First, a history lesson: Seth Killian once argued that assists are an evolved form of the classic 2D fireball, and it changed the way I look at assists forever. To better illustrate this principle, let’s contrast fireballs with beams: fireballs and beams are entirely different entities, though superficially similar: both deal damage from afar, and your character is not directly involved with the damage dealing (the projectile is). However, the beam is meant to deal immediate damage or creating immediate space. Fireballs are different - they move slowly, and their purpose is not necessarily to deal damage directly, but to create an object independent of your character that your opponent must deal with. Fireballs can be used to protect approaches, and they can be used to create obstacles against your opponent's approach.
Any assist, even one such as Haggar's Double Lariat, is like a fireball with no startup or recovery time relative to your point character. You might see the Mayor of Earth spinning on your screen when you call him out, but it's really just a pretty graphic that clouds what he actually is: a fireball that sits in one spot for a moment before disappearing. When Marvel 1 utilized assists, they were closer to the classic fireball than they are now in Marvel 3. In Marvel 1, a character appears on the screen and provides an effect, completely independent of your character, and then disappears. While assists were all limited in their number of uses, the most daunting consequence of a bad assist call in Marvel 1 was simply having 1 less assist to call.
In Marvel 2, Capcom decided that Marvel 1 assists were simply a little too powerful, simply because there was no consequence to their poor usage outside of lost utility; you could be reckless without significant penalties. In Marvel 2, your teammates became your assists; suddenly you had to be much more careful with your assist calls, because while the Marvel 1’s numeric limitation on uses was removed, any damage your teammate took while being called as an assist was real damage - the assist itself could be attacked and hurt.
In Marvel 3, assists have been toned down further. Not only do most assists have no invulnerability at all, but assists take an additional 50% of normal damage when called, and they do not benefit from damage scaling if they are hit outside of the point character. Like with Marvel 2, assists can still be juggled infinitely in a variety of forms that a point character cannot. Why mention all of this? Capcom has done a reasonably good job of balancing assists this time around; this game has no equivalent of Captain Commando's Captain Corridor. Instead, the power of an assist tends to correlate to how vulnerable that assist is. Sentinel Force is doubtlessly a very powerful asset for any team; nothing fills the screen up quite like it, but the assist comes out slowly, and any damage Sentinel takes causes all of the drones to expire immediately. It is a high-risk, high-reward assist. Capcom seems to have been more generous toward defensive assists like Haggar's Double Lariat, at the expense of the characters those assists belong to being weaker on point than most characters. Understanding the balance behind the assists in this game, and the nature of the assist, is essential to choosing the proper assists for your team.
I wish I could list assists by a "type", but assists are far too various in this game to do that. Only a handful of assists really fit into one neat concept. Most of them change depending on what character the assist is helping out. For example, if I made a list of assists that allow a character to relaunch, Ryu's Hadoken would not typically be placed on that list. If you play Wesker, though, you can use a combination of Samurai Edge and Ryu's Hadoken assist to relaunch. There's just too much to consider for categorizing assists.
What I have done is provide some considerations for what assists can do; from there, it's up to you to decide which assists provide the benefits your characters need. Ideally, you choose assists that fit several of your character's needs, or that fit one need extremely well:
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Approaching: These assists help you close the distance between you and your opponent while retaining your safety. For example, if you call Taskmaster's Aim Master L while advancing upon your opponent with Viewtiful Joe, your opponent is put in a position where he cannot easily attack Joe without getting hit by the Aim Master L. So, your opponent either has to figure out an attack method that negates your approach, or opt to defend. Your goal is, of course, to limit your opponent's options to "defend" as much as possible.
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Lockdown: Speaking of defense, isn't it great when you can force your opponent into a situation where he simply has to sit and block your series of attacks because your offense is just so fantastically unstoppable? Lockdown assists, like Amaterasu's Cold Stars, are great for forcing your opponent to sit in a blocking position for a long time without any recourse. Lockdown assists in this game are particularly strong because while a character is blocking an assist, the ability to pushblock is effectively removed from their table of options. Use the lockdown period to advance a strong offense against your opponent, or go for a tick throw.
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Combo Extension: Every character in this game can do good damage, but everyone can do more when backed up by an assist that allows a combo extension. On the most basic level, these are assists that hit a grounded opponent and allow you to relaunch for another air series, adding considerably more meter gain and damage. The more you understand your character, the better you will understand combo extension opportunities, however. Every character has a solid list of assist options for extending combos, and some assists, like She-Hulk's Torpedo, can extend combos for the game's entire cast.
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Combo Creation: Every character has a unique feature in this game. For most characters, these unique features allow for unique assist combinations to create combos that would work for no other character. Dr. Doom can OTG relaunch by himself without any outside assistance, and he can even perform multiple OTG relaunches by his lonesome. Captain America’s Charging Star assist isn't just a great way to cover space, but it also causes a hard knockdown, a state which allows for Dr. Doom to OTG relaunch his opponent. Dr. Doom is one of a handful of characters that are able to guarantee a follow-up from Captain America’s Charging Star.
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Space Creation: Some assists can be simply laid down, and now your opponent has this massive wall to climb before you can be approaches. Assists like Dante's Jam Session, Sentinel's Sentinel Force, and Haggar's Double Lariat all perform this role, but in very different ways. The goal of these assists is to force your opponent to play a defensive role for a moment, which allows you to take an offensive role.
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Crossover Counters: When blocking, if you push forward and call an assist, that assist will appear on the screen and perform its assist, but you will now be in control of that assist, as it has become your new point character. If you use Dr. Doom's Plasma Beam as a crossover counter, it's not significantly different from calling him as an assist. If you call Viewtiful Joe's Groovy Uppercut as a crossover counter, though, this actually leads into a full combo; you might even build your meter back while dealing significant damage to your opponent! Some assists gain invincibility when used as a crossover counter - assists you might think are terrible for one of your characters could be a closet game-winner.
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Resets: Similar to combo creation, some assists are superb at creating situations that allow a reset for your character. For example, when using Wesker, use Samurai Edge to OTG your opponent after a combo, call Dormammu's Dark Hole, and Phantom Move L. Your opponent has to block Dark Hole as he recovers from Samurai Edge, and Wesker's teleport makes this very difficult to do reliably. If your opponent succeeds, you are still in a good position to pull off a command throw on your opponent as he recovers from blockstun.
There is so much more to assists than the above, but it's much too deep for just one person to explore and report on. Some assists fit a character so perfectly that you wonder how you might survive without them. Super-Skrull backed by Sentinel's Sentinel Force, Wolverine backed by Akuma's Tatsumaki Zankukyaku, Wesker backed by Iron Man's Unibeam or Dr. Doom's Plasma Beam - these are combinations that are seen every day in the competitive scene, and it's because these assists don't just provide a basic function, they completely alter what the point character is capable of. Super-Skrull gains access to tick throw set-ups via Elastic Slam that are impossible to defend against reliably, Wolverine gains a safe, meterless Berserker Slash combo and an extension off of his OTG, and Wesker gains instant combo-ability off of his teleports. These benefits go beyond categories. Explore all facets of your team, and you may be surprised at what you can do.
A good team has a set of characters in which each benefits from their partners’ assists. While you can build a team entirely around a powerful point character, neglecting synergy between your team in differing orders makes you a prime target for a snapback; how will your team fare when its order is reversed?