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Schilling received 230 votes out of 440 ballots, with 330 votes needed for election this year.
In his career, Schilling was 216-146 with a 3.46 ERA and a Wins Above Replacement total of 80.7, which ranks 26th all-time among pitchers.
Acquired by the D-backs in July 2000, Schilling pitched in Arizona through 2003 and went 58-28.
In 2001, Schilling was 22-6 with a 2.98 ERA, and he went 23-7 with a 3.23 ERA the following year. Along with Randy Johnson, Schilling formed one of the most dominant one-two combinations in baseball.
Johnson won the National League Cy Young Award in those two seasons, with Schilling finishing second each year.
Schilling had a reputation for being a big-game pitcher and he certainly lived up to that with the D-backs during their run to the 2001 World Series championship.
In the NL Division Series that year, Schilling won two of the five games against the Cardinals, including the clincher. In 18 innings, he allowed just one run while tossing two complete games.
In the NL Championship Series against the Braves, he won his lone start, once again tossing a complete game while striking out 12.
Finally, in the World Series, Schilling made three starts, including the Game 7 clincher against the Yankees, and had a 1.69 ERA. He shared World Series Most Valuable Player honors with Johnson, who was inducted into the Hall of Fame last summer.
Other players on this year's Hall of Fame ballot with ties to the D-backs included Alan Trammell, who was a bench coach under Kirk Gibson from 2011-14, shortstop David Eckstein, who played for Arizona in 2008 and third baseman Troy Glaus, who played for the D-backs in 2005.
Trammell received 40.9 percent of the votes in his final year of eligibility.
Eckstein received two votes, while Glaus did not get any, which means both will be dropped from next year's ballot.