Call it Bud’s revenge. The coach who didn’t want to be here -- and who wasted no time in upping sticks once the regular season was done -- took a team that played at a .250 pace over its first 40 games and rendered it not-lousy-enough. As of Jan. 8, the Hawks held the NBA’s worst record. Then, for reasons unknowable, they upped their game. They played .333 ball over the final three months. They wound up with the fourth-worst record. What were they thinking?

The team Mike Budenholzer left behind entered the draft lottery with the fourth-best chance to land the No. 1 pick. The Hawks nudged upward Tuesday night, if only just. They’ll pick third, which means the two biggest prizes – the Arizona big man Deandre Ayton and the Slovenian wing Luka Doncic – are apt to be gone.

The team that finished with the league’s worst record – Phoenix, which the Hawks beat 113-112 on March 4 in one of the biggest games of the season-long tankathon – owns the No. 1 pick. From New Year’s Day on, the Suns were 6-36. That’s how you do it.

The catch now is that the player many consider the third-best in this class – Marvin Bagley III of Duke – mightn’t be the guy the Hawks want at No. 3. It’s possible they’ll take Jaren Jackson of Michigan State, who’s not nearly as polished a scorer as Bagley but who projects as a better defender. Of the many big men who’ll go early, Jackson is the furthest from being a real contributor.

Which isn’t to say he’d be a terrible pick. The Hawks have two other selections in the first round, and they’ll probably be seeking a point guard at No. 19. Dennis Schroder, who’d pretty much worked his way out of this organization’s good graces already, might have talked his way out of town earlier Tuesday by suggesting he didn’t want to keep finishing next-to-last in the East. (Note to D.S.: The Hawks actually finished last in the East.)

When you commit to tanking, you can’t be thinking short-term thoughts. Whoever goes No. 3 could wind up being a better player than Ayton, the presumptive No. 1. When last the Hawks picked No. 3, they landed Al Horford, whose NBA career has far outstripped that of Greg Oden’s, that year’s No. 1. (The No. 2 guy, name of Durant, turned out OK, though.)

Sacramento, which lost three fewer games than the Hawks but moved up to No. 2, could pick someone other than Doncic. But the Hawks don’t control the board in the way they might have had Budenholzer not bled 24 wins out of a team that shouldn’t have topped 20. Sometimes having a good coach is a terrible thing.