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MMR or MatchMaking Rating is a number used by League of Legends to represent a player’s skill level. Your MMR determines the opponents you play against and is unique for each game mode. WhatIsMyMMR specifically tracks solo non-premade games played in ranked, normal, and ARAM queues. Read more about MMR on Riot’s website.
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The site provides 
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Nope, sorry. The “equal to rank” estimate only translates your percentile to a more accessible format. For example, not everyone knows that top 1% is Diamond, but everyone knows that Diamond is pretty good™. Ultimately, Ranked, Normal, and ARAM game modes are all separate from each other with distinct game mechanics and/or player bases.
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Estimates only use data from games played solo in the last 30 days. Premade games are excluded because players in a party can have very different MMRs which causes poor matchmaking and inaccurate 
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MMR goes up when you win and down when you lose (see the section above on accuracy for caveats). As such, the most straightforward way to gain MMR is to maintain a positive win rate. Although the difference between your team and the opposing team’s average MMR affects the amount gained or lost, in practice most games are “fair” and contain teams with similar MMR. A good rule of thumb is +10 MMR for a win and -10 MMR for a loss.
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Ranked game modes use League Points (LP) as a competitive layer on top of MMR. LP gains and losses depend on your MMR and the average MMR for your rank. When playing above the average MMR for your rank you’ll gain more LP than lose. Conversely, you’ll lose more LP than gain when below the average MMR. Note that MMR and LP are different from Elo rating, the old ranking system that Riot removed in Season 3.
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No, dodging in champion select does not affect MMR. However, Ranked queues have various LP and promotion series penalties for dodging.
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Yes! WhatIsMyMMR provides a comprehensive public API for developers who want to use 
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Hi, I’m Josh! I built WhatIsMyMMR as a weekend project for personal use and eventually released it publicly in 2016. The site is surprisingly expensive to run each month and is only possible through the support of my amazing supporters on Patreon. I’m also on the lookout for sponsors. Have something that you want to show off to millions of players? Let’s chat!