Originally Posted by
Stone
And also I never understood why boots are so important? Is it because of that speed boost for only 300 gold?
In a less condescending answer:
For the sake of simplicity, let's assume everybody has melee range, the same movement speed, the same stats, easy to use point and click skills that provide no mobility, no objectives to play around, and perfect play. Let's also assume League is a 1v1. In this situation, boots are slot inefficient, since the stats they provide for taking up an item slot is lower than what a different item could provide. In this situation, boots are generally useless.
However, let's assume that you could be in an X v Y fight, where X and Y can be either 1 or 2, and X represents your team, and Y represents the other team. In this situation, let's also assume that everybody starts the fight out of range from enemy. Let's dissect the 2 important possible scenarios, 1v1s and 2v1s (since 1v1s are functionally 2v2s in this setup, and 1v2s and 2v1s are the same but reversed). First scenario, it's a 1v1, and we've shown already that boots are slot inefficient. No need to go further.
Second scenario, it's a 2v1 (favor your team). Logically, the enemy would retreat, since it's a 12 item slot vs 6 item slot, meaning they will lose on paper 100% of the time. If nobody on your team has boots, and the enemy team has boots, that enemy player can run away and avoid the fight. That fight is functionally a draw. If your team has boots, and the enemy does not have boots, then you can run down the enemy and kill them, functionally winning. If both teams have boots, then it is functionally a draw.
So what does this mean? It means that you have 2 teams, with 2 possible states (boots or no boots), providing a 2x2 grid of possible outcomes. In the row denoting your team has boots, your possible outcomes in a 2v1 is either winning, or draw. Without boots, your possible outcome in a 2v1 is always a draw. You cannot win the fight since you can't initiate the fight. As such, boots are the crucial factor in this situation dictating whether the more populated team will win, and boots are the crucial factor dictating whether the less populated team can draw.
This is incredibly simplified but, since League is a team game, it's reasonable to assume that 1v1s are rare due to the mere presence of players trying to make plays, and 5v5s with perfect setups so that everybody is engaging equally in such a way that mobility is a non-factor are also rare, so it's safe to assume that the possible results of 1v1s and their multiples are uncommon. This means that the disjointed matchups, where one team has a clear advantage, are common occurrences. Which means that these outcomes are the most valuable to play around, and not having boots in these scenarios only provides losing or draws as possible outcomes. Even in a 5v4, with the 4 not using boots and the 5 are, the item slot matchup is 25 v 24 items, favoring the 5 side. Meanwhile, your possible outcomes with boots are only winning and drawing. As such, it is significantly more valuable to have boots.
This is also excluding the fact that, once you include objectives, macro level play (e.g. rotations) gives much more value to the team with boots, since they can move from objective to objective faster and outpace the team without boots.
I won't tl;dr this because otherwise I'm just stating boots are valuable. The proof is required to understand the conclusion.