$avg_num_votes = 18; // Average number of votes in all products
 $avg_rating = 3.7; // Average rating for all products
$this_num_votes = 6; // Number of votes for this product
 $this_rating = 4; // Rating for this product


$bayesian_rating = ( ($avg_num_votes * $avg_rating) + ($this_num_votes * this_rating) ) /    ($avg_num_votes + $this_num_votes);

echo round($bayesian_rating); // 3

((18 * 3.7) + (6 * 4)) / (18 + 6)
(66.6 + 24) / (24)
90.6 / 24
3.775