Mmr Calculator

by
Reviewer: David Chen, MBA, Game Design Consultant

This MMR Calculator utilizes a standard Glicko-2 approximation model with a fixed K-factor for rapid, predictive rating change calculation.

Welcome to the Matchmaking Rating (MMR) Calculator. This tool helps you estimate how your rating will change after a match, based on your current skill level and the rating of your opponent. Simply input your current MMR, your opponent’s MMR, and the match outcome to get your predicted new rating.

MMR Calculator

Predicted New MMR

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MMR Calculator Formula

The calculation is based on the simplified Elo rating system:

Expected Score (E) = 1 / (1 + 10^((R_opponent - R_current) / 400))
MMR Change = K * (Actual Score (S) - Expected Score (E))
New MMR = R_current + MMR Change

Formula Sources: Wikipedia Elo Rating System, FIDE Rating Regulations

Variables

  • Your Current MMR (R_current): Your starting Matchmaking Rating. This is the foundation for the calculation.
  • Opponent’s MMR (R_opponent): The rating of the player you competed against. The difference in ratings determines the expected outcome.
  • Match Result (S): Your score for the match. Win = 1, Loss = 0, Draw = 0.5.
  • K-Factor (K): A constant that determines the maximum possible change in rating after a single game (typically 32 in stable systems). The calculator uses K=32.

Related Calculators

What is MMR Calculator?

The MMR Calculator is an essential tool for competitive gamers and league organizers. It provides transparency into the mechanism by which skill ratings are adjusted after competition. MMR, or Matchmaking Rating, is a numerical value representing a player’s skill level in a competitive game, used by the system to match players against opponents of similar skill.

The core concept revolves around the idea of an expected score. If you defeat a much higher-rated opponent, your rating change will be significantly larger (positive) than if you defeat a lower-rated one. Conversely, losing to a much lower-rated opponent results in a substantial penalty. This calculator makes that prediction simple and instantaneous.

How to Calculate MMR (Example)

Let’s use an example where R_current = 1500, R_opponent = 1650, and the result is a Win (S=1), with a K-factor of 32.

  1. Determine Rating Difference: $1650 – 1500 = 150$.
  2. Calculate Expected Score (E): $E = 1 / (1 + 10^{(150 / 400)}) \approx 0.306$. This means the 1500-rated player was expected to win 30.6% of the time.
  3. Calculate Change Factor: The difference between the actual score (Win, $S=1$) and the expected score ($1 – 0.306 = 0.694$).
  4. Calculate MMR Change: $MMR\ Change = 32 \times 0.694 \approx +22.2$.
  5. Determine New MMR: $New\ MMR = 1500 + 22.2 = 1522.2$.

Frequently Asked Questions (FAQ)

  • What does K-factor mean? The K-factor is a coefficient that determines the volatility and maximum change allowed in a single rating update. A higher K-factor means ratings change more drastically after each game.
  • Is MMR the same as Elo? MMR is a general term used by game developers for their internal rating systems. While many are based on the Elo model, they often include proprietary modifications, such as uncertainty (Glicko-2) or division/tier mapping.
  • What is an “Expected Score”? The Expected Score (E) is the probability of player A winning against player B, based solely on their current rating difference. If the players perform better than their expected score, their MMR goes up.
  • Why did my MMR change by so little when I won? This usually happens when you defeat a significantly lower-rated opponent. Since the system already heavily favored you, the victory was expected, resulting in a minimal rating gain.
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