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In an interview with Adrian Wojnarowski of Yahoo, Morey criticized Cuban at length and hit back at Cuban's claim that the Rockets don't value chemistry.
He said that if Cuban cared about chemistry, he wouldn't have dismantled the team that won the 2011 NBA championship.
From Yahoo:
"Hey, if Mark believed so much in chemistry, he wouldn't have busted up a title team for cap room. He's trying to reunite a lot of those people now, bringing back the center [Tyson Chandler] from that title team. Maybe he's got some chemistry religion recently.
"He's tripled his analytics staff. If he's equating analytics with not caring about chemistry, well, he's tripling down on it ... We don't care about chemistry, but he busted up a championship team for what he hoped cap room could do."
He added this parting shot: "But let's be clear: If the money's equal between the Rockets and Mavericks, I think players are picking Houston. Every time."
Morey is widely regarded as one the NBA's smartest decision-makers. He's a pioneer in the league's move toward analytics. The James Harden trade that turned Houston into a contender was one of the most lopsided trades in recent league history, and it was all Morey's work. He has done a genius job of construction a top-eight team out of thin air.
But it looks like Cuban - one of the league's great instigators and entertainers - has gotten under his skin here.
This whole thing all started when Morey texted Cuban and asked if he would trade Dirk Nowitzki in the summer of 2013. Cuban was taken aback. He initially thought Morey was doing it to taunt him, he later told a Dallas radio station, before concluding that the inquiry was the result of Morey not understanding the importance of team chemistry.
"It says a lot about their approach more than anything else. They just have a different understanding and approach to chemistry than we do. Some teams, and that's not just the Rockets, just put together talent and the talent takes care of itself," he said.
In an earlier interview with ESPN, Cuban said the Rockets would benefit from a rivalry with the Mavs because they could use help selling tickets.
The rivalry went up a notch earlier this summer when the Mavericks made a monster $46 million offer to Rockets free agent Chandler Parsons. Morey had the right to match the offer and keep Parsons in Houston, but it would have crippled the team's salary cap situation going forward and made it impossible for them to sign a max-level free agent in the future. Morey called the deal Cuban gave Parsons "one of the most untradeable" NBA contracts he has ever seen.
To add insult to injury, Parsons signed the contract in an Orlando nightclub with Cuban at his side.
It has been a frustrating offseason for Morey. He tried to sign Carmelo Anthony and LeBron James this summer and failed. His back-up plan - signing Chris Bosh in the event that LeBron left Miami - fell through as well. And in the he most unexpected of all, he lost Parsons to a rival team.
Cuban gleefully taking shots at Morey is no surprise. Morey responding so forcefully is, and it shows just how effective Cuban's tactics have been over the last year.