Let's say, one relief pitcher comes into the game with his team leading 4-1, with no out in the ninth inning.
The opposing team batters him for five runs and takes a 6-4 lead.
The next inning, the pitcher's team scores three runs to retake the lead.
Then a new pitcher come on and holds the lead and finishes the game.
In this situation, I suppose the pitcher who blows the lead in the ninth gets the win, and the subsequent pitcher gets the save. However, there is a saying that the official scorer "can" award the victory to the "effective pitcher," not the one who gave up the lead.
Is that a really common thing in MLB? Thoughts and opinions would be appreciated.