That didn't happen for either one last season, but that could very well change for both in 2012-13.
With Golden State ranked 13th in the Western Conference and Milwaukee tied for eighth in the East, these teams pulled the trigger on a five-player swap on March 14 that sent Ellis, Ekpe Udoh and Kwame Brown to the Bucks for Bogut and Stephen Jackson, who was dealt to San Antonio a day later for Richard Jefferson.
Coincidentally, Ellis' first game in a Bucks jersey was March 16 in Oakland, where he finished with 18 points, four rebounds and four assists in a 120-98 rout of his former team.
Milwaukee won nine of 13 after Ellis' arrival but faded down the stretch to miss the playoffs for the fifth time in six seasons.
The Warriors, meanwhile, ended up 23-43 and out of the postseason for the 17th time in 18 seasons. Bogut didn't suit up for the Warriors at all in 2011-12 after fracturing his ankle seven weeks before the trade.
The oft-injured center missed 38 games earlier this season - including a 109-102 loss at Milwaukee on Jan. 26 - to strengthen his ankle, and he's been back three since sitting out six with a back injury.
Bogut finished with 11 rebounds and a career high-tying four steals in Friday's 94-88 loss to Houston.
Golden State (35-28) fell to 2-1 on a seven-game homestand and had its lead over the seventh-place Rockets cut to one game.
"We didn't put the pressure on them. We settled. I think that was the difference," said coach Mark Jackson, whose team is three in front of the ninth-place Los Angeles Lakers.
If Bogut is allowed to play back-to-back games, he'll match up with Larry Sanders, who's averaging 9.0 points, 9.1 rebounds and a league-best 3.2 blocks.
The teams' trade also opened the door for Warriors second-year guard Klay Thompson, who has taken over Ellis' spot alongside Stephen Curry. Thompson, a 16.5 ppg scorer this season, has reached 20 or more in a career-best four consecutive games after tallying 22 on Friday.
He scored 19 on Jan. 26, while Curry led all scorers with 26 points.
Ellis and point guard Brandon Jennings had 20 apiece to help Milwaukee (30-29) win for the sixth time in seven meetings with Golden State.
The Bucks, eight games ahead of Toronto for the eighth seed, have been getting big production from their backcourt. Ellis is averaging 25.6 points on 52.6 percent shooting over the last five games, while Jennings is scoring 16.3 per contest with 16.0 assists during a double-double streak that's reached a career-best three games.
Their strong play coincides with the arrival of J.J. Redick from Orlando. Redick averaged 15.4 points in his first five games with his new team - Milwaukee won four of those - before finishing with three in Wednesday's 117-101 loss to the Los Angeles Clippers.
Forward Ersan Ilyasova suffered a left bone bruise in that defeat and is questionable for the second stop on the three-game trip. Ilyasova had 18 points and 12 rebounds in the earlier matchup with Golden State.