On Sunday in Seattle, for the fourth year in a row — enough for a full class of college prospects — Major League Baseball will hold a streamlined version of its amateur draft. From an event with unlimited rounds to one with 50 rounds, then 40, and now just 20, the draft is exclusive and efficient, in keeping with baseball’s restructured minor league system.

But efficiency has a cost: the countless long-shot careers that may never be realized. Dozens of current major leaguers turned pro after being drafted in rounds that no longer exist. They are grateful for their timing.

“Twenty rounds doesn’t seem like quite enough,” said Kevin Kiermaier, the center fielder of the Toronto Blue Jays who was picked in the 31st round by the Tampa Bay Rays in 2010. “I mean, if it was like that now, then I would have never had an opportunity.”

Kiermaier, 33, is perhaps the best modern example of the talent that once bubbled far below the surface of the draft. Chosen 941st overall from a community college in Illinois, he has won three Gold Gloves, played in the World Series and earned more than $60 million in an 11-year career.

Four players who made the All-Star team last summer — David Bednar, Nestor Cortes, Ty France and Joe Mantiply — were also chosen after the 20th round. So were two members of the Houston Astros’ World Series-clinching lineup last fall (Chas McCormick and Martín Maldonado) and several other longtime major leaguers, like Jesse Chavez, Seth Lugo, Kevin Pillar and Rowdy Tellez.

Two Hall of Famers (Mike Piazza and John Smoltz) were drafted in extinct rounds, as were several others with a case for Cooperstown, like Mark Buehrle, Keith Hernandez, Andy Pettitte and Jorge Posada. Many low-drafted players could have stayed amateurs and tried to improve their draft position the next year — but their careers, of course, would have then unfolded differently.

“Cutting the numbers down, you’re going to have to create other opportunities for those kinds of players that would have been drafted to come into the game,” said Omar Minaya, a former general manager and longtime scout who now advises the Yankees. “Players do develop late sometimes, so it’s good that M.L.B. is doing things to put those infrastructures in place.”

Starting with the 2021 season, teams have been limited to 180 players under club control — there was no limit before — and four domestic farm teams, plus one or two “complex teams” that operate from the spring training base. Short-season Class A teams were eliminated, partly because of the calendar; in 2021, the league shifted the date of the draft from June to July, to coincide with the All-Star Game and raise its profile.

Some teams that were cut are now part of M.L.B.’s predraft league, created for scouts to get one last look at prospects before making their picks. Other teams have joined so-called partner leagues — the American Association, the Atlantic League, the Frontier League and the Pioneer League — partially funded by M.L.B. but independent of any specific franchise.

Undrafted players, in theory, can join one of those teams in hopes of attracting interest from M.L.B. But removing them from the draft acknowledges the staggering odds against them.

“When a player signs a professional contract, you want that player to have some chance of one day becoming a major league player,” said Morgan Sword, M.L.B.’s executive vice president for baseball operations. “That’s why players become minor league players, because they want to one day become major league players. And we did have a lot of players in the system who had — what’s the right way to say it? — almost no chance of ever reaching the major leagues.”

Then again, to paraphrase Jim Carrey in “Dumb and Dumber,” there is a huge difference between almost no chance and no chance. A draft selection — whatever the round — certifies that a major league franchise sees something in a player, and often that is all the player wants.

“It was definitely nice to know that they picked me for a reason, and I could get to go show it off and play my game,” said Zach McKinstry, the Detroit Tigers’ regular leadoff hitter, who was drafted by the Los Angeles Dodgers in the 33rd round in 2016. “I got an opportunity right when I signed. I spent three days in Arizona and then they sent me to low A and I played on a championship team that year.”

McKinstry, who played at Central Michigan University, was a backup before a teammate’s injury gave him a chance to elbow his way to the Dodgers. He was keenly aware that most minor leaguers — especially when the draft lasted 40 rounds or more — were needed only so the better prospects had somewhere to play.

“There’s a lot of injustice in the game, real or imagined, so there would be a lot of negative thoughts in those scrums in the outfield during batting practice,” said Bob Scanlan, a San Diego Padres broadcaster who pitched nine seasons in the majors after signing as a 25th-round pick in 1984. “There was a lot of talk like: ‘You know you don’t mean anything to this organization. You’re just here as a filler piece. Why are you even working your tail off?’”

Scanlan was 17 when he signed with Philadelphia, turning down U.C.L.A. for the allure of the quality coaching he would get in pro ball. In recent decades, though, college programs have become more sophisticated, with advanced facilities and instruction that offered an appealing alternative to the dusty outposts that once made up the low minors.

“The development time is less and less with the caps on the total number of players, so the guys you would pick late are probably going to go to college,” said Matt Arnold, the Milwaukee Brewers’ general manager. “Signing and then going to Helena, or wherever, is going to be less appealing than a really nice A.C.C. or SEC school — and even those second-tier programs have a lot of things they can sell.”

Sword said the costs of improvements across the minor leagues — in ballparks, travel, nutrition and salaries — far outweigh the savings from eliminating so many draft picks; “it’s probably nine figures per year leaguewide,” he said. Sword added that in 2021, more than 200 players jumped from partner leagues to the affiliated minors.

“The paths for those types of guys to the big leagues exist just as they always have,” he said. “It’s just that the path is different than it once was.”

Even so, it stands to reason that with half as many draft picks as there were just four years ago, hundreds more players from each class are now giving up their baseball dreams for more realistic careers. Arnold, who grew up in Bakersfield, Calif., rooting for a since-departed Class A team, wonders about the impact of losing so many acolytes for the sport.

“A lot of those guys, even if you were a 35th rounder from the middle of nowhere, you go home and you start an academy, and now you’re a hero,” Arnold said. “You’re a guy that played pro ball, and you bring it back home. And maybe he wasn’t great, but he carries the game with him as a steward in a way that I think we’ll miss.”

The guys who make it, perhaps, will have to preach a little louder. Kiermaier, for one, embraces the role.

“I look back at how everything evolved for me, and I’m so thankful for my journey,” he said. “I’ll never forget that I was a 31st rounder. I’m proud of that. That number means a lot to me.”