It's time to take a look at the best players in D-backs history who are not in the National Baseball Hall of Fame.

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The rules are the player had to have some real history with the D-backs, and he gets credit for his entire career, not just his time in Arizona. Also, he has to be retired -- so, no Paul Goldschmidt or Zack Greinke.

With that in mind, here’s the Top 5:

1. Curt Schilling
Schilling once again fell short of election via voting by the Baseball Writers' Association of America in 2022, his final year on the ballot. He could eventually be inducted via the Today’s Game Committee, but until that happens, he will top this list for the D-backs. Acquired by then-GM Joe Garagiola Jr. prior to the Trade Deadline in 2000 in what was more of a heist than a trade -- the Phillies received Omar Daal, Nelson Figueroa, Travis Lee and Vicente Padilla in return -- Schilling took his career to another level in Arizona.

Schilling was good, not great, for the D-backs in 2000, but he more than made up for that over the rest of his time. In '01-02, he combined to go 45-13 with a 3.10 ERA and a 148 ERA+. Schilling not only racked up the strikeouts with 609, but he managed to walk just 72 over that span.

The D-backs don’t win the World Series in 2001 without Schilling, who was named co-MVP along with Randy Johnson. He tossed a pair of complete games against the Cardinals in the NL Division Series, allowing one run over 18 innings. He had another complete game in his lone appearance against the Braves in the NL Championship Series, allowing one run, and he compiled a 1.69 ERA in three World Series starts against the Yankees.

2. Luis Gonzalez
Gonzalez will be forever known as “Mr. Diamondback,” and he could just as easily be No. 1 on the list if the criteria only considered time with Arizona.

While Gonzalez will forever be remembered for his base hit off Mariano Rivera that won the 2001 World Series for the D-backs, his impact on the franchise runs even deeper. He and his wife made their home in Arizona even after he retired, and they’ve become known for their work in the community.

The acquisition of Gonzalez from the Tigers in exchange for outfielder Karim Garcia on Dec. 28, 1998, received little attention, but it would go down as one of the best trades in franchise history.

In his first three years with the D-backs, Gonzalez posted OPS+ marks of 138, 130 and 174. His 2001 season was one for the ages, as he hit 57 homers while slashing .325/.429/.688.

Gonzalez’s No. 20 was the first number retired by the D-backs (aside from Jackie Robinson’s 42), and he currently works for the team as special advisor to team president/CEO Derrick Hall. Gonzalez has an office in Chase Field and keeps a busy schedule with team events.

3. Steve Finley
Finley had a remarkable career that often gets overlooked. He won five Gold Gloves for his outstanding defense. He began his career as a speedster -- 44 steals in 1992 -- but as he developed a better feel for the strike zone, he also developed power, slugging 30 or more homers in four seasons. He finished his career with 304 homers and 320 stolen bases.

Signed as a free agent before the 1999 season, Finley won Gold Gloves in his first two years in Arizona and was a big part of the reason they won three division titles -- and a World Series -- from 1999-2002.

In his five full seasons in Arizona, Finley only played in fewer than 150 games once, and he appeared in all 104 games in 2004 before being dealt to the Dodgers.

During the D-backs' magical run to a World Series title in 2001, Finley slashed .365/.441/.462.

4. Mark Grace
Grace was one of baseball’s most consistent performers in the 1990s -- in fact, he collected the most hits of anyone during the decade, with 1,754. He also led in doubles, with 364.

Grace’s left-handed stroke at the plate was a thing of beauty. Over his 16-year career, he totaled 2,445 hits, good for 120th on the all-time list; his 511 doubles ranked 56.

Grace spent 13 years with the Cubs before joining the D-backs for the 2001-03 seasons. But while his time in Arizona may have been short, it certainly was memorable.

D-backs manager Bob Brenly gave Grace the start at first base over Erubiel Durazo in Game 7 of the 2001 World Series, and Grace responded by going 3-for-4, with one of those hits a single off Rivera to open the decisive ninth inning.

5. Brandon Webb
Webb makes this list over third baseman Matt Williams. Had Webb not sustained a career-ending shoulder injury in the prime of his career, who knows just how good he would have been.

Webb burst on the big league scene in 2003, posting a 165 ERA+ in 29 games (28 starts). He should have won the NL Rookie of the Year Award, but because his record was just 10-9 -- and wins were still considered a big deal at that time -- he finished third in the voting.

Webb won the NL Cy Young in 2006, when he had a 152 ERA+, and finished second in the voting in each of the next two seasons. It was a dominant stretch during which he went 56-25 with a 3.13 ERA and a 150 ERA+.

“His sinker is so good, he could tell you it was coming and you still couldn’t hit it,” catcher Chris Snyder said at the time.

Webb left his Opening Day start in 2009 with shoulder soreness and would never pitch in the big leagues again.