It was a night of near-misses for the Miami Heat at the NBA draft lottery in Chicago—four near-misses, to be exact. As assistant general manager Adam Simon sat in the private drawing room before the televised event, he held a list of four-number combinations that could have lifted the Heat into the top four picks. But the ping-pong balls had other plans.

For the No. 1 pick, the Heat were eliminated after just the first ball rose. The No. 2 pick brought the same result after the second ball. The No. 3 pick offered a moment of hope—a re-draw after the Utah Jazz's combination was mistakenly drawn—but again, the Heat were out by the second ball. And with the No. 4 pick, it was déjà vu: eliminated on the first ball.

That left the Heat at No. 13, their original slot, extending a frustrating lottery streak. In 38 seasons and 12 lottery appearances, the franchise has never moved up. It's a sobering stat, but one that shifts the focus to the real work ahead.

Simon and the Heat's scouting staff remain in Chicago for the draft combine, a pivotal week of physicals, measurements, testing, and interviews. Under NBA rules, the Heat must use a first-round pick this year—they can't be without one in consecutive seasons—so the June 23 draft is a must-play hand.

There's reason for optimism. Last year, the Heat found a gem at No. 20 in Illinois guard Kasparas Jakucionis, who delivered a promising rookie season with 52 appearances and 12 starts. If the Heat can replicate that success at No. 13, this lottery disappointment could become a distant memory.

Here are five prospects who could intrigue the Heat at No. 13: