“The amount and information that he takes in, in my mind, it’s impossible for me to try to do,” said Zack Godley, a younger Diamondbacks starter. “I can’t fathom trying to think of all those little things when I’m just trying to throw a pitch. What he does is amazing. His thought process on everything is just on a different level than anyone else.”

To get on that level with Greinke in December 2015, the Diamondbacks had to stand out. He had just opted out of his contract with the Dodgers after going 19-3 with 1.66 E.R.A., the best in the majors in 20 years. He was closing in on a deal with the San Francisco Giants before Arizona’s owner, Ken Kendrick, overwhelmed him, eager to lift a team that had just improved by 15 victories, to 79-83.

Greinke has generally been excellent for the Diamondbacks, going 45-25 with a 3.53 E.R.A. Of the 48 pitchers to make at least 80 starts in the last three seasons, Greinke is tied for ninth in ERA+, a metric that adjusts for ballpark factors and rates him as 27 percent better than the league average.

“He’s deserved every dollar,” said Derrick Hall, the Diamondbacks’ chief executive. “He’s been the pitcher we hoped he’d be when we signed him. It’s not his fault we haven’t gone as far as we hoped.”

Hall added: “In no way can we look back with any regret.”

Even so, the Diamondbacks lost their gamble to capitalize on the prime of Paul Goldschmidt, a star first baseman signed to a below-market contract. The team missed the playoffs in Greinke’s first and third seasons — with a wild-card victory and division series loss in between — and Goldschmidt was traded in December to the St. Louis Cardinals.

Other stars from the 2017 playoff team have left via free agency over the last two winters, including starter Patrick Corbin and outfielders J. D. Martinez and A. J. Pollock. The Diamondbacks will have a payroll of roughly $125 million this season — second-highest in their history — but the team is comically top-heavy.

Greinke will make nearly five times the salary of any of his teammates; the next highest-paid Diamondback is outfielder David Peralta, at $7 million. Hall said the Greinke contract had made it harder to afford other premium talent, but the team was still happy to have him.