A very simple way to retrieve and sort posts by relevancy based on overlap with taxonomy terms

simple-related-posts.php

/**
 * First attempt at sorting posts by 'relevancy' based on how much overlap there with respect to terms in a taxonomy
 *
 * Usage: $posts =  sh_get_related_by(1,'post_tag');
 */
function sh_get_related_by( $post_id, $tax, $args=array() ){
	$terms = get_the_terms(1,$tax);
	if( !$terms )
		return false;

	$terms = wp_list_pluck($terms, 'term_id');

	$args = wp_parse_args(array(
		'suppress_filters'=>false,
		'tax_query'=>array(
			array(
				'taxonomy' => $tax,
				'field' => 'id',
				'terms' => $terms,
			),
		),
		'post__not_in'=> array($post_id)
	), $args);

	add_filter('posts_fields', 'sh_related_field',10,2);
	add_filter('posts_orderby', 'sh_related_orderby',10,2);	
	return get_posts($args);	
}

function sh_related_field( $w, $q ){
	remove_filter(current_filter(),__FUNCTION__);
	return $w. ', COUNT( wp_term_relationships.object_id) AS r';
}
function sh_related_orderby( $w, $q ){
	remove_filter(current_filter(),__FUNCTION__);
	return 'r '.$q->get('order');
}

/* Example */

$posts =  sh_get_related_by(1,'post_tag');
printf('<table style="border:1px solid black"> 
	 <tr >
           <td style="padding:5px;border:1px solid black">%s</td>
	   <td style="border:1px solid black">%s</td>
           <td style="border:1px solid black">%s</td>
         </tr>', 
         'Title','Terms','Relevancy');

foreach( $posts as $_post){
	printf('<tr>
                 <td style="padding:5px;border:1px solid black">%s</td>
                 <td style="border:1px solid black">%s</td>
                 <td style="border:1px solid black">%s</td>
               </tr>',
		get_the_title($_post->ID), 
		get_the_term_list( $_post->ID, 'post_tag', '', ', ', '' ),
		$_post->r
	);
}
echo '</table>';
echo '<hr>';