Two players can have 1600 MMR

That is regarding placements at the beginning of the season and is completely irrelevant to this thread

No, it does actually.

If you MMR sucks, you quite frankly will have a MUCH harder time climbing to get a better rank, as the system will notice this and throttle your LP gains.

On the flip side, if you have a much higher MMR than your current rank should, it does the exact opposite.

So in essence, you are very wrong, as MMR has a lot to do with rank, it just isn't the exact measurement of rank like in seasons before the terrible bronze/silver/gold etc ranked ladder. MMR just says where you "should" be rank wise, just not where you are currently.

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League of legends elo system. ELOs (E.G. gold/bronze/silver/challenger) are just a fancy sheet over the MMR system. What really matters is MMR in league. You get placed based off MMR, not ELO. That gold 3 player is probably getting 25 lp a win and that plat guy is probably losing 25 a loss...

This is the second time in two days you misuse the terms MMR and ELO mate.

MMR and ELO are the same thing. Its the SAME system. ELO was a system designed for chess, league used it for their ladder, and then rephrased the term to "MMR" at the beginning of season 3.

There is not a MMR system AND an ELO system. There is an MMR/ELO system, and the League System. You really need to understand the difference between these so you don't confuse other players by misstating things, I understand you are trying to help, but you need to correctly identify the things being discussed if you want to actually help other players mate.

One more time for you:

MMR=ELO. They are the same thing.

League System is the thing with divisions and tiers and League Points. It is neither MMR nor ELO. It is an entirely separate system.

Elo = MMR

You clearly didn't play when the ELO system was the main system.

Tiers (Bronze, Silver, Gold, Platinum, Diamond, Master, and Challenger) are divided into Divisions (Bronze 5, Bronze 4, Bronze 3, Bronze 2, Bronze 1, etc.)

When the ELO system was the main system, you started each season with 1200 ELO. You had 5 placement matches. If you got above 1200 ELO in those 5, you were matched with good players. If you weren't, you were matched with players who could barely even play a game at a passable level against beginner bots. This was dubbed "ELO Hell".

The Leagues system is what's currently used to figure out who you'll be matched up with, while the MMR system, which is 100% identical to the ELO system, is moved to the background to determine how much LP you'll gain/lose per win/loss.

In Normals, matchmaking is also still made using the ELO/MMR system.

If you don't believe me, here's a link to a post made at the beginning of the season that talks about all of this, confirming everything I say here is correct: http://boards.na.leagueoflegends.com/en/c/gameplay-balance/E9nkYATc-psa-regarding-ranked-placement-and-seedings-for-all-who-are-confused

Basically, the post says that MMR = ELO, but it's behind the scenes now and it doesn't determine your rank so people don't get stuck in ELO Hell playing with people who can barely win a bot match when they deserve to be matched with better players than that.

I can understand your confusion, however, as many people do still use the terms "Low ELO" and "High ELO" when talking about the different ranks. These are simply terms carried over from the days of the ELO system, which was reworked into the Leagues system in Season 3. When people say Low ELO or High ELO, they are referring to lower ranks (plat and below) or higher ranks (diamond+), however they are also misusing the terms.