Talk:Movement speed/@comment-28582998-20160529020138/@comment-26110806-20160531142423

Hey. I'm the maker of the video and after seeing the section on Malphite, in this wiki, I feel I need to clear some misconceptions.

Malphite's slow is not a usual slow. It will actually take away from the flat movement speed of the enemy, not the total. This means if Malphite A is at 10k movement speed and Malphite B uses his Q on him, he will steal 2600 movement speed, but Malphite A will be at 0 movement speed, because the amount stolen is higher than his flat movement speed.

For this reason, slow reduction is irrelevant. However, if the slow worked normally, slow reduction would still be irrelevant. The section also implies this requires URF, when it doesn't. Let me explain:

Malphite's Q lasts 4 seconds and has a cooldown of 8. With 40% cdr, you can get it to 4.8 seconds. Let's say Malphite A Q's Malphite B at time=0. I'm also assuming Q's travel time is 0. Malphite A is sped up while B is slowed. At t=3, B Q's A. A has the stolen movement speed and also a slow. B has a slow and also stolen movement speed. However, when t=4, A no longer has any stolen movement speed and B is no longer being slowed. This means that movement speed was transfered from B to A to B again without the influence of slows. This can be repeated for as long as you can hold the process.

To calculate how much of a multiplier to movement speed you need to actually have no convergence, you need to know the steal is 26% and the movement speed cap is 50%, which means you need a multipler of 1/(0.26*0.5)=7.69. Any multiplier below that will converge to a number, increasingly higher. At that limit, it's infinity. Above that limit, it's also infinity, just goes up faster. This is a geometric series, btw. To prove it diverges for multiplier>7.69, you can just say that means the ratio between n and n+1, at infinity, is above 1, which is a common proof for divergence.

We used URF not because it was necessary, but because it was easier. A lot easier. At the time, the math pointed that in classic game mode, though you could break the 7.69 limit, it was very close to it, which meant messing up = no record, and believe me when I say it's very hard to coordinate 2 full teams of players to do something like this. But in URF, people could just spam their movement speed boosts, so timing wasn't so hard as in classic.