“MY SHIT doesn’t work in the playoffs”, Billy Beane, the general manager of the Oakland Athletics, famously said in “Moneyball”, the Michael Lewis book and subsequent Brad Pitt film about how he succeeded in Major League Baseball (MLB) on a shoestring budget by playing the percentages. Mr Beane’s teams consistently won enough during the six-month, 162-game slog of the regular season—sufficiently long for random fluctuations to cancel each other out and the best clubs to rise to the top—to make the sport’s post-season tournament year after year. But the brief five- and seven-game playoff series that determine the game’s champion were scarcely more predictable than coin flips: the club with the best regular-season record typically wins the World Series about 20% of the time. Be it because of simple bad fortune or his players’ alleged lack of mental and emotional resilience and intestinal fortitude, Mr Beane’s teams always seemed to flame out once the calendar turned to October.

In one sense, the 2016 MLB playoffs have stuck to this anything-goes script. Favourites like the Boston Red Sox have been knocked out early, and numerous see-saw games have included comebacks that straddled the line between improbable and impossible. But one pattern is emerging this post-season that runs counter to Mr Beane’s lament: the clubs that have managed their bullpens as modern statistical analysis recommends seem to be advancing, whereas those that have adhered to hide-bound tradition are being sent home.

In general, managers have a much smaller impact in baseball than they do in sports like, say, American football, where every play is called from the sidelines. And when it comes to utilising starting pitchers, there simply isn’t much room for innovation: because starters need regular rest, they generally adhere to a once-every-five-days schedule, and stay in the game until they are removed for fatigue or ineffectiveness. In contrast, the number of ways to deploy relievers, who enter for brief stints after the starter departs, is virtually limitless. They can be used for just one batter or multiple innings at a time, come in shortly after a game begins or only at the very end, and appear four days in a row or never for two weeks. And there is nothing to stop a manager from using a starter in relief during the 80% of games he does not start.

Despite this inherent flexibility, however, modern managers have settled into a mind-numbingly rigid pattern when it comes to reliever usage. Whomever they deem their best arm in the bullpen gets anointed as The Closer™. That job essentially entails entering exclusively when their club leads by three runs or less in the final inning, or is tied entering the ninth inning while playing at home, and pitching no more than a single inning, usually to finish the game. This method deviates vastly from mathematically optimal usage, which would reserve the top pitcher for the most important situations, regardless of when they occur.

In fact, the standard playbook calls for squandering a closer’s precious pitches at highly inconsequential moments. Teams with a three-run lead and just one inning left to play go on to win 97% of the time, meaning that even a far lesser arm than a closer’s would likely be sufficient to preserve a victory. Conversely, wins often hinge on events that occur long before the ninth inning, and in tie games or even with the batting team leading. For example, according to the leverage index (LI) statistic, a plate appearance with the bases loaded and two out in the top of the eighth inning with the visiting team up by one run is 2.69 times as important as an average situation. However, it would be highly unorthodox to use a closer in this context: most managers would entrust those crucial pitches to a weaker reliever, sharply increasing the odds that their opponents extend their slender lead enough to put the game out of reach. Moreover, “standard” reliever usage takes no account of matchups: if three consecutive lefties are scheduled to bat with the game on the line, a southpaw reliever who specialises in retiring same-handed hitters might be a wiser choice than a right-handed closer.

This sclerotic management technique was the unwitting handiwork of Jerome Holtzman, a sportswriter who devised a statistic in 1960 that he called a “save” in order to measure the impact of shut-down relievers. Roughly speaking, it meant entering with a lead of three or fewer runs and finishing the game without relinquishing it, though there were a few additional wrinkles. The number took decades to catch on, and for most of the 1970s and 1980s, teams wisely deployed “fireman” relievers like Goose Gossage, Rollie Fingers and Bruce Sutter whenever an opposing lineup presented the greatest threat. But once Dennis Eckersley began to flourish by pitching exclusively in situations that met Holtzman’s criteria, clubs began to pay relievers based on how many saves they accumulated. It wasn’t long before the cult of the closer developed, based on the fallacious notion there was something special and unique about the ninth inning, and that only a fearless, mustachioed, chaw-chomping, hard-throwing right-hander could have the mental and emotional wherewithal to withstand its demands. In response, relievers began to covet the closer role, and to resist entering games in situations that would not pad their save totals. As early as the mid-1990s, quantitative analysts were already decrying the new approach to bullpen management as a textbook example of a statistic dictating behaviour rather than simply measuring it. But without an equally straightforward metric of reliever effectiveness to use in contract negotiations, such pleas fell on deaf ears.

The very first game of the 2016 post-season was the most vivid demonstration imaginable of the folly of this approach. Zach Britton, the Baltimore Orioles’ closer, is an absolutely superlative, borderline-unhittable reliever: his 0.54 earned-run average (ERA), a standard measure of pitching effectiveness, this season was the single best mark in all of MLB history. The American League’s (AL) wild-card game, a one-game playoff, pitted Baltimore against the Toronto Blue Jays. The contest was tied at two after six innings, and Toronto made sure that every subsequent batter faced a dominant reliever. Sure enough, they held the Orioles scoreless from that point on. In contrast, Buck Showalter, Baltimore’s manager, held Mr Britton back so that he would be available to close out the game if his team were to take the lead. Unfortunately for Mr Showalter, there would be no lead to preserve. With his club’s entire season on the line, the manager instead deployed Ubaldo Jiménez, a mediocre-at-best pitcher whose 2016 numbers were downright ghastly, to face the heart of the Blue Jays’ batting order. It should have surprised no one when Mr Jiménez promptly surrendered a devastating, game-ending home run. The Blue Jays are still standing today, though they trail in the AL Championship Series. Meanwhile, Mr Showalter will now have a long six months to rue his slavery to the save rule before his club plays another game.

Conversely, the other teams remaining in the post-season have unshackled their ace relievers from the strictures of conventional closer usage. The most progressive manager has been Dave Roberts of the Los Angeles Dodgers. Kenley Jansen, his dominant closer, did not complete two innings’ worth of work in a single game or enter before the eighth inning at any point during the past three regular seasons. Fully 95% of his appearances over that span have been for an inning or less. Nonetheless, during these playoffs, Mr Roberts has transformed Mr Jansen into a 1970s-style fireman. Three of his five appearances so far have lasted longer than an inning, and the same number have started before the ninth.

Most dramatically, during Mr Jansen’s past two games, Mr Roberts has innovatively paired him with Clayton Kershaw (pictured), baseball’s best starting pitcher. In a riveting, winner-take-all contest on October 13th, Mr Roberts brought in Mr Jansen in the seventh inning, almost unprecedentedly early for a closer. But with a one-run lead, no outs and one man on base, the LI of that situation was 2.27, making it more influential even than entering in the ninth to protect a one-run lead. Mr Jansen got the job done, pitching 2 ⅓ crucial scoreless innings. However, he also demonstrated the risks of bringing in a closer early when he tired in the ninth, issuing back-to-back walks to put the tying and winning runs on base.

A more traditional manager might have stuck with his closer even when he was clearly faltering, or alternately brought in a lesser pitcher for the most important plate appearances of the season. But Mr Roberts had an ace—in both senses of the word—up his sleeve. Although Mr Kershaw had pitched just two days earlier, and had not appeared in relief since 2009, he told his manager he would be available if the situation required it. Sure enough, Mr Roberts summoned him to secure the final two outs, an all-but-unprecedented role reversal for a starter and a reliever. Mr Kershaw duly retired both hitters, and the Dodgers advanced. Three days later, Mr Roberts had his two aces join forces again, with Mr Kershaw shutting out the Chicago Cubs for seven innings and Mr Jansen shouldering the relatively heavy load of another two-inning save, to polish off a 1-0 victory. It is of course possible that Mr Roberts is overworking his best arms, and that they may tire out as the playoffs proceed. However, it is highly likely that had he not done so, the Dodgers’ season would already be over.

This post-season’s other lesson in free-thinking bullpen management comes from the Cleveland Indians, who currently lead Toronto three games to one in the AL Championship Series. In July the club traded for Andrew Miller, another one of baseball’s elite relievers. But rather than shoehorn him into the closer’s role, Cleveland deployed him as an old-school fireman, letting him pitch whenever the game was on the line, as early as the sixth inning. In the playoffs, they have ratcheted up his usage even more, calling on him for three two-inning stints in games they won by a single run, and two more appearances in games they claimed by two. Mr Miller has responded by miraculously getting even better than he was during the regular season: he has struck out fully half of the 60 batters he has faced, allowed just nine to reach base, and not surrendered a single run. Mr Miller has only a single save to his name this post-season. But he has probably been the most valuable contributor so far in October to a team that is one win away from the World Series.

A bit of caution remains in order before sports statisticians claim vindication regarding this long-standing hobby horse. We’ll never know how these games would have turned out had the managers made different decisions. Clearly, the fact that these star relievers have performed in line with their lofty reputations has mattered far more than the order in which they were summoned. And in turn, their efforts probably had less impact on the outcomes than that of their fellow batters and starting pitchers, who generally matter far more than bullpens. Anyone who bases their baseball wagers on reliever usage patterns is likely to leave Las Vegas penniless within a week.

At the same time, relievers—and the way managers utilise them—do take on extra importance in the playoffs. During the regular season, a typical closer pitches about 4% of a club’s innings. In the post-season, with more days off between games and five months of rest to look forward to, their share can be stretched to nearly three times as high. And a team with three bullpen aces, like the 2014 Kansas City Royals, can get fully one-third of their playoff pitching out of well-nigh-unhittable relievers. In turn, this improves the effectiveness of a club’s starting rotation as well: starters tend to perform worse each time they go through the opposing batting order, and removing them early prevents them from suffering this penalty. Moreover, aggressive managers can further strengthen their bullpens by using starters in relief—as Mr Roberts did with Mr Kershaw, or as the San Francisco Giants did in the 2014 World Series with the indestructible Madison Bumgarner. If the 2016 playoffs are any indication, the long, unfortunate reign of the Proven Closer may itself be drawing to a close.