart in the background, with Francisca, Flamberge, and Zan Partizanne occasionally flying past as well.
Inkopolis Tower: A fight on top of Inkopolis Tower. Occasionally, the Great Zapfish will fall from the sky and wrap itself around the tower. If a fighter touches it, they will be electrocuted and knocked back slightly. Eventually, the Great Zapfish will be abducted by an Octarian UFO.
Ram Village: Outside of Mycen's house, which fighters can climb on. There's also an orange tree, which will occasionally drop oranges as food when attacked if items are turned on. Mycen's roof has a lower portion by the door as well as an upper portion and is made up of soft platforms. The stage has no lower blast lines.
Sky Arena: Max Brass's arena, with his giant head in the background looming over us all. The audience is removed, giving the stage bottom blast lines. The center is slightly raised above the edges, which have railings. The Max Brass statue stretches out over the stage enough to be stood on as a semi-soft platform.
Remix: A Rhythm Heaven stage that functions similarly to WarioWare, Inc. The main fight happens on a fairly basic stage in the art style of the game, with fighters being taken into well-known Rhythm Heaven minigames. Unlike WarioWare, however, instead of completing the task to get a reward, they must dodge the characters in the game. For example, if they're pulled into Fan Club, the monkeys will damage them by clapping.
Snipperclips: At first a stage with no lower blast lines, the center part of the platform is made up of the purple paper that Snip and Clip must cut through in Make the Cut levels, which will slowly be broken away as attacks hit it. Occasionally, something will fall from the top center of the stage: slime, which will fill any holes in the paper or slide around the top of the stage, slowing down fighters that get stuck in it; a bowling ball, which will break through the paper and meteor smash any fighters underneath it; a basketball, which will bounce in place but can be attacked to fly hazardously around the stage; a pencil, which will fall over and bury fighters that it hits; or a hamster in a ball, who will roll offscreen in a random direction, damaging any fighters he hits. An exclamation point will appear before anything falls. Snip and Clip can be seen in the background in random shapes.
Tetris: Players fight in a giant Tetris puzzle as blocks fall from the sky. If a fighter is crushed by a block, they will be dealt damage and buried. Blocks can be attacked to be destroyed, or will disappear when an entire row is filled like in normal Tetris.

Modes

I'd love to see some form of the fake-leaked Tower of Smash from Smash 4.
Smash Run, with the ability to interact with other players like in City Trial, would be welcome back.
Please make Classic Mode actually function like 1P Mode from SSB. That is, after all, why it's called Classic Mode.
I wouldn't mind another Adventure Mode.

Items

While a serious long-shot, the Breidablik would be an interesting Poke Ball- and Assist Trophy-like item specifically for the Fire Emblem series. There are a number of secondary characters who would never make it as fighters but could be effective and unique assist characters.
The Bug Net or Fishing Rod from Animal Crossing could be a neat way to give all fighters access to longer-range grabs.
One or all of the Rods from The Legend of Zelda (specifically as they appear in Breath of the Wild) would be neat.
Depending on how Inkling's moveset works, there are lots of item options from Splatoon. The various Bomb subweapons would work, or simply a Splattershot or even a Roller to bury your opponents.

Assist characters

Make it possible to turn on/off certain summons! Please!

Pokemon

Diancie could use Diamond Storm to rain sharp diamonds down on the stage. They wouldn't be able to go through platforms, making her particularly deadly on Final Destination and Omega forms.
Hoopa could use Hyperspace Hole to block off the blastlines, causing launched players to either loop around the stage or just reverse directions (if there are no bottom blastlines).
Litten could function identically to Fennekin.
Grubbin uses Dig to hide under a platform like a Pitfall, but when a character steps on them, they are paralyzed by Spark instead of buried.
Wishiwashi flops uselessly on the stage like Goldeen at first, but if attacked, it will change into its School Form and attack all fighters.
Bewear: uses Bind, grabbing onto a random opponent and attempting to drag them off-screen a la Nabbit.
Tsareena: uses Trop Kick, functioning identically to Waluigi.
Turtonator: uses Shell Trap, exploding upon being touched.
Necrozma: uses Photon Geyser, which is a massive pillar of light in the middle of the screen, catching and damaging everyone caught in it.

Assist Trophies

Nabbit: works identically to as a stage hazard.
Kamek: sprinkles his magic over the fight a la Yoshi's Island, either:
- causing the summoner and their teammates to grow, or
- causing the summoner's opponents to shrink.
Bring back Resetti, please.
Katrina: creates a tarot card, with different results:
- Red card with black circle: the summoner starts tripping randomly.
- Blue card with black circle: the opponents start tripping randomly.
- Red card with white circle: the opponents are healed slightly.
- Blue card with white circle: the summoner is healed slightly.
Yiga Blademaster: stands in one place and swings his Windcleaver, not only dealing knockback to anyone he hits but also launching gusts of wind.
Azura: sings and dances, boosting the stats of the summoner and their teammates.
Polar Bear: walks around, causing earthquakes when it jumps.

Breidablik

Palla, Catria, & Est: use their Triangle Attack, Palla and Catria coming from the top corners of the screen and Est coming from the middle bottom.
Delthea: uses Aura, creating white rings of light that chase enemies like weaker Blue Shells.
Arden: moves slowly towards an opponent, swinging his sword for massive damage and knockback if anyone moves into his range.
Lilina: uses Forblaze to create two pillars of fire on either side of her.
Eirika: stands in place and does a few sword moves, which trap and deal quite a bit of damage but not much knockback.
Lyn: same as usual.
Micaiah: creates a thin pillar of light around her, healing anyone inside of it. The summoner and their teammates heal slightly faster.
Nowi: transforms into a dragon and starts storming around the stage.
Azura: same as above.