Why are the best relievers not used when they are most needed?

During Saturday’s ALCS game 6 the Red Sox’s manager John Farrell took out his starter in the 6th inning. They were leading by 1, but had runners on first and second with no outs. This is a hard situation to get out of without giving up a run. The chances of scoring with an average pitcher are about 64%. I am sure that with a top of the line pitcher, like Koji Uehara, this number goes down substantially. So what does a typical manager do in this situation? Because managers like to save their better relievers for the end, and it’s only the 6th inning, they will bring in a mediocre one instead. This is what Farrell did and 2 batters latter the score was 2-1 Tigers. To really understand why this is bad move, the chances of a mediocre pitcher giving up runs when starting an inning is about 28%.  So why not bring in your best reliever when the game is actually on the line? Here is an article by John Dewan with a good in -depth discussion.  Note that the Red Sox won the game 5-2 and Koji Uehara was brought in the ninth inning to get 3 outs with the bases empty and a 3 run lead.