The Orioles lost Tuesday night without using Zach Britton, one of the game’s best relief pitchers. It was a do-or-die game that went to extra innings, but Buck Showalter held his closer for a save situation because the closer is the closer. While there’s some argument for maintaining bullpen roles and hierarchies over the course of a 162-game season, sticking to that kind of mentality in a single-elimination game defies comprehension. If there were ever a time to use your closer early, it’s when a single run could end your season. Showalter didn’t and he’s watching the ALDS from home rather than a dugout.

On Thursday, Terry Francona took a different approach. In Game One against Boston, Francona went to Andrew Miller, his own relief ace, with two outs in the fifth inning. His club led 4-3 with Brock Holt, Boston’s No. 2 hitter, coming to the plate. Francona made the decision that Trevor Bauer was done and it was time to go to the pen. Francona called on Miller for six outs, followed by Bryan Shaw for two and Cody Allen for five.

In other words, Francona managed a playoff game exactly the way the numbers suggest it ought to be managed. He didn’t concern himself with roles or save situations, he just went to his best pitchers for as long as he thought they would be effective. The process was spot on, and fortunately the results followed.

But there has been one line of critique developing as the baseball world discusses Francona’s bullpen revolution; Miller didn’t enter the game in a high-leverage situation.

In fact, the leverage index when Miller entered the game was 0.57, which we classify as a “low leverage” situation. We’ve been talking about managers using their best relievers in high-leverage moments for years, and when Francona finally made the leap, he managed to bring him in at a point when, according to the numbers the game didn’t necessarily hang in the balance. A few people made this point, indicating that while Francona’s willingness to go to Miller that early was a welcome sign, the situation he chose wasn’t ideal because it wasn’t a critical spot.

This is a textbook example of why leverage index isn’t a perfect tool for measuring the importance of in-game situations — and, as a result, why stats like Win Probability Added (WPA) aren’t good measures of player value even if you want to award credit based on context.

Leverage index measures the potential swing in win expectancy given the state of the game. In other words: if, during a given plate appearance, the win expectancy could swing wildly depending on the outcome of the plate appearance, the leverage index will be high. Down one in the eighth with men on second and third with two out? That’s high leverage. If the pitcher gets out of it, his club will have a one-run lead with an inning to play; if he gives up a hit, his club could be trailing by a run with only an inning to play.

Miller’s spot wasn’t high leverage last night because there were five innings of baseball left and no one was on base. If Miller gave up a home run, the result is a tie game with five chances to come back. If he got an out, it was a one-run lead with four chances left for Boston. The difference between those two game states isn’t that significant, which is why the leverage index wasn’t that high. But this is why leverage index can’t be your only guide when managing the bullpen in a playoff series.

Francona rightly figured that Bauer was just about done. If you want to quibble with his tactics, perhaps he could have let Bauer face the less impressive Holt, used a righty specialist for Betts, and then called on Miller for Ortiz. That’s a reasonable critique. But if Bauer had gotten Holt and then Shaw had gotten Betts in the sixth, the leverage wouldn’t have been much higher when it was Miller’s turn to pitch. It still wouldn’t have looked like a spot for your ace.

But it was. Miller was rested and ready to throw something like 40 pitches, meaning he was in line for two-plus innings of work on Thursday. He’s unquestionably the best arm they have, although Allen is also quite good. If you bring Miller out of the pen first, whenever Bauer is done, you get him into the game at the point at which a single run would tie it. Miller’s job was to hold the Red Sox at bay as long as possible, which he did. If you go to Otero or Shaw in the fifth and sixth, you’re increasing the odds the Red Sox score.

You might think this is semantics and that Francona had to use Miller plus Allen plus someone else to get through the game and it didn’t matter in what order it occurred. That’s partially true, except that using the best guy first let’s Francona dictate the world inherited by the lesser relievers. In other words, Miller came in when the leverage index was low because he was the best option for keeping it that way. For this reason, despite pitching more innings with essentially the same lead, Cody Allen’s WPA was higher in the game than Miller’s simply because he pitched later. Logically, we know that’s silly. Allowing a run in the sixth counts the same as one in the ninth; it just feels worse in the ninth because you’re almost home.

The point isn’t to use your best relievers in the biggest moments. The point is to maximize your odds of winning the game. Usually those things work well together when your starters are going six or seven innings and you’re using your relievers for one inning each and are aiming to give them clean innings.

In playoff games, that’s not the right mentality. If a manager needs 4.1 innings from his bullpen, he wants the best guy out there first so that he can keep the other team from scoring. If Cleveland had scored a bunch of runs against the Red Sox’ pen, Francona could have saved Allen entirely. As long as Miller doesn’t get wasted with too many plate appearances against the bottom of the order, using him for two innings in the middle of the game is better than using him for two innings at the end. He knew in that moment that it was a one-run game. He had no idea what was going to happen if he saved him for later.

Francona got Miller for two innings, the presumed maximum he was able to go, and gave the rest of his pen a better situation than if he had used his worse relievers and put Miller into the eighth and ninth. It’s a small thing, but it’s meaningful. You avoid low leverage in the regular season because you don’t want to waste your relievers and make them unavailable for future games. But Miller was obviously pitching in this close game; it doesn’t matter when he would pitch, as long as he gets the heart of the order/proper platoon matchups.

Every playoff inning in a non-blowout is high leverage. Don’t let the leverage index fool you. Hopefully Francona’s willingness to use Miller — and Miller’s comfort serving as the fireman — becomes a model for managers around the league.