AS RECENTLY as 2014, North America’s Major League Baseball (MLB) appeared to be mired in a new dead-ball era, with the lowest level of scoring observed in a full season since 1976. With pitchers throwing harder than ever, an enlarged strike zone putting batters at a disadvantage and big-data-driven defensive shifts increasing the odds that fielders scoop up the balls that hitters do put into play, the downward spiral in offence appeared to have no end in sight. Shortly after taking office in early 2015, Rob Manfred, the sport’s commissioner, said he hoped to “inject additional offence into the game”, and even floated banning defensive shifts as a potential remedy.

In what at the very least looked like a striking coincidence, the trend began to reverse just a few months after Mr Manfred assumed the reins. Starting in the second half of the 2015 season, scoring surged enough to erase the decline seen during the previous six years. The home-run rate rebounded to the highest level of the decade.

But if late 2015 represented a reasonable equilibrium, the trend didn’t stop there. Since then, the power surge has only intensified, and the rising tide is lifting all boats. Aaron Judge, a little-heralded rookie, has set the tone with a steady barrage of majestic blasts of unfathomable distance. Even Scooter Gennett, a journeyman infielder, got in on the action a few weeks ago by becoming the 17th player in MLB history to club four homers in a single game. Overall, home runs have increased by nearly half since 2014.

The league-wide home-run spike has been just as baffling as it was abrupt. In recent years, quantitative analysts have considered a wide variety of possible explanations, ranging from steroids to weather to changes in batting strategy. None of these factors, even when taken together, came close to accounting for the phenomenon.

Only this month has a credible explanation emerged at last for the mystery, as two new studies point to the same culprit: the ball. In one, published in The Ringer, a sport website, two prominent baseball statisticians, Ben Lindbergh and Mitchel Lichtman, sent several dozen game-used balls to the Washington State University Sports Science Laboratory. It found that, when compared with those from previous season, the more recent balls had minor physical differences conducive to flying further, including a slightly higher coefficient of restitution (a technical measure of bounciness), a lower seam height and a smaller circumference.

The second study, by Rob Arthur of FiveThirtyEight, used MLB’s own camera-tracking data to measure the effect of air resistance on the ball, by comparing the speed of a pitch at the moment of release with its velocity when the ball crosses home plate. He found that the drag coefficient, which measures air resistance, has declined enough since 2015 to explain as much as a 15% increase in home runs. Although this figure has fluctuated in the past, leading to occasional short-term peaks and troughs in run-scoring, a change of this magnitude has never lasted this long. “We may never have a single ‘smoking gun’ proof” that the ball is responsible, Mr Arthur says. “However, as evidence from multiple sources mounts, it has become very likely.”

MLB has not acknowledged any change in the ball. It recently made a study of its own available to Mr Lindbergh that revealed no structural differences. However, its guidelines for the characteristics of game-worthy balls are extremely flexible: at the extreme, two balls so different that the same impact would send one flying 49 feet (15 metres) further than the other could both pass muster with the league.

So far, there is no way to determine whether MLB has done anything to produce the slicker, longer-flying ball, or whether the league achieved its desire simply by a happy accident. The changes to the ball are so small that they could easily stem from unplanned quirks in the manufacturing process: the change in seam height detected by Mr Lichtman’s study is less than three-thousandths of an inch. For his part, Mr Lichtman is willing to believe it is inadvertent, speculating in an e-mail interview that “these variations are natural variations in the manufacturing process and may be hard to control”.

At the same time, the fact that Mr Manfred got what he wanted so quickly provides reasonable grounds to suspect that the league may not have been a purely innocent bystander. The notorious ad campaign by Nike in 1998 with the tag line “chicks dig the long ball” made the notion that the league favours a homer-happy game into a mainstay of popular culture. There is robust empirical evidence to support this claim: one study in 2008 found that the public, regardless of sex, voted for home runs with their wallets to a striking degree: each longball, it determined, put around 2,000 additional fans in the stands. It also established that home runs in particular are the draw, rather than run-scoring by any other means. (MLB attendance last year was actually slightly lower than in 2014, but it might have been lower still had the power surge not occurred.)

At first glance, the beneficiaries of these minor changes in a baseball-manufacturing plant in Costa Rica would appear to be MLB hitters. However, if all of them are aided to the same degree, then their value relative to each other—and thus their salaries and teams’ fortunes—would remain unchanged. In fact, the shift has helped some players far more than others. The ones who have benefited the most are those who have padded their home-run totals with fly balls that just barely creep over the fence—drives that would have been much less valuable only a few years ago. Some of them wouldn’t have even been fly balls: the livelier ball has driven hitters to swing harder and aim higher, eschewing ground balls and accepting strikeouts in exchange for potential home runs.

Thanks to ESPN’s Home Run Tracker, which records the distance (along with several other variables) for every longball in MLB, it’s possible to identify who has gained the most from a slicker ball—and thus who might be at peril of losing much of their value if the ball reverts to its prior form. The site classifies homers as “just enough,” “plenty,” or “no doubt,” and the number of “just enough” home runs—those that just barely cleared the fence—neatly parallels the size of the increase since 2014. In other words, today’s “just enough” was yesterday’s “not enough.”

The most extreme examples of players who have benefited from the lively ball are Mookie Betts of the Boston Red Sox (pictured, who has hit 24 “just enough” homers out of a total of 51 since the middle of 2015) and Jay Bruce of the New York Mets, with 31 out of 66. Some players more commonly associated with the power surge, such as Mr Judge, are less susceptible to changes in the ball: because he tends to propel the ball nearly into orbit, only 19.4% of his 31 homers have been “just enough,” compared with a league average of 30.8%. Even though a softer ball would reduce his power output, it would probably make him a more valuable player, since he would lose a far smaller share of his homers than his opponents would.

Unfortunately for Mr Judge, the most likely outcome is that the ball will stay juiced. Even if the changes were a pure coincidence, they have fulfilled Mr Manfred’s wish for more offence. And given the historical relationship between home runs and attendance, it’s unlikely the owners of MLB teams will protest. The present controversy may lead to more oversight of the manufacturing process, which may also make it more likely that MLB will get whichever sort of ball it desires.

Whatever changes await, they won’t be such a mystery next time. According to Mr Arthur, getting to the bottom of such alternations “would be much quicker than last time, because we know how to do these studies now”. In the unending quest to isolate player skill from the array of confounding factors, measurement of the effect of the baseball will soon take its place alongside the rest of the sport’s established range of analytical tools.