NASHVILLE, Tenn. — Two-time Daytona 500 winner Michael Waltrip has joined the ownership group of the Nashville Kats, a founding franchise of the Arena Football 1 league.

The Kats announced Waltrip joining the group Friday along with his craft beer company Michael Waltrip Brewing. The ownership group already includes former NFL coach Jon Gruden with Jeff Fisher, a former coach of the Los Angeles Rams and Tennessee Titans, majority owner.

“We now have three living legends attached to the Nashville Kats — Jeff Fisher, Jon Gruden, and Michael Waltrip — all with the ultimate goal to win championships and raise the AF1 to its ultimate potential along with any team associated with the AF1,” said Bobby DeVoursney, the Kats’ CEO and managing partner.

Waltrip’s brewery now is the team’s official craft beer. The team also plans a “Waltrip Winner’s Circle” fan zone for the upcoming season.

The Kats play the Southwest Kansas Storm on Sunday in Clarksville in the AF1 semifinals.

AWAITING TAKEOFF ON the Boston Red Sox‘s charter flight early Sunday evening, Rafael Devers sat with his teammates playing cards. The trip to Seattle would take a little more than six hours, and games were a reliable way to pass the time, a carefree bonding exercise for a team coming off a sweep of the rival New York Yankees. This was going to be a good flight.

Before the Boeing 757 lifted off, Red Sox manager Alex Cora approached Devers with a solemn look on his face. He had news, and there was no easy way to say it: Devers had just been traded to the San Francisco Giants. Devers was gobsmacked. He gathered his thoughts and belongings, said goodbye to his teammates, strolled off the plane and into a cab, and rode off to the next phase of his life.

For months, the tension between Devers and the team had simmered. What started in spring training as a repairable mismanagement of Devers’ future — and his ego — by the Red Sox degraded into something far too familiar for the organization. Devers, according to a person familiar with his thinking, felt “lied to and betrayed” by the Red Sox. Cora, long one of Devers’ chief supporters and advocates, supported his expulsion. Craig Breslow, the Red Sox’s chief baseball officer whom Devers publicly badmouthed amid the hostility, played hatchet man. Red Sox ownership, which at first wanted to mend the relationship between the parties knowing that two years earlier it had guaranteed him $313.5 million to play a central role in a forthcoming resurgence, lost faith and greenlit the deal. And just like that, the last remaining member of Boston’s 2018 championship team, the kid who had signed with the team as a fresh-faced 16-year-old and a dozen years later had grown into a three-time All-Star and one of the best bats in the major leagues, was gone. The simmer had boiled over.

Devers wasn’t the only one blindsided. When the news broke, Red Sox fans did not believe it. They did not want to believe it. It was happening. Again. The package heading to Boston — left-handed starter Kyle Harrison, outfield prospect James Tibbs III, hard-throwing reliever Jordan Hicks and young pitcher Jose Bello — felt light for a player with the track record and productivity of Devers. It felt all too similar to the underwhelming return of the trade five years ago that sent future Hall of Famer Mookie Betts from the Red Sox to the Los Angeles Dodgers.

Eighty-six years of failure leading up to their 2004 World Series win had calloused Red Sox fans and the organization alike. Even as the team became the most successful in the sport, with four titles in a 15-year span, dysfunction was never far from the surface. While winning those rings, the team suffered a historic collapse in 2011, last-place finishes in 2012, 2014 and 2015 — complete with made-for-tabloids drama about chicken and beer in the clubhouse — and the disastrous Betts trade. The one constant was an ugliness that personified the exits of some of the most prominent pieces of the Red Sox’s success.

Theo Epstein, a lifelong Bostonian and the architect of the curse-breaking 2004 team, grew so tired of his clashes with ownership that he quit on Halloween a year after his triumph and exited Fenway Park in a gorilla suit. He returned, only to later abscond for the Chicago Cubs. Terry Francona, the manager for the championships in 2004 and 2007, left alongside Epstein in 2011, was smeared anonymously for his usage of pain pills — he denied the allegations — and went on to win four division titles and go 921-757 in 11 years with Cleveland. Players were not spared the drama, either. Ace Jon Lester wanted to re-sign with the Red Sox, only to get lowballed; he followed Epstein to Chicago. Betts preferred to remain in Boston, but not at a discount — and the Red Sox shipped him out. Manny Ramirez offered perhaps the best description of life with the Red Sox a day before they traded him to the Dodgers in 2008, telling ESPN Deportes: “Mental peace has no price, and I don’t have peace here.”

The Red Sox have everything an organization could want — a rabid fan base, a gorgeous stadium, a successful television network, a history that dates to the turn of the 20th century — and still find themselves regularly salving self-inflicted wounds. Chaos is every bit as much the Red Sox’s brand as the Green Monster. The current iteration comes not from the detritus of a long-standing lack of success but an operating philosophy that better resembles plucky mid- and small-market teams than a financial leviathan. The Red Sox are big-market baseball in a funhouse mirror, a distorted reflection of what could be — and should be.

Breslow is not naïve to the chaos. He grew up in New England and spent five seasons pitching for Boston. Epstein hired Breslow in 2019 with the Cubs and entrusted in him the organization’s pitching program. The Red Sox poached him to replace Chaim Bloom in October 2023 with a specific mandate: Whatever it takes, remake the Red Sox to rekindle the early-century glory days. That’s even when it means trading the team’s best player.

RAFAEL DEVERS GREW up a Boston Red Sox fan in Samana, Dominican Republic. The Red Sox were the unofficial team of the small Caribbean island that had grown into the most fertile hotbed of talent in the world. The team’s biggest stars — David Ortiz, Manny Ramirez, Pedro Martinez — were Dominican. Devers turned 8 three days before the 2004 championship. Nine years later, when the Red Sox were barreling toward their third title in a decade, he signed with them for $1.5 million.

At 20, Devers arrived in Boston as a hitting savant, his left-handed swing loaded with power, and stabilized a third-base position that had been a revolving door. In his first full year, Devers shook off an inconsistent regular season to drive in nine runs over 11 postseason games, capping a 108-win campaign widely regarded as the best in the team’s century-plus history.

After carrying the highest payroll in MLB in 2018 and 2019, owner John Henry tightened the purse strings. And when Betts was shipped out in 2020 and longtime shortstop Xander Bogaerts followed him west to sign as a free agent with San Diego for $280 million — $100 million-plus more than Boston’s final offer — the restlessness of Red Sox fans hit overdrive. Save for a surprising run to the American League Championship Series in 2021, mediocrity had become a Red Sox norm. The days of Papi and Manny and Pedro were nearly two decades in the rearview. Devers was their lone homegrown every-day player.

He represented an opportunity for the Red Sox to illustrate they remained dedicated to the now as much as the future. Making moves to mollify restless fans is a hallmark of bad organizations, but with declining viewership on NESN and empty seats at Fenway, ownership pushed to lock up Devers long-term. Multiple high-ranking officials in the baseball operations department opposed the idea. They were overruled. In January 2023, Devers agreed to a 10-year, $313.5 million contract extension that would begin in 2024.

It was the largest commitment in franchise history. Executives around the game questioned the wisdom of the deal. Yes, Devers had grown into a consistently excellent hitter — from 2019 to ’22, his OPS+ ranked 25th among the 247 hitters with at least 1,000 plate appearances. And, sure, in a market like Boston, where fandom is religion, placating the masses matters. But the questions, in their minds, outweighed those factors. How soon would Devers need to move off third base, where he was a below-average defender? How would his body, always squatty, age? How often did long-term contracts for one-dimensional players work out? Just because it was a deal that needed to happen didn’t make it a good one.

No signs of discord or regret surfaced until February. Boston’s recent aborted attempts at contending — team chairman Tom Werner famously said the Red Sox intended to go “full throttle” into free agency after the 2023 season, only for them to spend $50 million total and go 81-81 — had failed, but this year was going to be different. Amid all the losing, Bloom had drafted and developed a cadre of position-playing prospects. Breslow traded three, plus a hard-throwing right-hander, for ace Garrett Crochet in December. He signed World Series standout Walker Buehler to join Crochet in an overhauled rotation and veteran closer Aroldis Chapman to shore up the back end of the bullpen. And despite the presence of Devers, Boston found itself in the mix for third baseman Alex Bregman, whose free agency had lingered to the cusp of spring training.

When the prospect of Bregman going to Boston surfaced, Breslow assured Devers’ camp that nothing serious was afoot — and that if it were, he would let Devers know. Cora wanted to meet with Devers in the Dominican Republic during the offseason, but Devers did not respond to messages, which was not entirely surprising — he typically goes off the grid upon his winter retreat to Samana — but disappointed some in the organization. Though the Red Sox were simultaneously pursuing Bregman and St. Louis Cardinals third baseman Nolan Arenado, there wasn’t enough confidence in a deal being consummated with either to flag Devers.

Then Boston made its final offer to Bregman as negotiations with other teams wound down: three years, $120 million, with opt-outs after the first two seasons. Within an hour, Bregman accepted. Devers found out when the news broke. He was not panicked — Red Sox officials said privately they planned on using Bregman at second base — but the move registered as curious nevertheless.

When Devers showed up at spring training, the team broached the idea of him shifting to designated hitter. Their computer model said the best version of the 2025 Red Sox would feature reigning Minor League Player of the Year Kristian Campbell at second base, Bregman at third and Devers at DH. Devers was livid. A player’s position is part of his identity. He was a third baseman. Beyond that, though, was a breach in the trust implicit in a contract of Devers’ magnitude.

At the very least, if the Red Sox were intent on him moving positions, he wanted to ease into the new role. Play a couple times a week at third base and take the rest of his at-bats as DH. No, he was told. This was what was best for the team.

The front office’s tack reinforced the feeling in the clubhouse that the organization’s reliance on analytics for decision-making had come at the expense of productive interpersonal communication. At the same time, players acknowledged that Devers DHing probably would allow them to field their best lineup. After initially saying he wouldn’t DH, Devers wound up relenting. After Cora told him to not even bother bringing a glove to the spring training fields, he was comfortable that at least he could focus only on hitting.

Everything changed on May 2. First baseman Triston Casas suffered a season-ending knee injury. The internal options were limited. Breslow approached Devers about moving to first. Devers couldn’t believe it. He had already changed positions against his will once. Now the Red Sox were asking him to do it again. The disrespect galled him.

The team didn’t believe the ask was too much. They hadn’t asked him to be a clubhouse leader, a role for which he wasn’t particularly well-suited. They didn’t belabor his fitness or weakness in the field. This is what the money was for: to play where the team needed him to play and keep raking like one of the best hitters in the world.

He was holding up the latter part of that ask. Amid all of the consternation, Devers was evolving into perhaps the best version of himself yet. In the 73 games he played with Boston this season, he walked 56 times — just 11 short of his career best. He was still hitting for power and neared the top of the big league leaderboard for runs batted in. For a team trying to integrate Campbell as well as rookies Roman Anthony and Marcelo Mayer, Devers was a rock in the No. 2 hole. Teams in transitional phases like the Red Sox need players on whom they can rely, and Devers’ bat was nothing if not reliable.

His refusal to play first, though, coalesced ownership, the front office and the coaching staff. If they were going to build the sort of winning culture that permeated the organization throughout the 2000s and 2010s, what sort of message did it send that the team’s best player refused to do what they felt was best for the team? After Devers told the media he would not play first, Henry, Red Sox CEO Sam Kennedy and Breslow flew to Kansas City, where Boston was playing, to speak with Devers. He met again with Henry for breakfast the next day, according to a source. Devers indicated he would prepare to play the position in 2026 if the team wanted to move him there full-time. While publicly the Red Sox deemed the meetings productive, they knew what was happening next.

Rafael Devers was getting traded, public consequences be damned.

EARLY IN BRESLOW’S tenure as chief baseball officer, he hired a consulting firm called Sportsology Group to assess Boston’s baseball operations department. The wide-ranging evaluation was something out of “Office Space,” an attempt to cut the fat accumulated while Boston cycled through heads of baseball ops. Ben Cherington took over from Epstein in 2011 and won a World Series in 2013. Two years later, the Red Sox hired Dave Dombrowski over him. Ten months after Dombrowski won a World Series, he was fired and replaced by Bloom, who lasted four years.

Any objective assessment would note that perhaps the problems originated with organizational instability — that the Red Sox had grown bloated, in part at least, because they so often made changes. Regardless of how it came to be, the recommendations included the elimination of jobs across multiple departments. Around 50 people were fired last year, sources said. The professional scouting department was gutted. Some of the positions wound up being filled, but it was clear to those who stayed and went: This was Breslow’s team, and now he would remake it in his own image.

Since the cuts, Breslow’s circle of trust has been small and his reliance on the team’s analytical model heavy, according to sources, leaving some longtime employees embittered. Breslow loyalists fear the consequences of that, with one saying: “There are definitely turncoats internally plotting against Bres.”

The Devers trade only heightened the palace intrigue. Front office officials from other teams mostly lauded the deal for Boston, looking at San Francisco’s willingness to take on the remaining $254 million over the next eight-plus seasons as a win for the Red Sox. But models exist to strip the emotion out of decision-making and use decades of history — and dozens of other inputs about players’ skills gleaned from the cameras that track their every move — to objectively analyze. There is no accounting for a fan base’s adoration of a player.

“Boston absolutely botched this entire Devers situation,” one rival official said, “and somehow it all resulted in them getting to dump what was both an underwater contract and a distraction while also getting a bunch of value back in return.

“It was like, ‘Oops, we overpaid for a decade of our bat-only star, pissed him off publicly, then continued to bungle every subsequent opportunity to get things right. Why don’t you give us a controllable midrotation starter and your first-round pick from last year and help us get out of it?’ “

At the same time, a rival general manager said, “These are the Boston f—ing Red Sox. You don’t trade your stars.”

It’s a fair point. The Red Sox’s competitive-balance-tax payroll topped out in 2019 at $243.7 million. Each of the past two years, they ran a CBT payroll that ranked 12th in the big leagues. The Devers trade puts them comfortably under the CBT threshold. Perhaps they reallocate the money at the trade deadline. Perhaps they don’t.

That the reinvestment is even a question is what really gnaws at Boston fans: They see with abundant clarity that the Red Sox did not learn their lesson from the failed Betts trade. In a market like Boston, financial flexibility is a red herring, playing for the future a false prophet. When the Los Angeles Dodgers and New York Mets and New York Yankees and, yes, even the San Francisco Giants balance today and tomorrow, it has to be about now and the future. The plight of the large-market team in an uncapped sport is that it has zero excuses not to act like one.

Breslow’s investment in his process is wholesale; he believes, regardless of the opinion of outsiders or adversaries within, that he is the right person with the right plan to turn the Red Sox into champions again. He knows that the return for a player with more than a quarter-billion dollars owed will not add up to the quality of the player independent his contract — that the savings are regarded an asset every bit as important as Harrison or Tibbs.

The Miami Marlins made the same compromise when they shipped Giancarlo Stanton and the remaining $290 million on his deal to the Yankees for a pittance of talent — but what Breslow doesn’t understand is that this scenario likens one of the proud franchises in baseball to a bottom-feeder. An organization with Boston’s financial might should be the one acquiring superstars others can’t afford, and waving away that advantage is the truest waste of all, one that opens up the organization to criticism that no amount of championships over the past quarter-century can rid.

That’s why the Devers deal has unleashed such a poisonous recourse. With Boston fans frothing to consume any nugget that reinforces their belief in Breslow’s incompetence, the discussion around the Devers deal has devolved into falsehoods taking root. There are small ones, like Devers being mad at Campbell for volunteering to play first base — he wasn’t mad, multiple sources said — and bigger ones like the report claiming that a person who interviewed with the Red Sox for a baseball operations job went through five rounds of AI-only questions.

The team was concerned enough to release a statement Wednesday night shooting down the report, and three sources familiar with the team’s hiring practices said they use a company called HireVue, which uses AI to ask questions and record video, to screen prospective employees early in the hiring process. Other organizations around baseball use the same software.

Even so, the acknowledgment that it could be true speaks to the state of the Red Sox. The day after the trade, when Breslow and Kennedy held media availability, they acknowledged the flaws in their process — particularly Breslow needing to better communicate with players.

The handling of Devers was an easily avoidable mistake that devolved into a franchise-altering decision. Knowing your personnel is paramount, and whether it’s an unwillingness to meet Betts where he was or dealing Chris Sale to Atlanta only to see him win the National League Cy Young Award last year or moving Devers because of what comes down to a lack of communication, it screams for a self-audit.

Earlier this year, Carl Moesche, a Red Sox area scout in the Pacific Northwest, was logging off a Zoom and said, “Thanks, Bres, you f—ing stiff.” The comment was heard by those in the virtual room. Moesche was fired. His words were catnip to those aggrieved by the Devers trade. And if a low-level employee’s gripe can turn into a rallying cry for paying customers, it might be time for an attempt to eliminate chaos from the franchise’s playbook.

RAFAEL DEVERS IS going to play first base for the San Francisco Giants. Maybe not this weekend, when the Red Sox come to town, but it will happen soon. And as much as those in the anti-Devers camp point to the double standard, one person close to him said there’s another takeaway to glean.

“Sometimes it’s not the message,” he said. “It’s how the message is delivered.”

The message from the Giants was clear: We’re thrilled you’re here, and we see the importance of transparency. Buster Posey, the future Hall of Famer who took over Giants baseball operations over the winter, and manager Bob Melvin walked Devers through the state of the franchise. With Gold Glove third baseman Matt Chapman signed for six more years, the Giants see Devers as a first baseman and DH. San Francisco’s best prospect, Bryce Eldridge — whom the Red Sox initially targeted in discussions with the Giants before recognizing that the Giants would not budge from their position that he would not be in any Devers deal — plays first and is expected to debut in the major leagues this season. When that time comes, Devers will know.

Which is all he really wanted in the first place. The original sin of opacity spiraled into a mess of the Red Sox’s own making. Devers didn’t exactly acquit himself well, but the onus is on the franchise to create an environment in which players gravitate toward selflessness. Breslow and Kennedy said the lack of “alignment” between the organization and Devers — they used the word a combined 14 times in Wednesday’s news conference — left them with no choice but to trade him. They spoke of building a championship culture. But no player determines that culture single-handedly: It starts with ownership, filters down through management and manifests itself through players bought into ideals and values.

There is no clearer reminder than Devers’ willingness to play first base in San Francisco. The Giants did not care that Devers’ deal might not age well. After being spurned by Aaron Judge and Shohei Ohtani in free agency, they needed a middle-of-the-order bat to win now and gladly went underwater to capture it. Modern organizations are not defined by their models as much as their risk-reward matrices.

Assessing the trade on returns in 2025 alone is short-sighted, although it illustrates the push and pull between now and future. The Red Sox’s future remains bright, and in other regards they’ve made savvy decisions. In Crochet, they targeted a front-line starter, gave up tremendous prospect value and signed him to an over-market extension. In Carlos Narváez, Breslow acquired the Red Sox’s catcher of the present and future — from the Yankees no less — for Elmer Rodriguez-Cruz, a soon-to-be-22-year-old right-hander in High-A. While the eight-year, $60 million contract for Campbell has not paid dividends — he was optioned to Triple-A on Thursday after struggling for the past six weeks — evaluators remain bullish that he’ll mature into a middle-of-the-order force.

Until then, though, his demotion just adds a layer to the Devers story. If not for Boston’s belief in Campbell’s ability to succeed at the big league level in 2025, Bregman could have manned second base, Devers third — and he would still be wearing a Red Sox uniform instead of chatting up Barry Bonds behind the Giants’ batting cage. That image stuck in the craw of those pained by the trade. If Devers is going to talk shop with a legend, it should be David Ortiz.

But it isn’t. Ortiz lamented the trade — and Devers’ role in it — as much because Devers could have been, should have been, just like him: a Red Sox hero. Instead, he is a San Francisco Giant, ready to stand in against his former teammates, waggle his bat and do what too many have had to: find his peace somewhere other than Boston.

Pitching is about keeping hitters guessing — and about walking the line between overusing certain pitches to the point of predictability and underusing others that have quietly confounded opponents in limited doses. Now more than ever, each MLB pitcher’s repertoire is scientifically calibrated, from the shape of the ball’s arc as it approaches the plate to the spin it carries and how it looks coming out of the hand. Modern pitchers take their pitch selection as seriously as a Michelin chef planning a gourmet menu.

But even with all of that sophistication, there are inefficiencies in how pitchers deploy their stuff. Many years ago, I dove into the game theory behind pitch selection, and specifically which pitchers were throwing their different pitch types in an optimal way versus those who could stand to tweak their pitch mix a bit to achieve better results.

The thought process went like this: We know from Statcast data how frequently each pitcher throws each type of pitch, and thanks to websites such as FanGraphs, we also know how effective each pitcher’s pitches have been at preventing runs. (We now even know how good each pitch should be based on its characteristics, such as velocity, movement, spin and other factors.)

From this data, we can then find cases where there are mismatches between a pitcher’s most effective pitches and the ones he uses the most.

Of course, not every pitch can be scaled up without diminishing returns. But in general, pitchers who lean more heavily on their best pitches are likely getting more out of their repertoire than those who don’t.

I then developed what I call the Nash Score for pitchers (so named for the Nash equilibrium of Game Theory, which describes a state in which any change in strategy from the current balance would result in less optimal results). Nash Scores work by comparing the runs a pitcher saves with each pitch in his arsenal to the average runs saved by all of his other pitches combined.

Pitchers with low (good) Nash Scores have achieved a close balance in effectiveness between their most-used pitches and the rest of their repertoire, which implies that any change in pitch mix would make them less effective overall. Meanwhile, pitchers who have high (bad) Nash Scores are either using ineffective pitches too much or not using their best pitches enough, suggesting that a reallocation might be needed.

Now is a good time to update Nash Scores for the current era of MLB pitchers.

Let’s highlight the top-15 qualified starters and relievers who have achieved the greatest balance according to their Nash Scores over the past three seasons (with recent years weighted more), as well as the 15 who might be leaving performance on the table.

But first, here is a chart showing all qualified MLB pitchers — using a three-year weighted pitch count — with their Nash Scores plotted against their Wins Above Replacement:

Explore the full, interactive chart.

Now, let’s get to the rankings, starting with the most balanced starters in our sample:

Irvin, Crochet among most optimized starters

Note: Listed rates for pitch types are usage share over the past three seasons and run values per 100 pitches for that pitch, relative to the average for the rest of their pitches combined.

The award for the league’s most balanced starter belongs to perhaps an unlikely name: Washington Nationals righty Jake Irvin. Irvin has been an average pitcher at best in his three MLB seasons, with an ERA of 107 (100 is average and lower is better) and a FIP (Fielding Independent Pitching) of 114, and he has never even had 2 WAR in a season yet. But in terms of maximizing his repertoire, the case can be made that no pitcher is getting more out of what he has to work with.

Over the past three seasons (again, with more weight on more recent data), Irvin has almost exclusively used three pitches: four-seam fastball, curve and sinker. Each was within 0.2 runs per 100 pitches of the average of his other offerings, meaning he found the mix where basically all of his pitches are equally effective — the whole point of this entire exercise.

Now, Irvin has drifted a bit away from equilibrium in 2025, using more of his curve (and less of his fastballs) despite them being more effective, so it’s worth keeping an eye on whether he continues to optimize his Nash Score. (Especially since his best-shaped pitch is actually his slider, which he almost never uses!)

Among the rest of the top 15, several other pitchers showed a knack for maximizing their stuff. Garrett Crochet — the nasty left-hander who broke out last year and was dealt from the Chicago White Sox to the Boston Red Sox — pairs an elite fastball with an even more dominant cutter (plus a bit of a sinker-slider), giving him one of the game’s best (and most equalized) pitch mixes.

Fellow Red Sox hurler Kutter Crawford follows the same template, with similarly effective four-seamers and cutters making the bulk of his repertoire. Others strike the balance differently: Jesus Luzardo and Freddy Peralta use more off-speed stuff, while Ryan Pepiot and Corbin Burnes rely on strong fastballs as their primary pitches — but only use them about half the time. And then there are guys such as Taj Bradley and Taijuan Walker, who lead with shaky main pitches, but throw them so infrequently that the rest of their pitches help equalize the overall mix.

It’s also no surprise to see Tarik Skubal, arguably the best pitcher in baseball, grace a list of hurlers who pick from their arsenals in the most efficient way. What everyone on the list has in common is a pitch selection largely in equilibrium, where effectiveness and usage are closely aligned.

Sewald, Poche among most optimized relievers

You’ll likely notice that the top relievers tend to be more optimized (with lower Nash Scores) than the top starters, which is probably an artifact of a few factors: First, relievers usually throw just a couple of pitch types, so it’s inherently easier to align usage with effectiveness when there’s less to balance. Second, those pitches are often thrown in short bursts at maximum intensity, which allows pitchers to rely more heavily on their strengths without diminishing returns. And finally, relievers don’t need to navigate a lineup multiple times, so they can lean on their best pitches more without the same concerns about stamina or predictability that starters face.

That said, some relievers do a better job of balancing than others. Though he has been nursing an injured shoulder since April, Cleveland’s Paul Sewald had been the best over the past few seasons — the two pitches he used 99.7% of the time, a four-seamer and a slider, were both within five hundredths of a run of each other in terms of effectiveness per 100 pitches. The batter knows one is likely coming… but they’re both equally tough to hit.

This was a very common theme among the top relievers, too: Each of the next four names on the list (Colin Poche, Tanner Scott, Joe Jimenez and Alexis Díaz), and eight of the top 11, used a version of that same pitch mix, with fastballs and sliders of near-equal effectiveness making up the vast majority of their pitches. Hey, if it works, it works.

But those who bucked the trend are also interesting. Philadelphia’s Orion Kerkering, for instance, flipped the tendency and relied mostly on a slider with the four-seamer as a change-of-pace pitch. Milwaukee’s Elvis Peguero was exactly 50-50 on sliders and sinkers (though both abandoned him earlier this season, and he has bounced between MLB and AAA), while Nats closer Kyle Finnegan introduces a splitter into the equation — and there’s longtime veteran closer Craig Kimbrel with his knuckle-curve (though it hurt his Nash Score).

Not all of these relievers have been lights-out, but many were, serving as great examples of how to stay effective even when hitters have a good guess at what’s coming.

Blanco, Kelly among least optimized starters

Now we get into some truly fascinating cases, where it’s important to remember that you can still be a great pitcher while still having a deeply strange, and seemingly suboptimal, mix of pitches.

There seem to be a few ways to land on this list: First, and most straightforwardly, you could have a far less effective No. 1 pitch than the rest of your arsenal, meaning you might stand to throw it less and the others more. Both of the top two above, Houston’s Ronel Blanco and Arizona’s Merrill Kelly, have primary four-seamers that are at least 1.5 runs worse per 100 pitches than their other options, and secondary off-speed pitches that are at least 2.4 runs better than the rest — classic cases where the Nash Score would suggest bringing them closer to balanced until the difference begins to flatten out.

Then there are cases such as Joe Ryan, Michael Wacha, Dylan Cease, Chris Sale and Michael King, in which their No. 1 option is clearly the best, but they throw other, much less effective pitches nearly as much, reducing the advantage of a dominant primary pitch. Spamming the top choice might lead to diminishing returns, but there’s room to give there before it starts being a suboptimal strategy.

And finally, we have the odd case of Paul Skenes — and Gavin Williams too, but Skenes is more fun to dissect — in which somehow the primary four-seamer is less effective than the other pitches, and so is the secondary breaking pitch, suggesting the need to dig deeper into the bag more often. But how can you argue that Skenes isn’t doing the most he can? He literally leads all pitchers in WAR. The thought he could optimize his stuff even more is terrifying.

Kahnle, Bender among least optimized relievers

Finally, we get to the less optimal end of the reliever spectrum. And as stable as the opposite side was, with a bunch of guys using their boring fastball-slider combos to carefully record outs, this one contains more varied pitch mixes. Well-represented, for instance, is the phenomenon I found with R.A. Dickey the first time around — that despite his knuckleball being both his best pitch and the one he used most often, the Nash Score implied he should throw it even more because it was much more effective than the rest of his offerings.

While we don’t have any knucklers in the bunch this time, we do have guys such as Detroit Tigers setup man Tommy Kahnle, whose lead pitch is a changeup (not a fastball) so effective that it’s nearly four runs per 100 pitches better than the rest of his repertoire. Pitchers who work backwards like this must mix in fastballs to keep hitters honest — but at the same time, the fastballs are much less valuable that using them slightly less might be good even if it makes the change less effective. (Anthony Bender, Brenan Hanifee, Steven Okert, David Robertson, Greg Weissert and Cade Smith were in this category as well, among others.)

Just as odd were the cases of Ryan Helsley, Justin Lawrence and John Brebbia, whose primary pitches were far less effective than their secondary options, despite each essentially having only two pitches to work with. The numbers might be asking for those hierarchies to be flipped around.

And finally, there are guys such as Kenley Jansen, who spam one solid pitch — but they don’t have much else to work with, so any deviation worsens performance, even if the Nash Score still dings them for imbalance.

In the end, no metric — not even one rooted in Game Theory — can capture the full complexity of pitching. But Nash Scores do give us a window into something that’s often hard to pin down: How much a pitcher gets out of what they’re working with, and whether they’re winning the rock-paper-scissors aspect of the batter-pitcher showdown.

Some get the most out of average stuff through smarter allocation. Others leave value on the table despite electric arsenals. In either case, the path to better performance might be as simple (or difficult) as throwing the right pitch at the right moment just a little more often.