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The anticipated impact of Custom Special Moves on gameplay and balance (Statistics!)

Thinkaman

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There already exist many threads discussing the potential legality of customization options for both Wii U and 3DS titles. Please go to those threads to discuss the specifics of tournament policy or personal preference. This thread is for theory-based discussion over the the specific meta-game implications of allowing custom special moves.

Hey guys, I'm Thinkaman. For those who don't know me, I was a very active smasher in the Midwest from 2007-2010, and still play here and there. I also made Balanced Brawl with Amazing Ampharos during this time, and learned more than I ever wanted to know about the 666 different matchups in Brawl.

When special custom moves were originally announced, I was quite skeptical; I was worried it would be a waste of development time that would prove irrelevant to both competitive and casual multiplayer. However, after some thought and reading, I'd like to share some realizations that made me change my mind completely.

At the heart of everything is this simple statistical fact:

Taking the best of three options results in a more consistent, higher average result.

This is used as a mechanical cornerstone in lots of games, especially tabletop games. Often times tabletop games will generate characters by having players roll multiple dice and use the highest results. Fire Emblem usually computes actual hit probability by rolling twice, and taking the highest result.

Suppose you roll a six-sided die. You have an equal chance of getting 1, 2, 3, 4, 5, or 6.

A graph of this distribution is as boring as you'd expect:



You have equal odds of getting all 6 outcomes. It's flat.

The mean (average value) is 3.5
The nominal variance (standard deviation) is 1.708
The variance relative to the range is 28.46%

Now let's compare that to rolling the same die 3 times, and taking the highest result:



You now have much higher odds of getting a higher outcome. It's very rare to get a 1, and extremely common (>60%) to get a 5 or 6.

The mean (average value) is 4.958
The nominal variance (standard deviation) is 1.144
The variance relative to the range is 19.06%

When we compare the values, we can easily see that the average value went up, but the variance went down; it is now about two-thirds its original value. While there are still outliers, the results are overall far more closer in value than before.

But what does this mean for Smash?





Characters taking the best of three special move options results in more consistent, stronger average characters.

Not really that surprising, but let's try some numbers as an example.

Let's rank all special moves 0-100, where 0 is Sing and 100 is Shuttle Loop. To keep things simple, let's assume all moves are evenly spread across this ranking. (This isn't exactly true, but it's close enough and won't affect our conclusions.)

So for the set of all special moves, according to our rankings:

The mean (average percentile) is 50.0
The nominal variance (standard deviation) is 29.155
The variance relative to the range is 28.87%

But now what if we give every character 3 equally random options, take the "best", and judge it according to the default percentiles?

The mean (average percentile) is 75.248
The nominal variance (standard deviation) is 19.558
The variance relative to the range is 19.364%

Just like before, the variance is now about two-thirds its original value. The moves are overall stronger and more equal in value, and more equal moves means more equal characters.

Still not getting it? Let's think about this holistically for a second, with examples.



Shuttle Loop is almost definitely the best special move in Brawl. It's invincible, it's safe, it transitions into a powerful and safe glide attack, it provides incredible off-stage control and recovery, it does solid damage, and it is a reliable kill option. The move had to be changed considerably for Smash 4, due to how insane it was.

If you were to give Brawl Meta Knight players the option of instead taking some new different move, Meta Knight doesn't get any stronger; they are all still going to take Shuttle Loop. The other option could be an incredible 98th percentile move, and everyone is still going to take the 99th percentile Shuttle Loop.

Alternatives don't help you if your current options are already top tier.



On the other hand, if your current move is Sing, you have nowhere to go but up. It is literally impossible for a functioning move to be worse than Sing in 1v1 gameplay.

Smash has lots of mediocre moves like this. Pk Flash, Din's Fire, Egg Roll, Sheik's old down-b... the list goes on and on. This is not because Smash is poorly designed, but because Smash has so many modes of play. (Many of those moves are great in teams or FFA!) We are already seeing this pattern continue in Smash 4. (Rosalina's down-special is a good example.)

While guys like MK can't benefit much from alternate options, characters who are low-tier due in part to crappy or niche specials have the potential to gain a great deal.



"But wait, what if a move option is broken? What if Meta Knight gets an EVEN MORE broken option over Shuttle Loop?"

Sure, it could happen. But that hypothetical broken move is just as likely to end up on Ganondorf. And while a single move of that caliber wouldn't make much of a difference on Meta Knight, it would have single-handedly skyrocketed Ganondorf into the mid-tiers of Brawl.


Dang it Ganon, that's not what I meant.

Special move options should reduce matchup polarization.

What's polarization? Polarization is the side of balance no one ever talks about.

Polarization is one side having an advantage in a matchup, even if the characters are overall on the same tier. (Because of other matchups polarized in the other direction!)

If in Starcraft Terran always beat Zerg, who always beat Protoss, who always beat Terrain, we wouldn't ever call this a "balanced game." We'd call it Rock-Paper-Scissors, and no one would watch it.

In Smash, the main contributors to polarized matchups are:
  1. Chaingrabs
  2. Disjointed Hitboxes
  3. Recovery Limitations
  4. Projectiles
  5. Approach Limitations
  6. Grab Limitations
Special moves have essentially no impact on the chaingrabs, but a big impact on all the others.

Many characters who face opponents with a significant advantage in hitbox disjoint across their entire moveset rely on special moves to compete. This is because special moves commonly involve projectiles or sudden character movement, both of which can nullify the fundamental range advantage.

A shift towards more powerful specials make hitbox disjoint less critical in matchups.

Almost all characters rely on their specials for recovery. Not just up-Bs; specials in all 4 positions are used by various characters to recovery both horizontally and vertically; sometimes as alternatives, sometimes as a combination.

Letting characters with poor recoveries consider different options, even if they are also poor, avoids toxic matchups where there default recoveries are easily exploitable.

Many slow, ground-based characters have an innate weakness against projectiles. Faster running speed in Smash 4 is a big help, but it will surely still be a factor.

Projectiles are the only category that has high potential to get worse. However, it is unlikely design for spammable projectiles to be given randomly to characters who had none before, so the actual negative impact of this will probably be limited. At worst, characters with spammable projectiles might get options that are slightly more exploitable.

However, it is also likely that characters most harshly exploited by projectiles could get new options (movement-based attacks, reflectors, super armor) to get around them.

Many characters struggle in matchups where they are forced to approach, but have no valid options for doing so.

Just like with recoveries, letting characters with poor approach options pick specials with this in mind has the potential to avoid exploitation and help them a lot.

Finally, some characters with poor grab ranges, punishable grab cooldowns, or weak throws are vulnerable to defensive opponents.

Letting players with poor anti-defensive options prioritize command grabs, projectiles, or safe-on-hit moves will help them from getting camped.

Consider how Mario's alternate options address all of the criteria that effect his poor matchups:



While it remains to be seen how well these alternate options actually address Mario's concerns, they are certainly topical.

All this leads us to a key conclusion, separate from polarization...



Special move options should make the game more offensive.

Special moves can be used "defensively", but they rarely have anything to do with actual defensive mechanics. A character's defense is a primarily a property of their general movement parameters, cooldown frame data (especially on dodges), shield safety, and out-of-shield threat.

Special moves have relatively little to do with those things. Up-B-out-of-shield and the rare spammy, safe, zoning move (usually projectiles) are the only things that contribute primarily to the defensive game.

On the flipside, everything else about special moves is offensive use:
  • Command grabs
  • Movement-based attacks
  • Extra shield damage
  • Multi-hit attacks (Disproportionately good against shielding or dodging)
  • Super armor
  • Projectiles used for approach
  • Reflectors (Punishes defensive projectile spam more than approach)
  • Charge-Up mechanics (Punishes not approaching)
Special moves are, overall, the most offensive class of moves. (Followed by aerials) If the relative power and importance of special moves increases, the game is likely to shift slightly towards more offense.

I personally am in favor of a more defensive game, but the facts are what they are. I am more than willing to enjoy a more offensive game with superior balance and fewer polarized matchups.



Special move options should reduce skill skew.

Skill skew is where something exhibits different balance at different skill levels. This is why new players think Roy and Ike are the best characters, and that Ice Climbers and Diddy Kong are awful.

The need and difficulty of balancing to different skill level is the source of many balance problems, just like the need and difficulty of balancing to different modes. (Like how Kirby Stone, Falcon Punch, and Din's Fire are overpowered against new players, and nearly useless against an experienced opponent 1v1.)

Skill skew affects projectiles and extremely slow/predictable attacks more than any others. The overwhelming majority of these moves are special attacks.

This means that competitive balance has a lot to gain from potential alternatives to these moves, where they are nearly useless in comparison to the lowest-common-denominator context they are forced to be balanced for.



Mythbusting time!

"Sakurai said that the special move options wouldn't be balanced!"

If I had a nickle for every time Sakurai was mistranslated or misinterpreted, I'd import a Japanese 3DS with half my loot.

Half the time when Sakurai says "balance" in an interview, including in this statement made at the E3 roundtable event, he is talking not about character balance, but balancing the accessibility and complexity of the game. The actual quote was talking about online play:
"However, to ensure balance, customization will not be available in the "With Anyone" mode."
This makes sense. Customization is a feature for the most hardcore. It is not appropriate for random online players to encounter unexpected moves they might have never seen before. This is a frustrating and annoying experience for players who have not explored the game fully.

"We shouldn't allow custom moves in competitive play, because they are not allowed online, even in For Glory mode."

So competitive play should only be on Final Destination? No wonder Ice Climbers were removed!

But seriously, the point of For Glory mode is a quick and dirty random fight--a decent game of Smash, as quick as possible. It is not comparable to tournament play, where we use longer stock matches, play full 1v1 sets, pick a variety of stages, and enable team attack.

"What about custom equipment? It looks broken."

Honestly, at this point we have no idea how equipment will affect the game. Very few of the points I have discussed about custom specials here applies to equipment.

We can totally have one without the other with minimal fuss though, if we want to. I guess we'll see?

"Custom options have never worked well in any other competitive game."

Street Fighter 4 does just fine with multiple Ultra options. Usually one option is better at a competitive level than the other, and the character would be worse if they were forced to use the weaker option.

Additionally, many games in other e-sports genres have many customization options, such as League of Legends. (However, these are much more comparable to equipment than custom special moves.)



Conclusion

Thinking about the way custom special moves are likely to impact the game made me go from being skeptical to loudly optimistic. It seems likely that custom special moves will be the defining trait of hardcore Smash 4, and result in superior character balance.

We need to do two things:
  • Make exploration of custom special moves a top priority upon release.
  • Advocate tournaments that assume legal custom special moves, unless something game-breaking is found.
It would be the saddest irony to spend the last year worrying about the competitive nature of Smash 4, and proceed to neglect its most competitive feature included specifically for the most hardcore players.

And seriously, screw Sing.
 
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Ryuutakeshi

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I think the safest thing to do would be to ban whatever specific custom move option proved to be gamebreaking but leave the others as legal.

This post raises some very good points and I'd love to see custom moves help keep the higher tiers more variable when it comes to characters.
 
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Ellipsis

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These are some well-reasoned points. If I wasn't already in favor of custom moves in competition, this thread would have swayed me.
And seriously, screw Sing.
Now if only there was a way to like a post twice.
 

Thinkaman

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I think the safest thing to do would be to ban whatever specific custom move option proved to be gamebreaking but leave the others as legal.
It's important to keep in mind that "gamebreaking" here means "actually game-breaking", as in freezes, infinites, or totally degenerate gameplay. We're not going to ban a move for being "really really good"; both Melee and Brawl did just fine with a bunch of "really really good" moves.

I mean, Melee Rest was literally a frame-1 OHKO. If we can live with that, we can live with just about anything.
 

Raijinken

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This basically says it all. Good job!

On the subject of stat equipment, that too could have a similar impact on average balance, but may need to be more regulated than custom moves, as something that looks foolish (reducing attack power on a character) could end up broken (enabling longer or infinite combos due to the reduced knockback).
 

Ellipsis

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On the subject of equipment, do we have any confirmation of whether the stat mods are randomized per item, or predetermined? See Kid Icarus Uprising for an example of random equipment stats.
 

Amazing Ampharos

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On the subject of equipment, do we have any confirmation of whether the stat mods are randomized per item, or predetermined? See Kid Icarus Uprising for an example of random equipment stats.
We have no idea. In general, the equipment system, while it still deserves testing and is maybe good, it a lot less promising than the move system, and we also know a lot less about it.
 

xLemmy_KoopaX

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Raijinken

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On the subject of equipment, do we have any confirmation of whether the stat mods are randomized per item, or predetermined? See Kid Icarus Uprising for an example of random equipment stats.
A Direct (I think, maybe a PotD) said that items of the same name may have different stats, but whether those are finite and preset or totally randomized remains to be seen.

Edit: It's no longer "to be seen". They're entirely random.
 
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KaZe_DaRKWIND

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I feel that the custom stuff should be its own tournament. That way certain people will focus on it and those who like it the way it is can stick to normal.
 

Ellipsis

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I feel that the custom stuff should be its own tournament. That way certain people will focus on it and those who like it the way it is can stick to normal.
Splitting the player base is a very dangerous thing for a community to do. It should not be a first resort.
 

Super_Queijo

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Well, wasn't the Tekken team part of the development of Smash4? They are good at this right?
 

JamietheAuraUser

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While I wouldn't be surprised if custom equipment has its stats "randomized", it's likely that there will be a formula that is followed by the game to stop an equipment item from giving stat gains disproportionate to its stat reductions. I also suspect that, like Kid Icarus: Uprising, there will be equipment that every player will get a copy of with preset stats, due to it being a reward on the challenge board.
 

Ellipsis

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While I wouldn't be surprised if custom equipment has its stats "randomized", it's likely that there will be a formula that is followed by the game to stop an equipment item from giving stat gains disproportionate to its stat reductions.
Not good enough. As long as each option affects the game differently, every Wii U at a tournament must have them all unlocked, just in case. Otherwise that's just not fair. That's a prohibitive amount of grinding, considering Wii U save files can't be copied from one system to another.
I also suspect that, like Kid Icarus: Uprising, there will be equipment that every player will get a copy of with preset stats, due to it being a reward on the challenge board.
This could work, in theory.
 

JamietheAuraUser

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Not good enough. As long as each option affects the game differently, every Wii U at a tournament must have them all unlocked, just in case. Otherwise that's just not fair. That's a prohibitive amount of grinding, considering Wii U save files can't be copied from one system to another.
Correct me if I'm wrong, but wasn't there a system update recently released for the Wii U that allows for copying of save files between systems?
 

Ellipsis

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Correct me if I'm wrong, but wasn't there a system update recently released for the Wii U that allows for copying of save files between systems?
Was there? If my experience is out of date, that could change things.

Edit: http://time.com/3018322/nintendos-wii-u-to-wii-u-transfer/ If that's what you were talking about, it won't work. That's a full system transfer. It clones your old Wii U onto your new one and removes the original.

If there was some other update, ignore this.
 
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LancerStaff

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While I wouldn't be surprised if custom equipment has its stats "randomized", it's likely that there will be a formula that is followed by the game to stop an equipment item from giving stat gains disproportionate to its stat reductions. I also suspect that, like Kid Icarus: Uprising, there will be equipment that every player will get a copy of with preset stats, due to it being a reward on the challenge board.
Back in KIU, none of the equipment from the treasure hunt was worth using. Pretty sure it'll be the same here.

Correct me if I'm wrong, but wasn't there a system update recently released for the Wii U that allows for copying of save files between systems?
That's a whole system transfer.
 
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鉄腕
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The only thing I'd be concerned with is that it seems you have to unlock special moves, which may prove to be a hassle for tournaments to organize.

That said, custom moves definitely seem like they could help breath new life into the metagame. I'm also sure there will be a fair amount of people who'll want to play as Mii Fighters, and banning custom moves would mean we'd have to probably ban them.
 

LancerStaff

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The only thing I'd be concerned with is that it seems you have to unlock special moves, which may prove to be a hassle for tournaments to organize.

That said, custom moves definitely seem like they could help breath new life into the metagame. I'm also sure there will be a fair amount of people who'll want to play as Mii Fighters, and banning custom moves would mean we'd have to probably ban them.
We know for a fact you need to unlock the moves, but it won't be a problem early on because it'll be 3DS only. And if we can transfer stuff like that to SSBU, we'll be set.
 

DairunCates

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So the variance relative to the range is equivalent to the tier gap between characters?
Yep. A lower variance means a lower overall difference between the weakest and strongest character. So, even though the custom moves will make EVERYONE stronger, they will, barring statistical anomaly, make the characters closer in relative power.

By the way, fantastic post. It's always good to see other game theorists and statisticians talk about games.
 

Plain Yogurt

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The only foreseeable problem I see is, assuming custom parts are banned, they're right next to custom moves in the menus. "Oops! I 'accidentally' equipped a part that boosted my launching power by just enough to kill you earlier!" Of course, if all part up/downgrades are significant enough that their effects are quite apparent then I suppose this wouldn't be a problem. Beyond that though I'm so ready for legal custom moves. None of the ones we've been shown look stupid broken yet and they could add so much to a character with the many combinations you could try.
 

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It's absolutely correct that custom moves, on average, benefit lower tier characters more than higher tier ones. MK had a lot of good moves that were almost never used because he usually had an option that was better, while Brawl Puff was notorious in terms of having useless specials, and would've benefitted from getting a reliable killing option instead of something as risky as Rollout/Rest or just plain useless like Sing. I suspect that most of these options will be manageable, and whatever isn't can simply be banned.
 

DairunCates

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The only foreseeable problem I see is, assuming custom parts are banned, they're right next to custom moves in the menus. "Oops! I 'accidentally' equipped a part that boosted my launching power by just enough to kill you earlier!" Of course, if all part up/downgrades are significant enough that their effects are quite apparent then I suppose this wouldn't be a problem. Beyond that though I'm so ready for legal custom moves. None of the ones we've been shown look stupid broken yet and they could add so much to a character with the many combinations you could try.
This is honestly pretty simple to fix. You just start flat-out DQ'ing anyone found with an item on their characters after a match in 3DS tourneys and for Wii U, the actions will presumably be done on stage. You also can probably just throw away all the custom parts on the tourney save file.
 

Ehn Jolly

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This is a pretty sweet post, and really changed my mind onf custom moves. I'm actually looking forward to seeing how they're looked at by the competitive community as a whole, but this really makes me think they should be included.
 

micstar615

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Wonderful post @ Thinkaman Thinkaman ! Besides the roster itself, custom moves are the one thing I'm REALLY hyped for, they'll add a lot of depth to the game for both casual and competitive smashers.
 
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lob

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wow.. this is really well written out. i think everyone agrees custom moves should be allowed competitively to some degree but you really did a good job with this dude
 

lob

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"What about custom equipment? It looks broken."

Honestly, at this point we have no idea how equipment will affect the game. Very few of the points I have discussed about custom specials here applies to equipment.

We can totally have one without the other with minimal fuss though, if we want to. I guess we'll see?
if it's anything like it was in kid icarus, equipment will be completely random. the chances of you finding equipment thats going to benefit your playstyle is one in a million, with a lot of buffs and changes either being useless or really overpowered. it might be better off to leave it alone for the first few months or year of the meta until we really figure out how equipment works
 

Plain Yogurt

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This is honestly pretty simple to fix. You just start flat-out DQ'ing anyone found with an item on their characters after a match in 3DS tourneys and for Wii U, the actions will presumably be done on stage. You also can probably just throw away all the custom parts on the tourney save file.
Ya know, come to think of it this kind of stuff will probably show up on the stats screen somehow anyways. Good point.
 

SmashChu

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The problem with the analysis (albeit really good) is it works on the assumption that there will be an option that is superior.

That's not how it works. Consider Awesomenauts. In that game, each character has 6 upgrades to their special moves. Some are worse than others yes, but others are chosen based on style or perference. For instance, on Yuri's timewarp, I got Heal, Fast Forward, and CC Immunity on it. Others will get a Lifesteal for it. I'll only grab lifesteal if I'm fighting Ayla, Vinney or another Yuir. You can do this with any character. With Lonestar's Dynamite, I get extra Stick, lifesteal and DOT, but you can replace the DOT for Explosion size, bounce and blind. All of them work. Yes, there are bad upgrades (Penny's and Swiggins seem to complain the most), but a lot of them are style or based on other upgrades you selected.

For Smash, it will be the same thing. Take Mario's fireballs. You may go normal or maybe orb. But maybe fast isn't good. You may chose them based on match-up (perhaps Orb is good against certain characters). So you can't look at this in a linear fashion because it's not. It's going to be living and breathing.
 

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Who turned back the time machine and invited you Thinkaman=???

:rotfl:

But nah, good post, and I gotta agree. We should test them. If there are a few broken ones, banned them (and wait for patches) instead of just banning all of them.

As for customized stats and items and that jazz, that stuff sounds like it would mess with the physics and make things too strong. Plus it's all grinding, which is the opposite of what a competitive fighter like Smash Bros. should be.
I mean, Melee Rest was literally a frame-1 OHKO. If we can live with that, we can live with just about anything.
It was a one hit KO either way though.

If you miss, you basically always die as Jigglypuff.
 
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BlkSheep642

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The problem with the analysis (albeit really good) is it works on the assumption that there will be an option that is superior.

That's not how it works. Consider Awesomenauts. In that game, each character has 6 upgrades to their special moves. Some are worse than others yes, but others are chosen based on style or perference. For instance, on Yuri's timewarp, I got Heal, Fast Forward, and CC Immunity on it. Others will get a Lifesteal for it. I'll only grab lifesteal if I'm fighting Ayla, Vinney or another Yuir. You can do this with any character. With Lonestar's Dynamite, I get extra Stick, lifesteal and DOT, but you can replace the DOT for Explosion size, bounce and blind. All of them work. Yes, there are bad upgrades (Penny's and Swiggins seem to complain the most), but a lot of them are style or based on other upgrades you selected.

For Smash, it will be the same thing. Take Mario's fireballs. You may go normal or maybe orb. But maybe fast isn't good. You may chose them based on match-up (perhaps Orb is good against certain characters). So you can't look at this in a linear fashion because it's not. It's going to be living and breathing.

I really like this response the most, mainly because of there being so many options, and it creating such depth, I'm really hoping that it doesn't effect balance too much, and it mainly relies on people's personal preferences and fighting styles. It would be cool to just have tournaments FILLED with "Oh, I've never thought of that combination of moves before" and "I thought that special move was useless!". Overall, I can see people being incredibly creative with everything
 

DairunCates

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The problem with the analysis (albeit really good) is it works on the assumption that there will be an option that is superior.

That's not how it works. Consider Awesomenauts. In that game, each character has 6 upgrades to their special moves. Some are worse than others yes, but others are chosen based on style or perference. For instance, on Yuri's timewarp, I got Heal, Fast Forward, and CC Immunity on it. Others will get a Lifesteal for it. I'll only grab lifesteal if I'm fighting Ayla, Vinney or another Yuir. You can do this with any character. With Lonestar's Dynamite, I get extra Stick, lifesteal and DOT, but you can replace the DOT for Explosion size, bounce and blind. All of them work. Yes, there are bad upgrades (Penny's and Swiggins seem to complain the most), but a lot of them are style or based on other upgrades you selected.

For Smash, it will be the same thing. Take Mario's fireballs. You may go normal or maybe orb. But maybe fast isn't good. You may chose them based on match-up (perhaps Orb is good against certain characters). So you can't look at this in a linear fashion because it's not. It's going to be living and breathing.
Well, it's handled linearly in the post to point out that this makes more characters viable than they would be otherwise by lowering variance. It goes without saying that there might be one or two moves that are circumstantially good (although, in most cases, when a player is given choice, one eventually comes out as the overall best after enough time with the meta-game. It's very hard for two different abilities to be exactly equal in usage).

Even then, though. That just makes the general point even better, because that gets into the concept of perfect imbalance. Extra Credits did a good video on this one.
By having options that will work against specific builds, you get an ever evolving meta-game instead of a static one. This drastically increases the viability of lesser used characters and reduces the effectiveness of tiers.
 

ENKER

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I'll join the chorus and say this post is awesome! I was not truly excited about customizable moves until reading this post and resulting thread. I SO hope they're allowed in tourney play now!

Also, I am a math guy so I definitely enjoyed your mathing here. The explanation really hit home for me.
 
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