There is a reason, at the very moment Gareth Southgate and his players were having obscenities and plastic cups hurled at them in Cologne on Tuesday, every leading UK bookmaker was slashing the odds on England winning Euro 2024.

It had nothing to do with a sudden surge of optimism or a flurry of betting activity. After all, who would lump any money on an England triumph after that?

It was because of the way the tournament has begun to take shape: the odds for England were cut along with Italy, Austria and Switzerland. The odds on French, Spanish, German or Portuguese glory drifted accordingly.

If it was a free draw after the group stage, as what happens in European club competition, it would be hard to look beyond Spain, Germany, Portugal and — as poorly as they have played so far — pre-tournament favourites France.

But the path was pre-determined. The knockout bracket looked unbalanced before a ball was kicked. It has been unbalanced further by France’s failure to win their group, meaning they join Spain, Germany, Portugal and Denmark in the top half of the bracket. Belgium, should they finish second or third in Group E, could end up there too.

On paper, the bottom quarter of the bracket looks reasonably strong: Switzerland facing Italy in Berlin on Saturday; England facing a third-placed team (quite feasibly the Netherlands) on Sunday. But Switzerland, Italy and England won one game each in the group stage. Add the Netherlands (or whoever finishes third in Group E — Romania, Belgium, Slovakia or Ukraine) and it becomes four wins from a possible 12.

To spell this out, in the bottom quarter of the draw, a team that has won just once in the group stage will reach the semi-final — where the worst-case scenario would mean facing Austria, Belgium or the Netherlands. The most likely semi-final permutations in the other half of the draw might be Spain or Germany vs Portugal or France.

It was put to Southgate on Tuesday, after a dire 0-0 draw with Slovenia, that England might have got lucky with how the knockout stage is shaping up. “We shouldn’t be seduced by which half of the draw,” the manager told ITV Sport. “We have to take a step at a time. Tonight was an improvement. We’ve got to improve to win the next round.”

In his post-match news conference, it was spelt out to him that England had ended up on the opposite side of the bracket to Germany, France, Spain and Portugal. “We have huge respect for all of the teams you’ve mentioned but equally, there are some very good teams on our side of the draw,” he said.

Not equally, though. As at the 2018 World Cup, fortune has smiled on England and on all the other teams who have ended up on that side of the bracket — not least Austria, who are entitled to claim that, by finishing ahead of France and the Netherlands, they have made their own luck.

In 2018, five of the six top-ranked teams in the knockout stage (Brazil, Belgium, Portugal, Argentina and France) ended up on one side of the draw, while the other half consisted of Spain (who had won only one of their three group games), Russia, Croatia, Denmark, Sweden, Switzerland, Colombia and England.

That World Cup was widely regarded as Belgium’s best chance of winning a major tournament, with so many of their ‘golden generation’ of players at or around the peak of their powers. But they paid a heavy price for winning Group G, beating Japan and Brazil but then falling to France in the semi-final. England’s prize for finishing second to Belgium in their group was a place in the gentler side of the draw, which led to them beating Colombia and Sweden before defeat by Croatia in the semi-final.

Euro 2016 brought a similar imbalance. Italy, under Antonio Conte, excelled in the group stage, but their prize for winning Group E was to be placed on the tougher side of the draw. They beat Spain 2-0 but lost to Germany on penalties in the quarter-final. Germany in turn lost to hosts France in the semi-final. On the other side, Portugal — who had scraped third place in Group F by drawing with Iceland, Austria and Hungary — reached the final by beating Croatia in the round of 16, Poland in the quarter-final and Wales in the semi-final.

Some competitions are based on a free draw, such as the FA Cup. Others, such as the NFL or NBA, see teams ranked on their regular-season record, which should theoretically ensure the two strongest teams in either conference end up on opposite sides of the draw.

International football competitions — including the World Cup, European Championship, Copa America, Africa Cup of Nations and Asian Cup — do not work like that. It is pre-determined from the moment the draw is made: the winner of Group A will play the runner-up of Group B, the winner of Group C will play the runner-up of Group D and so on.

The group-stage draw is seeded, but teams are allocated to each group by a random draw, which raises the possibility of the knockout bracket ending up lop-sided. Because the tournaments are condensed into a four-week or five-week period, with matches played in a host nation, it is felt beneficial to have a pre-determined structure for planning, travel and ensuring each team has enough rest between matches.

There are still inconsistencies. Austria will have a seven-day break between the end of their group matches on Tuesday and their first knockout round next Tuesday, whereas Spain’s opponents in the round of 16 (still to be determined) will have had just four days’ rest.

Everything about knockout football lends itself to variance. But it can be predicted with some confidence that a team that has performed miserably at Euro 2024 will reach the semi-final or feasibly the final. After a difficult group stage, England, Switzerland, Italy and others have had a soft landing. For one of them, it might even prove a springboard.

(Top photo: Andreas Gora/Picture Alliance via Getty Images))

Missing Bats, a special series this week in The Athletic, explores how baseball’s profound metamorphosis over the last two decades traces back to one simple idea — maximizing strikeouts at all costs — that became an industry-wide obsession. Explore the entire series here.

As a boy pitching on Little League fields in the suburbs of Los Angeles, Tyler Glasnow fixated on missing bats.

“Ever since I was a child,” Glasnow said, “any time I ever touched the mound, I just wanted to strike everyone out.”

Glasnow, a 6-foot-8, 225-pound starting pitcher for the Los Angeles Dodgers, grew to be taller than almost all of his teammates, with longer limbs but less control of his frame. Growing up in the first decade of the 21st century, pitchers were taught to value the same things pitchers prioritized in the 20th century, searching for soft contact and quick innings. An at-bat should not last longer than three pitches — a mantra that was harder for someone like Glasnow to apply. When he tried to be precise, bridling his body to control the location of his pitches, he lost his command. He was better served, he realized, trying to throw the baseball past the opposing batter and through the catcher, as hard as possible, as fast as possible, every single time.

He did not need soft contact if the hitters never made contact. In his mind, he conjured up a new ideal to chase.

“The perfect inning for me,” Glasnow said, “is nine pitches, nine strikes, three strikeouts.”

The simple concept Glasnow grasped as a child has come to reshape the game he plays as an adult. Like the embrace of the three-point shot in basketball or the advent of the downfield pass in football, modern baseball’s obsession with strikeouts has led to a jarring transformation.

For baseball to be its most compelling, the battle between hitter and pitcher must be waged on equal footing, and for most of the past century, the game didn’t stray too far from this fundamental stasis. But that balance has been upended by the primacy of the strikeout. The concept of pitching to contact has gone the way of the mid-range jumper. “Three pitches or less” sounds as antiquated as “three yards and a cloud of dust.”

Like the corner trey or the deep ball, missing bats makes intuitive sense. A pitcher who could generate strikeouts was always a valuable asset. What separates this era from its antecedents is that the skill is no longer limited to a small group of outliers, blessed with a god-given talent that can’t be taught. In the past 20 years, the industry has learned instead that it can create pitchers who can pile up strikeouts, with entire organizations churning them out with assembly-line efficiency.

“Pitchers are a lot more malleable than we initially thought,” New York Yankees pitching coach Matt Blake said. “Obviously, if you could strike guys out, that was exciting. But I don’t think we understood the true value of swing-and-miss.”

That realization affected the game’s rules, its best practices and its developmental pipeline. Teams rebuilt pitchers’ bodies to chase velocity, used biomechanical analysis to maximize spin rate, and altered pitching strategies to emphasize attacking with high fastballs as the desperate pursuit of strikeouts spread throughout the league like a virus.

For years, the symptoms of that viral spread have been discussed on nearly every baseball broadcast, and debated by those who fell in love with a different game. This week, The Athletic will explore the root cause of baseball’s metamorphosis: the concept of missing bats, from the origin of the idea, to the recognition of its value, through the widespread application of its importance, and ultimately to the cost of its proliferation.

These stories emerged from dozens of interviews with players, coaches, executives and analysts. The shift predates the so-called “launch angle revolution” of the mid-2010s, in which hitters started to sacrifice contact in search of slugging. The origins of the transformation involve a collection of curious outsiders, enraptured by access to an influx of data, and a handful of desperate lifers, clawing for a foothold in a ruthless game. The curious informed the desperate. The success of the desperate made others more curious. The subsequent feedback loop altered the course of baseball history.

The spiderweb of consequences from that shift reflects a new reality: The sport looks different than it did two decades ago because pitchers know how to miss bats, and strikeouts are now a prerequisite for big-league consideration.

“If you want to be a successful pitcher, you have to have strikeouts,” Arizona Diamondbacks pitching coach Brent Strom said. “You need some semblance of swing-and-miss.”

In 2006, the season before Major League Baseball began installing advanced pitch-tracking systems in all 30 big-league stadiums, the league-wide batting average was .269. By 2011, the year Glasnow was drafted by the Pittsburgh Pirates, as insight from the data trickled through front offices, the average had fallen to .255. The average plummeted to .243 in 2022. The strikeout rate has followed an inverse path: 16.6 percent of at-bats ended in a strikeout in 2006, 22.7 percent did in 2023. To increase offense and liven up the product, MLB last season introduced a pitch clock and placed restrictions on infield shifts; that helped bring the league-wide average back up to .248.

The rule changes could only do so much. Teams have learned the value of increased fastball velocity and breaking ball movement, wielding technology to heighten those qualities. An obsession with generating spin and velocity led to a reliance upon illegal foreign substances which led to a 2021 crackdown on “sticky stuff” which some players — including Glasnow — believe ultimately led to an uptick in arm injuries. This season, as MLB officials kvetched about another rash of arm surgeries to open the season, there was another round of dialogue about the reasons for all the pitching problems.

The answers all stem back to discoveries made years ago, when the curious began to inform the desperate. The scenes of innovation take place in locations both obscure and understandable: A psychology department in Iowa City. A ballpark office in St. Petersburg, Fla. A garage in the San Francisco Bay Area. A mound in a packed stadium in Houston. Together, they help explain why baseball looks the way it does in 2024.

“You’ll see a lot of people who played in earlier decades waxing poetic about ‘Guys shouldn’t be striking out as much’ or ‘We need to make more contact,’” Chicago White Sox senior advisor Brian Bannister said. “It’s not that the hitters aren’t trying to do that. It’s just really hard to hit a baseball. It was always the hardest thing to do in sports. And then we made it even harder.”

Dan Brooks did not intend to make his surname ubiquitous with strikeout rates. He was just trying to help a buddy struggling with Microsoft Excel.

By 2008, all 30 big-league stadiums featured a tracking system called PITCHf/x. Built by Sportvision, the company famed for generating the yellow first-down lines on football broadcasts, PITCHf/x utilized a triangular camera setup to detect each pitch’s velocity, release point, location, and horizontal and vertical break. The system logged pitches with more detail than ever before, a treasure trove for the burgeoning group of curious baseball fans searching for deeper insight into the game.

The data was publicly available if you knew where to find it. Brooks, an experimental psychologist studying for his PhD at the University of Iowa, knew where to find the data. And unlike his friend, he also knew how to use Excel to scrape the data. This PITCHf/x data would become the foundation for a website featuring sortable charts and tables that cataloged pitch types and their individual characteristics. The site also grew to include a real-time plot of the strike zone for games. It became a destination for enthusiasts. He called it BrooksBaseball.net, which, he mused years later, was “useful from a personal marketing standpoint, to whatever use that is in life.”

The PITCHf/x data offered answers that people in baseball had sought for decades. The usefulness of strikeouts was never a secret. The statistical guru Bill James had evangelized the value of missing bats since the 1980s. Sandy Koufax fanned more than a batter per inning in his five-season renaissance; Nolan Ryan did the same across a 27-season career. Randy Johnson captured five Cy Young Awards while finishing his career by averaging 10.6 strikeouts per nine innings. Before injuries capsized his career, Chicago Cubs phenom Mark Prior punched out hitters at the same rate as Johnson. “I had swing-and-miss stuff,” Prior said. “So I tried to lean into my strengths.” Most games, Prior recalled, “I tried to strike out the side every first inning.”

The conventional wisdom in the industry, however, suggested that only a certain type of pitcher could chase whiffs. The pitcher needed to harness elite weapons like Koufax or boast remarkable stamina like Ryan or pitch from a hellacious angle like Johnson. The average man could not produce those results — even if a studious, dedicated pitcher could figure out how to get into advantageous counts.

For years after the Los Angeles Dodgers hired him as a pitching coach in 2006, Rick Honeycutt experienced a consistent aggravation with young pitchers. The prospects arrived in the majors equipped with the physical capacity for success but deficient in the strategic acumen necessary to thrive. “Most of the time,” Honeycutt said, “they just didn’t have the ability to put guys away.” Teams searched blindly for answers, and as Arizona Diamondbacks general manager Mike Hazen said, “You would go through cycles of guys throwing the wrong pitch.”

PITCHf/x offered a better road map and Brooks was far from the only outsider to dive into the data. The legion of the curious included a semiconductor engineer with the serendipitous name of Mike Fast. He wrote a blog called Fast Balls and pioneered research into pitch framing, the skill exhibited by catchers for convincing umpires that balls were, in fact, strikes. (The idea proved so influential that one big-league analyst suggested you can study the spread of analytics across baseball by charting when teams improved their framing.) A math professor in West Virginia named Josh Kalk used the data to break down prominent starters and diagnose when pitchers might be injured.

The summer after PITCHf/x debuted during the 2006 postseason, a web developer and tech consultant in Chicago named Harry Pavlidis read a column in Slate about the emergence of “the new technology that will change statistical analysis forever.”

“It was before I even got to the end of the article when I realized what that meant,” Pavlidis said, “and pretty much immediately started my adventures with tracking data.” Brooks and Pavlidis connected at a conference held by Sportvision in 2009. Together they designed BrooksBaseball’s first batch of player cards, offering thumbnail tables of each individual player’s tendencies. By then, Brooks was fielding calls from reporters: A player told me about your site — how do I use it?

“It became clear that not only were baseball nerds on the Internet looking at PITCHf/x data,” Brooks said, “but actual major-league pitchers were doing it.”

But the teams noticed first.

In the fall of 2008, Josh Kalk received an email from James Click, then a staffer in the baseball research and development department of the Tampa Bay Rays. The unexpected message contained an assignment. The Rays were about to face the Philadelphia Phillies in the World Series. Click wanted Kalk, who taught at Bluefield State College, to answer some questions related to the release point of Phillies starter Jamie Moyer. Click had been reading Kalk’s work at The Hardball Times and on his own blog. He figured the academic might have some answers.

Kalk turned around a tidy and helpful response. The insight did not lead to the Rays defeating the Phillies. But Kalk’s analysis still impressed Click and his colleagues. By then, Rays general manager Andrew Friedman had begun to assemble a front office filled with over-educated obsessives. Click worked in a cubicle at Tropicana Field near fellow future chief baseball executives Chaim Bloom and Erik Neander. (Both Bloom and Click had written for Baseball Prospectus, as had another future top baseball executive, Peter Bendix, who was hired as a Rays intern in 2009.) The group studied the latest research from outsiders like Kalk and Fast while spending hours wading through the data themselves.

To win a baseball game in regulation requires the collection of 27 outs. The prospect of how to collect those outs had fascinated and vexed players, coaches and executives for decades. The PITCHf/x data that Brooks had made more accessible helped answer some of the questions. “We found out that the difference between no contact and contact was much greater than the difference between bad contact and good contact,” Click said.

That was not exactly a secret. In “Moneyball,” published in 2002, the author Michael Lewis had highlighted the work of sabermetrician Voros McCracken, who discovered that pitchers had little control of the results once a ball was put in play. As that theory took root, pitchers used the PITCHf/x data to hone the most direct method to regain some measure of control.

“If you want to be an effective pitcher at the major-league level, what’s the most effective thing to do? Don’t let guys get on base,” Click said. “What’s the most effective way to do that? Don’t let them hit the ball.”

To miss more bats, though, you had to answer a more fundamental question: What is an effective pitch at the major-league level? For that, they turned to Kalk. The team invited him to spring training in 2009 and convinced him to leave academia. “I remember all of us sitting around, saying, ‘This guy’s doing some pretty cool (stuff),” Click said. “We should probably see if he’s interested.’”

Like his new teammates, Kalk was a curious fellow. He disdained attention; he declined an interview request for this story. He held a master’s degree in physics from Michigan State. In his day job as a physicist, he studied the so-called “top quark,” once described as “an ephemeral building block of matter that probably holds clues to some of the ultimate riddles of existence.” In baseball, there were similar, if less existential, depths to the influx of pitch-level data.

For much of the sport’s history, a pitcher’s repertoire often stemmed less from his physical capabilities and more from his organization’s preferences. Some teams emphasized changeups and curveballs. Others favored sliders and sinkers. The Rays tended to instruct pitchers to attack hitters on a vertical plane rather than a horizontal plane, because the strike zone was taller than it was wide. But one size did not fit all. Anyone who has attempted to fit a square peg into a round hole can understand why this paradigm was not ideal. Yet few challenged it, in part because it was unclear how to formulate a precise plan for an individual.

While poring through the information, Kalk applied the Nash equilibrium, a game-theory concept gleaned from the world of mathematics, which posited that an individual could formulate an optimal strategy no matter the strategies of the opponents. (The concept was memorialized in the film “A Beautiful Mind” during a scene in which Russell Crowe as the mathematician John Nash asked, ‘What if no one goes for the blonde?’”) Applied to baseball, the principle suggested each pitcher possessed an ideal, individualized mixture of pitches. The percentages depended on the strengths and weaknesses of each pitcher. The proximity to equilibrium would appear in the data if the results of each different pitch were identical. Because of PITCHf/x, the analysts could now measure the effectiveness of each individual offering.

What Kalk discovered was that very few, if any, big-league pitchers approached this equilibrium. One of the first to come close was James Shields, a pitcher with a plethora of weapons. Shields could throw three different types of fastballs and an elite changeup. After a rocky season in 2010, though, Tampa Bay officials suggested he throw his curveball more often. Shields raised his curve usage from 13.5 percent to 21 percent in 2011 and achieved the best results of his career, making the All-Star team and leading baseball with 11 complete games. “Every year, we were always making adjustments to be able to pitch in (those) ideal pitch sequences, so that you’re not predictable,” Shields said. The Rays ranked 15th in baseball in strikeout rate in 2011 (7.11 strikeouts per nine innings); across the next three seasons, the team zoomed to first (8.47 strikeouts per nine).

With help perfecting his pitch mix, James Shields emerged as a front-line starter for the Tampa Bay Rays. (Al Messerschmidt / Getty Images)

Kalk worked remotely from West Virginia. After a few years, the Rays asked him to venture into the field more often. The team wanted to spread his wisdom across the organization. Friedman introduced Kalk to Kyle Snyder, a towering former first-round pick who Tampa Bay hired as a class-A pitching coach in 2012. A year later, when Snyder was promoted to coach at Double-A Bowling Green, Kalk sat him down. Kalk had prepared a PITCHf/x plot culled from Snyder’s own career, which ended in independent ball in 2011. The analyst showed the former athlete all the ways in which he could have pitched differently, had he known about the data. “It was one of the more powerful things for me in terms of not just my buy-in,” Snyder said, “but realizing how powerful this information was about to become.”

Kalk flipped past the page dedicated to Snyder and unveiled similar plots for Tampa Bay minor-league pitchers like Dylan Floro, Taylor Guerrieri and Jesse Hahn. Each plot contained clues for optimizing pitchers — not just which of their pitches were best, but why. “I’m like, I cannot believe what I’m looking at and how powerful this is in terms of just understanding physics and how the balls move,” Snyder said.

A year later, Snyder became the organization’s minor-league pitching coordinator. He reveled in his trips to the team’s Appalachian League affiliate in Princeton, W. Va., because the site was near Kalk’s home. Like so many in his profession, Snyder sought clarity on the most effective way to procure 27 outs. Kalk shined the light.

“I started peppering him with questions after I realized the asset that he was,” Snyder said. “I’m like, ‘Wait a second, man. Let’s start talking about this.’” The conversations opened Snyder’s eyes. There was no out more effective than a strikeout. “I’m like: OK, other than a ball getting to the backstop on a wild pitch or a passed ball, if a guy swings at strike three, he’s out!”

From his home office, located in the garage of his ranch-style house outside San Francisco, Brian Bannister played a little game with himself. After his career as a big-league pitcher ended in 2010, Bannister hoped to get into player development. But first he wanted to conduct some research. He logged onto BrooksBaseball and pulled up the PITCHf/x powered player cards built by Brooks and Pavlidis. They featured information on the frequencies with which players threw certain pitches and how effective they were. Bannister set a timer for 30 seconds. He had to scan each card and figure out how to make the player better. He spent hours each day studying the site.

“As I looked,” he said, “there was just some obvious, low-hanging fruit there.”

Bannister was the consummate insider. His father, Floyd, pitched for 15 years in the majors. Brian played at USC with Mark Prior. He reached the majors less than three years after the Mets drafted him in 2003. Yet he harbored the curiosity of someone willing to challenge baseball’s shibboleths. He considered Mike Fast his “original inspiration” for delving into pitching design.

Bannister was one of those players using BrooksBaseball while still in uniform. He embraced the data because he was desperate. After the Mets traded him, Bannister had a solid rookie season with Kansas City in 2007 before posting a 5.76 ERA the next season. Unable to generate strikeouts, Bannister tried to soften the contact he allowed. He ditched his four-seam fastball for a cutter and attempted to model a changeup off James Shields. Neither adjustment proved that fruitful: in 2009 and 2010 Bannister pitched to a combined 5.46 ERA.

He funneled his curiosity into one of his teammates: Zack Greinke. Greinke possessed the physical tools that Bannister lacked; he could make the baseball do whatever he desired. Together, they put together game plans and engaged in side quests, like seeing how slow a curveball Greinke could throw or how many different ways he could manipulate a changeup. In between innings, the duo would check out the results on BrooksBaseball’s real-time tracker. “We would go run in and see what our movement was,” Bannister said.

Royals teammates Zack Greinke and Brian Bannister worked together to unlock pitching secrets; it worked for Greinke, if not for Bannister. (John Sleezer / Kansas City Star / Tribune News Service via Getty Images)

In retirement, Bannister could apply that same inquisitiveness in a more targeted way. For two years, he logged onto Brooks’ website and timed himself trying to fix 50 different pitchers each day. He was not sure exactly what he was looking for, but he wanted to train his mind. “I was scanning things, like, ‘What are pitchers doing that they’ve been doing forever but actually doesn’t make a lot of sense?’” he said. He followed a principle espoused by famed investor Charlie Munger that most problems could be solved by looking backward. He studied elite pitchers like Greinke, Clayton Kershaw and Justin Verlander and compared them to lesser players.

“I would look at one pitcher whose fastball had a certain shape and I’d look at another pitcher whose fastball had the exact same shape,” Bannister said. “But this pitcher was horrible and this pitcher won the Cy Young Award. So I was like, ‘There’s got to be something more to this.’”

What Bannister decided was that conventional wisdom had led pitchers astray. They chased outdated ideals rather than utilizing their own individual gifts. They pocketed excellent offspeed pitches while using shoddy ones to excess. And most importantly, to Bannister, they threw far too many fastballs. “My mission for years has been to reduce fastball usage,” Bannister said. (Consider the mission accomplished: The league-wide fastball percentage fell from 57.8 percent in 2011 to 48.1 percent; for the past two seasons, for the first time in the pitch tracking era, hitters were more likely to see an offspeed pitch than a fastball.)

Bannister thought more pitchers should follow a philosophy culled from video games called “min-maxing.” It made sense on an intuitive level: Throw your best pitches as much as possible and your worst pitches as rarely as possible. “What do you do best? Let’s do more of it,” Bannister said.

In 2013, Brooks invited Bannister to speak at the analytics conference Saber Seminar. A year later, Bannister gave a demonstration using a radar system called TrackMan that had been popular in golf. The audience included Boston Red Sox analyst Tom Tippett. Boston hired Bannister to work in scouting and player development. Bannister soon learned he much preferred the latter to the former.

Late in the summer of 2015, Bannister crossed paths with Rich Hill, a journeyman pitching for Triple-A Pawtucket. Hill had recently turned 35. He had flamed out as a starter and then again as a reliever. He wanted to give starting one last try. Bannister studied the data on Hill’s arsenal and discovered his curveball was excellent. Hill already threw the pitch quite often. Bannister wanted him to throw it even more. They sat together for an hour before a game as Bannister outlined how Hill could use his curveball like Greinke used a changeup, varying speeds and grips to alter its movement.

“All I said was, ‘I think you have one of the best curveballs in the world,’” Bannister said. “He was ready to almost quit the game and retire. And I said, ‘Go throw a curveball until you can’t throw it anymore. And throw it a bunch of different ways.’

“Almost $100 million later … he did that and he took my advice and ran with it.”

The Astros saw something in Collin McHugh that even he didn’t realize was there. (Adam Hunger / Getty Images)

In December of 2013, soon after the Houston Astros pulled him off the scrap heap, Collin McHugh received a phone call from Astros assistant general manager David Stearns.

“We’ve targeted you for a while,” Stearns said, as McHugh recalled.

The sentiment may have sounded far-fetched, the sort of well-meaning pabulum any team feeds a new addition. McHugh had spent much of the previous season in the minors after getting whacked around in short stints with the Mets and the Rockies. He was not eager to spend another year as a member of the Colorado Springs Sky Sox.

“I wanted to get out of Colorado so badly,” said McHugh, who had been desperate enough to follow his own curiosity. He ventured to the Venezuelan Winter League to experiment with new sequences and rebuild some confidence. He was an open book when he met with Astros pitching coach Brent Strom that first spring. Strom had a simple suggestion: Throw your curveball more often.

The advice was rooted in data. The Astros were run by Jeff Luhnow, a former McKinsey consultant and St. Louis Cardinals executive hired by Houston owner Jim Crane in 2011 to resuscitate a moribund franchise. As Luhnow tore down the big-league roster, he populated the front office with a collection of curious outsiders. He brought Sig Mejdal, the director of decision sciences, from St. Louis and he brought Kevin Goldstein, the pro scouting coordinator, from Baseball Prospectus. One of the first people Luhnow hired was Mike Fast.

Fast, who declined an interview request for this story, was “a brilliant guy,” said Strom, who pitched for several seasons in the majors before beginning a lengthy coaching career. Strom overlapped with Luhnow in St. Louis before following the executive to Houston. Strom worked closely with Fast. Strom kept his mind open and excelled at relaying the granular insight to players. “What I realized quickly — and I’d always known it — but you didn’t have to have played this game to know what the f—- you were talking about,” Strom said. “They dove into a lot of things that a lot of us as players never even realized.”

So when Strom told McHugh to throw more curves, it was not just because the pitch looked good to the naked eye. Fast had studied the PITCHf/x data and found McHugh’s bender contained similar characteristics to elite curveballs thrown by All-Stars Felix Hernández and Adam Wainwright. In time, as McHugh established himself as a solid big-league starter, he received more suggestions. “They always wanted a harder curveball,” McHugh said. “And I told them, ‘I can’t throw it any harder. I’m trying.’”

The insistence on adding velocity to offspeed pitches stemmed from an organizational failure. In March of 2014, the same spring in which the Astros welcomed McHugh to the team, Houston released an unremarkable outfielder named J.D. Martinez. When Martinez broke out later that season with the Detroit Tigers, Luhnow wondered where his team had erred. In reviewing the decision, Astros officials realized they had ignored data gleaned from their own TrackMan radar systems, which demonstrated that Martinez had begun to hit the baseball much harder. The Astros hadn’t heeded the data’s insight.

“It created this idea in our mind that this data is valuable and we’re ignoring it,” one former Astros official said.

As Martinez blossomed into an All-Star in Detroit, Luhnow and Crane received a presentation about the value of the TrackMan system from Fast and Brandon Taubman, a former investment banker hired as an analyst in 2013. Taubman had researched the system and learned that the most prolific investor in it was the Rays. He requested enough money to surpass Tampa Bay and install TrackMan technology at every level of Houston’s developmental pipeline. The Astros decided to prioritize studying the new information gleaned from the machines.

The reason the Astros wanted McHugh to increase his curveball velocity stemmed from Fast’s research. Using TrackMan, Fast and Mejdal created a model that could effectively place a grade on each individual pitch. The research unearthed a series of conclusions that bucked conventional wisdom. The two-seam fastball has a platoon split, while the four-seam fastball does not. The changeup didn’t just have to be thrown against opposite-handed hitters. And most crucially, breaking balls with heightened velocity were more effective than slower breaking balls with more movement.

“That’s why you see these guys throwing 87 mph sliders now,” one big-league executive said. “It might have fringe-y spin and movement. But the fact that it’s hard makes it miss bats.”

McHugh could not generate that sort of velocity. No matter how hard he tried, his curveball was always going to clock in around 75 mph. But someone like Lance McCullers, a first-round pick in 2012, was a different story. In the coming years, the Astros would use the data to turbo-charge aces like Justin Verlander and Gerrit Cole, rearrange the arsenals of future All-Stars like Charlie Morton and Ryan Pressly, and shape the careers of unheralded Latin America signees like Bryan Abreu and Framber Valdez. Taubman traversed the minor-league affiliates to spread the gospel.

“When we got an idea and believed in it, we did it everywhere,” one former Astros official said. “We did it with the big-league team. We did it with the minor leagues. We did it with amateur scouting. We did it with international scouting. We did it everywhere.”

The Astros front office eventually collapsed in infamy. Taubman was fired in October of 2019 for an outburst directed at female reporters in a pennant-clinching celebration. Luhnow was fired three months later after an MLB investigation determined Houston used an illegal sign-stealing system en route to the World Series in 2017. Fast left for the Atlanta Braves. Mejdal followed fellow Astros alum Mike Elias to Baltimore’s front office. Goldstein returned to writing for a brief period before joining the Minnesota Twins. In the years since, Astros executive alumni have lamented that the scandals have overshadowed the innovations shepherded by the organization, like how the team secured the final outs of the 2017 American League Championship Series.

Facing the Yankees in Game 7 of the 2017 ALCS, Lance McCullers Jr. min-maxed his team to the World Series. (Cooper Neill / MLB via Getty Images)

Up four runs in the sixth inning of Game 7, Astros manager A.J. Hinch asked McCullers to tame the Yankees. In 2015, the season McCullers debuted, Houston pitchers ranked 12th in the sport in strikeout rate, with 7.99 per nine innings. By 2017, the Astros were striking out 9.91 batters per nine, better than every team but Cleveland, another franchise on the forefront of the game’s obsession with supercharging pitchers. McCullers was part of the difference. Facing the Yankees, he yielded a single to the first batter he faced before mowing down the rest of the opposition. He leaned on his breaking ball. By the eighth inning, with the team’s first pennant since 2005 within sight, he simply stopped throwing anything else.

The final 24 pitches McCullers threw were knuckle curveballs, hammers that approached 88 mph. As Fast’s research from years before had suggested, the pitch was further weaponized by added velocity. “I remember watching it,” McHugh said, “thinking: This is unbelievable. They cannot hit it.”

The Yankees lineup was not attempting to string together singles. No team had homered more in 2017 than the Bronx Bombers. The lineup had joined the launch angle revolution, a movement spurred by the improvements in pitching that had started years earlier in Tampa Bay. McCullers wielded the sort of weapon capable of putting down a rebellion, min-maxing in the most pressurized moment of his career.

The Yankees swung and missed seven times during McCullers’ finishing flurry of two dozen curveballs. They put the ball in play precisely twice.

“Houston doing what they did,” Bannister said, “was finally leveraging it at scale.”

In the summer of 2018, Tyler Glasnow was floundering. He demonstrated enough talent to impress scouts but struggled to throw strikes. The Pirates instructed pitchers to locate the ball down in the zone and try to pitch to contact. Glasnow couldn’t do it. After three seasons in Pittsburgh, his ERA was 5.79. Pittsburgh used him as a middle reliever before bundling him into a prospect package to acquire Tampa Bay starter Chris Archer.

Tampa Bay had bigger plans for Glasnow. He was desperate enough to be curious when Rays officials approached him. The Tampa Bay pitching coach was Kyle Snyder, the former big-leaguer who had learned so much from Josh Kalk. The team wanted to turn Glasnow loose as a starting pitcher. Snyder asked Glasnow to reconnect with the spirit and skill that buoyed him in boyhood. He instructed Glasnow to throw the baseball down the middle, through the catcher, as hard as he could. His fastball and his curveball were good enough to beat hitters in the zone. There was no need to waste time trying to hit corners.

In time, Glasnow absorbed insight gleaned from the previous decade, from all the trial and error of the curious and the desperate. The Rays prescribed him a plan that fit his profile rather than their stylistic preferences. His fastball velocity increased as he replaced two-seam sinkers with elevated four-seam heaters. He reoriented his pitching axis to north and south, rather than east to west. He junked his changeup and eventually swapped it for a slider, which allowed him to use his fastball less often. He started throwing his curveball harder and harder.

The alterations improved Glasnow’s command while maintaining the quality of his arsenal. In his first start with Tampa Bay, Glasnow punched out five batters in three innings. Six days later, he set a new career-high mark for strikeouts with nine — in only four innings. During his six seasons as a Ray, he struck out 12.5 batters per nine innings. Despite his inability to stay healthy, Glasnow’s potential enticed the Dodgers, now run by former Rays general manager Andrew Friedman, to acquire him last winter. The Dodgers lavished Glasnow with a four-year, $115 million extension.

On May 10, in his ninth start as a Dodger, Glasnow flirted with his ideal inning. It came against the San Diego Padres. Manny Machado fouled off a pair of fastballs before staring at a slider. Jurickson Profar could not catch up to an elevated, 96-mph heater. Xander Bogaerts whiffed on a pair of fastballs. Fourteen pitches. Nine strikes. Three strikeouts.

“I don’t think,” Glasnow said, “I’ll ever pitch to contact.”

With reports from The Athletic’s Zack Meisel and Chad Jennings.

(Top illustration by Eamonn Dalton / The Athletic. Photos of Bannister, McCullers and Glasnow: by Sarah Stier / Getty Images; Rob Tringali / Getty Images; Kevork Djansezian/Getty Images)

The debate around the U.S. men’s national team going into Sunday’s Copa America group-stage opener was about the balance between performance and result.

The consensus landed on this: in a tournament, the results are all that matter.

The hope is that performance goes along with that, and against Bolivia, there were positives to take away in both categories. The U.S. dominated possession and generated numerous chances. They limited Bolivia to almost no real threats on goal. And they got that all-important result: a 2-0 win.

The United States will now head into the middle group game, against Panama, knowing that a win would essentially secure passage through to the knockouts. They must hope, however, that the nuance of this first result, instead of a three- or four-goal victory, doesn’t end up being the difference at the end of the group stage in a tournament in which goal differential is the first tie-breaker.

After the game near Dallas, the team insisted they were worried less about the score and more about the bottom line.

“Goal differential is important, but the most important thing is to get the win,” winger Tim Weah said. “Once you’re winning, you don’t have to worry about goal differential.”

The night started about as perfectly as the U.S. might have hoped. Less than three minutes in, Christian Pulisic curled a shot from the top of the box into the far corner to give them the lead. Just before half-time, Folarin Balogun doubled it.

Pulisic and Robinson celebrate the opener (Aric Becker/AFP via Getty Images)

In the second half, the U.S. time and again found space to attack a Bolivia team trying to find their way back into the game. But repeatedly, they didn’t take the chances created.

Pulisic forced a save from Guillermo Viscarra in the 60th minute. Ricardo Pepi registered six shots despite only coming on in the 65th minute — the most by a USMNT substitute in one game since Opta began detailed data collection of all U.S. matches in 2010.

“It’s about winning tournament games,” head coach Gregg Berhalter said. “We look at the final results. If you get some precise data, we probably have over three expected goals in the game (2.51). They had 0.18. That’s comprehensive.

“I guess there’ll be an angle, maybe from you (the media), that says, ‘OK, they should have scored more goals, should have created more chances.’ But it’s a 90-minute game, and over the course of a 90-minute game, we created enough chances, we denied them enough chances. We’re happy with the result. We move on.”

Berhalter acknowledged that Pepi, especially, was disappointed. As a former FC Dallas youth player, he was performing in front of a hometown crowd that cheered his entrance just after the hour mark.

Pepi has been an effective supersub. He scored all seven of his goals for PSV Eindhoven in the Netherlands’ top division last season (2023-24) off the bench, and going into Nations League play back in March had scored five times in his previous nine appearances for his country, all five coming as a substitute.

On Sunday, things just didn’t drop for him. Pepi had a chance in the box with his first touch of the game in the 67th minute, but couldn’t redirect Antonee Robinson’s cross. Then he forced a save from Viscarra with a 79th-minute shot.

In the 90th minute, it looked like Pepi would surely notch the U.S.’s third goal when Robinson’s cross found him again at the top of the six-yard box, but his close-range shot was kept out by Viscarra. When the rebound bounced off of Pepi and toward the net, Viscarra again denied him.

After the game, Weah said he told Pepi to “just stay focused, keep his head up”.

“There are days where you score a hat-trick, there are days where you don’t; I think that’s what comes with being a striker,” Weah said. “As we see, even with (Belgium’s 85-goal record-scorer Romelu) Lukaku and the Euros, he’s having a tough time.

Berhalter was satisfied with the 2-0 win — despite the missed chances (Aric Becker/AFP via Getty Images)

“The best of the best know how to just keep it together and we have another game, so he’s (Pepi) gonna have plenty of other chances to get it in the back of the net. And obviously, we have confidence in his ability in front of goal.”

Berhalter backed Pepi, too.

“I thought he had a great impact on the game,” Berhalter said. “In that short period of time, to have that many goal-scoring opportunities, to be that relentless with his running, with his pressing, with his hold-up play, he had an excellent game.

“I know he was a little bit disappointed after the game, but when you get that many chances in that short period of time against an aggressive team, you’re doing something right. And we’re confident that the finishing will come.”

A few hours after Sunday’s win, Uruguay beat Panama 3-1 to move level on points and goal differential but ahead on goals scored. The U.S. have CONCACAF rivals Panama next, in Atlanta on Thursday.

“There’s a lot of soccer to play in this group,” Berhalter said. “And it’s not done. We have two more games. We’ll always look at the chance creation as a marker of performance, and we created enough chances today. Most days, those chances are going to go in, and today they didn’t but that’s fine. We’re pleased with the result. The game was never in doubt.

“It’s a good starting point on which to build throughout this tournament.”

GO DEEPER

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(Top photo: Robinson chats with Pepi at the end of the match. Aric Becker/AFP via Getty Images)