The neutral game, or just neutral, is a phase during gameplay when no player has a situational advantage over the other. In this phase, either player's objective is to "win the neutral game", i.e. land a hit with possible follow-ups, or punish the enemy for a failed attempt to do so. A strong neutral game is crucial at top level play, as it is necessary to put the opponent in a disadvantageous position.
Some characters have an advantage during the neutral game, depending on the matchup. For example, a projectile may be used to pressure the enemy into making a move. Other possible advantages include attack range and mobility.
The neutral game can be looked at as a triangle of sorts, like Rock, Paper, Scissors, where each vertex overrides another. Grabbing goes through shielding. Shields can block attacks and leave opportunities to punish afterward. Regular attacks can outprioritize grabs due to their generally superior range and speed. This triangle mindgame adds a new layer of strategy. Players must anticipate what course of action in the triangle their opponent will take during the neutral game.
This way of looking at the neutral game does not encompass the entire picture, however; players generally have more than 3 options available to them (such as moving out of the way if they feel they are too close to the opponent, or using different attacks at a time). In addition, although shields do block attacks, many high level players will often space their attacks so as to make them as difficult to punish as possible, either by placing it as far away as possible while still connecting with the move, or by overshooting behind them to limit the opponent's out-of-shield options in the case of aerials. In fact, the attacks they use in this situation could be safe (or in most cases, simply difficult to react to on shield without good prediction) even if not spaced properly, thus baiting players to preemptively use their out-of-shield options to punish the opponent (if they recognize this, they can opt to escape or continue shielding instead). Stage position also greatly affects which options are viable for either player; the player who takes the center of the stage has much better options than the player who is closer to the ledge. Thus, a player that successfully pressures the opponent into limiting their own movement by forcing them to use more defensive options or move to the ledges of the stage generally wins the neutral game, since they will know exactly how to counter these options and punish them.
A character's effectiveness in the neutral game comes down to three main factors: mobility, attack speed, and range. Good mobility grants easier movement and repositioning, and can allow a character to respond quickly when they find an opening, or retreat to escape pressure. Fast attack speed makes a character unpredictable, and can be used to force reactions and create openings. Characters with long reach in their attacks can fight at a safe distance, and range also encompasses projectiles, which are essential for applying pressure and limiting the opponent's options. While a character who is proficient in all three areas will have a powerful neutral game, some characters are dominant in the neutral despite lacking in one aspect. Falco in Super Smash Bros. Melee and Super Smash Bros. Brawl has below-average mobility, but his Blaster is a potent projectile, and he boasts fast attack speed as well, and his strong neutral is a large reason behind his top-tier placement in both games.
A common mistake made by beginners is to always approach the opponent with the exact same option, such as dash attack or dash grab, without putting much thought into how the opponent might also want to approach or if they aim to punish these options. Without any level of unpredictability or situational awareness, it can be very difficult to mount an offense against a better player. Understanding the difference between engaging the opponent (i.e. approaching through movement to win neutral by positioning) and actually attacking them is a key point in neutral and not grasping it will hurt the player more often than not.