Matchmaking Ruins Everything

<p>Imagine a 1v1 game (like chess), four players of equal skill, and initial MMR values of 3.</p> <p>Everyone in this example has the same underlying skill, therefore everyone should have similar MMR values. The ideal MMR histogram would essentially be a single column at 3 (with some oscillations).</p> <p><img alt="" src="https://miro.medium.com/v2/resize:fit:707/1*fcITtQZrGcS7LhnIN8l5ng.png" style="height:404px; width:643px" /></p> <p>ideal MMR histogram of 4 players of equal skill</p> <p>With Elo or Glicko, this is indeed what happens&nbsp;<strong><em>as long as matchmaking is random</em></strong>. However, once skill-based matchmaking (SBMM) is added to the mix, it all goes to shit.</p> <p><img alt="" src="https://miro.medium.com/v2/resize:fit:770/1*TyFG0ilNpqZphxJ6_6E7AA.png" style="height:350px; width:700px" /></p> <p>MMR histogram of 4 players of equal skill with perfect SBMM</p> <h1>ASCII Example</h1> <p>With&nbsp;<em>perfect</em>&nbsp;SBMM, the MMR distribution will become uniform over time &mdash; exactly the opposite of what it should be. The &ldquo;correct&rdquo; MMR distribution in this case should be perfectly tall and narrow (constant), but SBMM leads to perfectly short and wide (uniform).</p> <p>This scenario is simple enough that we can step through it by hand:</p> <p><a href="https://medium.com/@charlie.olson/matchmaking-ruins-everything-053f51527289"><strong>Learn More</strong></a></p>