Bullpen construction is a psychological hierarchy. We need a lefty? We’ll look at the numbers? Hardly. It’s all about people and roles.
The closer is the fulcrum upon which the entire ‘pen rests. Without a closer, the mental state of every reliever is in flux. What is my role, he asks? The closer sets the order for the relievers in front of him.
Never mind a closer though. The ideal bullpen would have both a closer and a bullpen ace. The closer would show up in the ninth inning and save games. He doesn’t have to be the best guy. The best guy is the ace.
The ace gets used in high leverage situations. Bases loaded in the fifth? Bring him in! The game is on the line in that moment. Don’t wait to bring that guy in. Don’t wait until the game is out of reach. Don’t wait for a three-run lead in the ninth, and an easy save opportunity. Do it when you actually need him.
The problem with ideal bullpen construction is incentives. Pitchers are incentivized to seek out saves. (Remember, follow the incentives!) So the ace idea never takes off, because it’s not worth it to the ace. Another reason why bullpens are all psychological. The ace won’t be happy in that position.
But, if you just have the ace, and no closer is set (a closer by committee approach) then chaos ensues. So the best and most realistic way to build a pen? Set an order, and keep everyone happy.