ranking formula example -- stackoverflow.com/questions/16168727/

rankings.php

<?php
function get_rank($votes_min, $votes_item, 
    $rating_average_global, $rating_average_item) {
  return 
    ($votes_item / ($votes_item + $votes_min)) * $rating_average_item + 
    ($votes_min / ($votes_item + $votes_min)) * $rating_average_global;
}

$data = array(
  [5, 10],
  [55, 8],
  [76, 5],
  [8, 10],
  [102, 2]
);

$votes_min = 10;
$votes_total = 0;
$rating_average_global = 0;
foreach ($data as $row) {
  $rating_average_global += ($row[0] * $row[1]);
  $votes_total += $row[0];
}
$rating_average_global /= $votes_total;

$results = array();
foreach ($data as $row) {
  $results[] = array(
    get_rank($votes_min, $row[0], $rating_average_global, $row[1]), 
    $row[0],
    $row[1]
  );
}

usort($results, function ($a, $b) {
  if ($a[0] === $b[0])
    return 0;
  if ($a[0] < $b[0])
    return 1;
  return -1;
});

foreach ($results as $row)
  printf("rank - %3.2f, votes - %3d, avg - %3d\n", $row[0], $row[1], $row[2]);