I took out a bunch of code that's specific to topscore, so this may not compile. But all the important parts are there.

RRI_Pseudocode.php

<?php
protected static function computeRRIInternal($games, $teamsByTeamProxy, $options)
{
  $delta = 1; // percent change in scores since last round
  $round = 0;
  $powerRating = array_fill_keys(array_unique($teamsByTeamProxy), 100); // every team starts at 100

  while ($delta > $options['max_delta'] && $round < 100)
  {
    $delta = 0;
    $round++;
    $updatePowerRating = $powerRating;

    foreach($games as $game)
    {
      if ($game['home_score'] === null || $game['away_score'] === null)
      {
        continue;
      }

      $homeTeamId = $teamsByTeamProxy[$game['home_team_proxy_id']];
      $awayTeamId = $teamsByTeamProxy[$game['away_team_proxy_id']];

      $predictedHomeRatio = $powerRating[$homeTeamId] / $powerRating[$awayTeamId];
      $actualHomeRatio = $game['home_score'] / ($game['away_score'] ?: 1);

      if (isset($options['max_victory_ratio']))
      {
        $maxRatio = $options['max_victory_ratio'];
        $minRatio = 1/$maxRatio;
        $actualHomeRatio = min(max($minRatio, $actualHomeRatio), $maxRatio);
      }

      $homeDelta = 10 * (log($actualHomeRatio) - log($predictedHomeRatio)); // coefficient should be ~ 10% of the starting PR. this opinion is based on experimentation.

      $updatePowerRating[$homeTeamId] += $homeDelta;
      $updatePowerRating[$awayTeamId] -= $homeDelta;
    }

    foreach($powerRating as $teamId => $oldRating)
    {
      $delta += abs($oldRating - $updatePowerRating[$teamId]) / ($oldRating ?: 1);
    }

    $powerRating = $updatePowerRating;
  }

  arsort($powerRating);
  return $powerRating;
}