The Heat’s Secret Weapon? Players Who Were Snubbed on Draft Night.

BOSTON — Max Strus had spent two seasons punishing defenders as a shooting guard at Lewis University, a Division II school in Romeoville, Ill., before he delivered some news to his coach that was not entirely unexpected: He wanted to transfer to a major Division I program.

For the coach, Scott Trost, it was bittersweet. He was sad to see Strus go, but he also knew that Strus was ready for his next challenge.

“And who’s to say if he would be where he is today if he didn’t make that move?” Trost said.

On Wednesday night, seven years after he transferred to DePaul and nearly four years after he matriculated to the N.B.A. G League as an undrafted free agent, Strus was sinking 3-pointers and making defensive stops for the Miami Heat in their 123-116 victory over the Celtics in Game 1 of the Eastern Conference finals.

But perhaps the oddest part about his unlikely presence was that it was not odd at all — at least not for the Heat, who have a league-high nine undrafted players on their 17-man roster. On Wednesday, three of those players — Strus, Gabe Vincent and Caleb Martin — scored 15 points each while combining to shoot 16 of 27 from the field.

“I think it’s something unique that we’ve all gone through,” said Vincent, the team’s starting point guard, “and we know how difficult it can be. So we just try to motivate each other and keep each other going.”

The conference finals have coincided with pre-draft buzz of the highest (and tallest) order. On Tuesday, as N.B.A. hopefuls began to cycle through Chicago for the league’s scouting combine, the San Antonio Spurs landed the No. 1 pick in the draft, set for June 22 at Barclays Center.

Barring a cosmic catastrophe, the Spurs will select Victor Wembanyama, a 7-foot-4 teenager from France and the most celebrated prospect since LeBron James. A gifted player who has size and skill, along with an innate feel for the game — yes, he really did tip-dunk his own 3-point miss earlier this season — Wembanyama could be a transformational force for the Spurs.

But beyond Wembanyama and the rest of this year’s picks, teams have another roster-building option at their disposal: plumbing the pool of the undrafted, a strategy that has proved increasingly viable as basketball continues to expand its global reach and more talent rises to the surface.

“When you’re in that position, you’re willing to do anything,” said Martin, who was an all-conference player at Nevada but went undrafted in 2019. “And I think more teams are starting to appreciate that.”

Consider that 126 undrafted players, representing about a quarter of the league, found their way onto N.B.A. rosters this season. But no team leaned on the overshadowed, the snubbed and the slighted more than the Heat did, with undrafted players scoring a league-high 33.8 percent of the team’s points during the regular season, according to N.B.A. Advanced Stats. The Nets ranked second in that category, with undrafted players accounting for 24 percent of the team’s points.

Heat Coach Erik Spoelstra noted that two of his best players — Bam Adebayo and Tyler Herro, who has been sidelined with a broken hand since the first round — were high first-round picks. Forward Jimmy Butler, who was brilliant on Wednesday, collecting 35 points, 7 assists and 6 steals, joined the team in a sign-and-trade with the Philadelphia 76ers in 2019. But he was a late first-round pick, by Chicago, in 2011. In other words, the Heat like name-brand stars, too.

Some teams, like Oklahoma City and San Antonio, have stockpiled draft picks through trades, but the Heat have not. Instead, Spoelstra said, the team has needed to be creative about how to fill out its roster. Many of Miami’s undrafted players have come up through its G League affiliate, the Sioux Falls Skyforce. Spoelstra said players in the G League or from overseas are often just as talented as some N.B.A. reserves.

“It’s all about timing and fit, and what a player’s fortitude is,” he said, adding: “If you have a big dream and want to be challenged, we feel like this can be the place for a lot of those kinds of guys.”

And if Spoelstra needs any help gauging (or enhancing) that fortitude, he can turn to Udonis Haslem, a power forward who went undrafted in 2002, spent his first professional season in France and joined the Heat the following year. Now 42, Haslem has been with Miami ever since.

“I think organizations are doing a better job of doing their homework and not just assuming, because a guy didn’t get drafted, that he can’t help you win,” Haslem said. “You can’t measure character or discipline or accountability at the draft combine, and a lot of those things sometimes get overlooked.”

Haslem has played sparingly in recent seasons, but he has outsize influence in the locker room, including as the self-appointed dean of the undrafted. Those who are new to the team get a one-on-one conversation with Haslem, who tells them about his three championship rings and about how anything is possible. But they had better be prepared to work, because Haslem will be watching.

“I take it personally when an undrafted guy comes here,” he said. “I want them to be successful because I feel like that’s a piece of my legacy.”

His legacy now includes the likes of Vincent, who tore the anterior cruciate ligament in his left knee as a junior at the University of California, Santa Barbara. He was early in his rehab when Joe Pasternack was hired as the team’s new coach.

“The first call I got,” Pasternack said, “was from Gabe Vincent saying: ‘Coach, tell me what you need me to do. Do you need me to call the players? Set up a team meeting?’ That left an impression.”

Vincent was back in uniform for the start of his senior season. But after averaging just 12.4 points a game, he landed in the G League with the Stockton Kings. A few weeks into Vincent’s first season there, Pasternack had an opening for a full-time assistant and offered him the job. Pasternack believed in Vincent as a player, but he also knew he was grinding away without any guarantees.

“I just saw so many kids in the G League not going anywhere,” Pasternack said. “But I also thought he was such an unbelievable leader that he’d be a great assistant coach.”

Vincent politely declined the offer.

“I was sort of like ‘Joe, what are you talking about?’” Vincent recalled, laughing. “I don’t know why he keeps telling that story, and I’ve told him that: ‘Joe, this does not make you look good!’”

Vincent signed a two-way deal with the Heat during the 2019-20 season and slowly began to work his way into the rotation. He averaged a career-high 9.4 points a game this season. He is due for a significant payday this summer as an unrestricted free agent.

Strus thought he could someday make a living playing basketball in Europe. That was the goal when he was at Lewis University. It was not until his second day on campus after transferring to DePaul that his mind-set changed. Dave Leitao, who was then the team’s coach, told him that he could have a future in the N.B.A.

“It was huge,” Strus said. “I’d never been told that in my life.”

As a first-year pro during the 2019-20 season, Strus was cut by the Celtics and then tore his left A.C.L. in a game with the G League’s Windy City Bulls. He signed a two-way deal with the Heat the following season. On Wednesday, he grabbed the game’s final rebound.

“I’ve taken advantage of every opportunity they’ve given me here,” he said.