Foremost, there are two points I wish to make. Firstly, Melee at a TAS level is a perfectly balanced game. This is simply because all moves have start-up time, and so are beaten by a perfect, reactionary player. This means that there are certain intangibles that we must account for when creating a tier list. Secondly, the point I wish to make is that this tier list is not a "meta snapshot". If it were, it would be a strict analysis of tournament results over a given time period.
This tier list is, instead, a combination of theory with player potential ability. That is to say, it accounts for shifts in the meta that are likely to happen. However, it does not assume that players will ever do everything frame-perfectly. It accounts for a deal of human error, though it accepts that this human error is difficult to quantify.
Let's begin with an argument.
I'll begin with the following assumption that only the following characters are relevant in terms of top-tier threat. We will call these characters "Viable". (Yes, players such as Axe and Amsa have shown that they can consistently win with so-called non-viable characters, but so did Mango with Mario. For the sake of this tier list, we will assume that is a matter of skill differential rather than character ability.)
Ice Climbers, Marth, Fox, Falco, Jigglypuff, Peach, Captain Falcon, Sheik.
Given that the trend of this game has been toward tournament-success, rather than exploration of the game's nuances, we can agree that new players will be more likely to gravitate toward these top-tier threats as opposed to mid-tier and low-tier characters.
Given that new players are more likely to gravitate toward these viable threats than mid-tier and low-tier characters, the percentage of viable characters in tournament (compared to non-viable characters) will increase.
Given those assertions, this tier list is based solely on the matchups between those characters.
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Match-ups were decided based upon 5 main factors:
1. Punish game.
2. Combo-avoidance (Difficulty of landing a lengthy combo on the given character).
3. Recovery.
4. Edge-guarding.
5. Neutral game.
Neutral game is deemed the most important factor in this tier list.
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1: Marth.
Marth takes the number-one spot on this list. He ties for both the best punish game out of all the characters (Falco), and the best neutral game out of all the characters (Falco). On top of this, Marth combines his near-ideal weight for combo escapes, his solid recovery, and his near unparalleled edge-guarding abilities, to cement his position as the number one character. He is the only character in the game with an advantaged match-up against Fox, and match-ups have evolved to the point where Jigglypuff and Peach are now one-sided affairs (i.e. Marth now can kill them before 100%).
2: Fox.
Fox takes the number-two spot on this list. While his punish game is less consistent than some of the other viable characters, his blistering speed makes for a neutral game that is all-too-often a one-sided affair. Fox's neutral game completely outclasses other viable characters such as Sheik, Jigglypuff, or Peach. The main points which hold Fox back from his former position at #1 are his fast-falling nature, and his neutral game being weaker than Falco's or Marth's.
3: Sheik / Falco.
Sheik has the most consistent finishers in the game, from her simple kill setups to her edgeguards. This combines with a powerful combo game, and insane tech-chasing capabilities. However, she is held back by her poor neutral game, and her weakness to Jigglypuff, Fox, and the Ice Climbers.
Falco ties for both the best neutral game and the best punish game (Marth). However, much as with Fox, he is held back by the fact that he is a fast-faller. Additionally, he struggles both with Jigglypuff and Peach (both Puff and Peach have the tools to deal with his neutral game, and Falco doesn't have the tools Marth does to quickly finish their stocks).
5: Jigglypuff.
Jigglypuff has two losing match-ups in the top 8 (Fox, Marth), and does not have the significant tools in neutral to justify those weaknesses.
6: Peach.
Peach has three losing match-ups in the top 8 (Fox, Marth, Jigglypuff), and does not have the significant tools in neutral to justify those weaknesses.
7: Ice Climbers
The Ice Climbers have four losing match-ups in the top 8 (Fox, Marth, Captain Falcon, Peach). The Ice Climbers have the most potential for mobility within this list next to Falco, as there has been a consistent lack of development at the top level for this character.
8: Captain Falcon.
Captain Falcon is a sad character. He has an incredible punish game. However, as other characters' punish games improve to greater and greater heights, Captain Falcon's weakness in neutral to virtually every other top character is exposed. His high survival percentages matter very little considering his terrible recovery. He goes even with Marth, is advantaged against Peach and the Ice Climbers, and loses to everyone else.