Valkyries head coach Natalie Nakase watches her team during training camp in the Sephora Performance Center in Oakland on Tuesday.

Valkyries head coach Natalie Nakase watches her team during training camp in the Sephora Performance Center in Oakland on Tuesday.

Yalonda M. James/S.F. ChronicleValkyries owner Joe Lacob cheers a 3-point basket by Iliana Rupert in the second half against the Indiana Fever at Chase Center on Aug. 31.

Valkyries owner Joe Lacob cheers a 3-point basket by Iliana Rupert in the second half against the Indiana Fever at Chase Center on Aug. 31.

Carlos Avila Gonzalez/S.F. ChronicleValkyries guard Veronica Burton, left, and forward Gabby Williams answer questions during media day Tuesday at training camp in Oakland.

Valkyries guard Veronica Burton, left, and forward Gabby Williams answer questions during media day Tuesday at training camp in Oakland.

Yalonda M. James/S.F. ChronicleValkyries guard Veronica Burton, voted last season’s most improved WNBA player, practices Tuesday during training camp in Oakland.

Valkyries guard Veronica Burton, voted last season’s most improved WNBA player, practices Tuesday during training camp in Oakland.

Yalonda M. James/S.F. Chronicle

While the rest of the world was amazed by the way the Golden State Valkyries’ debut season ended — with a historic berth in the playoffs — the Valkyries themselves were frustrated.

“We didn’t win,” said head coach Natalie Nakase. “For us, that was a disappointment.

“Now we’re even more hungry because we got a little taste in the playoffs.”

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The Valkyries want more than a little taste. They have higher expectations. And in that regard, as Season 2 gets underway, the Valkyries’ perspective and that of the rest of the world are aligned.

Expectations, internally and externally, are sky high. Everyone will be watching to see what the Valkyries, who went 23-21 and lost a first-round playoff series to the Minnesota Lynx, will do for an encore. Two new expansion teams, in Portland and Toronto, will be trying to reach the bar that the Valkyries set. The team’s valuation continues to jump, now to a reported $850 million. Violet-clad fans are everywhere.

Valkyries general manager Ohemaa Nyanin explained the thinking behind a draft-day trade with the Seattle Storm.Valkyries forward Gabby Williams high-fives head coach Natalie Nakase before a preseason game against the Seattle Storm on April 25 at Chase Center.

And, internally, the clock is ticking on owner Joe Lacob’s expectation of a championship by the end of 2029. 

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“Joe Lacob sets the standard high, and I love high standards,” Nakase said. “I want to win. I love the fact that he challenges me, gives me a timeline, and only talks banners and rings.”

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That desire to win is what ultimately made free agent Gabby Williams decide on the Valkyries. She was speaking to several teams when she got a call from Lacob.

“My conversation with him versus any other team owner was completely different,” she said. “That’s what really got me over the edge to sign. He was speaking on his goals and objectives for the franchise, how badly he wants to win, how he’s going to do it, and that I would be stupid to go anywhere else.

“He was like, ‘I don’t see anyone doing it better than us.’ And I want to be part of something like that. I want to be with a team that you always see in the playoffs, in the Finals. And I truly believe this can be that team.”

Building on the culture, continuity and momentum that the Valkyries initiated last season is the goal in this second year. That was the driver behind the decisions made in free agency and the collegiate draft. General manager Ohemaa Nyanin cloaked her draft night maneuverings in mystery, when she drafted LSU’s Flau’jae Johnson at No. 8 and promptly traded her to Seattle for the No. 16 pick with little explanation. That No. 16 pick, Marta Suarez, was released in roster cuts, and on Wednesday it was reported Suarez would sign a developmental contract with the Phoenix Mercury. 

In the aftermath of those moves, the message seems clear that the Valkyries have a kind of player they want, a continuity they seek, and an intentional immediacy to all their player decisions. 

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“The timeline is front and center,” Nyanin said. While it seems there’s a bent for older players, Nyanin said that it isn’t necessarily age but the ability to fit into Nakase’s system and the connectivity between all players that are priorities. 

The Valkyries’ final roster, released Thursday morning, created additional questions. They waived fan favorite Kate Martin, who had been nursing a Grade 2 quad strain. The team included center Iliana Rupert on the roster, but announced that Rupert is pregnant and the Valkyries are filing for a replacement contract for Rupert, awaiting league approval. They only included one developmental player on the roster, Miela Sowah, leading to speculation that Martin may get the additional developmental slot, assuming she passes through waivers. But that’s a big assumption. 

Because of injuries to key players last season, Nakase feels no one got to see what the Valkyries could truly do in the postseason. Now the team is trying to pick up where it left off. Guard Tiffany Hayes — one of those injured at the end of the season — said there’s been “a smoothness” to training camp.

“From last year to this year, all of us kind of knowing the sets, knowing how each other moves, knowing each other’s tendencies, that could give us the upper hand on a lot of things,” Hayes said. “Coach said that we’re ahead of the curve.”

Even the key newcomers have connectivity with their teammates. Williams has played on the French national team with Janelle Salaün and Rupert. Center Kiah Stokes played for Nakase in Las Vegas and with Martin. 

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Nakase said the fit between all 14 teammates — the 12 on the final roster and the two developmental spots — is an all-important factor.

“How do they treat each other off the court? Are they hanging out outside of practice?” she said. “All those things matter. … It’s like having a long relationship. Six months that they’re going to be together. So how they move together is really important. You know if you’ve ever been in a bad relationship that’s tough. So (we want) a really healthy relationship.

“It’s got to be the fit that we’re looking for.”

Veronica Burton believes the culture that the Valkyries have built and plan to continue is directly connected to how they play on the court.

“I think it’s underestimated how much of an impact that has on winning,” Burton said. “When you play selflessly, when you play for each other, when you’re willing to play on both sides of the basketball. 

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“At the end of the day, I do think the character and the culture will come through on the court. It gets shown when we compete.”

After being with the team a little more than a week, Williams said she wasn’t surprised to learn that the Valkyries were disappointed by the way their first season ended, despite the history they made.

“Everyone here is here to win,” Williams said. “Being here and seeing how the organization is run, I definitely see why there are high expectations. I see why they accomplished so much in such a short amount of time.

“I only see it going up from here.”

Last season there were no expectations for the Valkyries. This season, there are some very weighty ones, both externally and internally.