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Later Monday, Maddux released a statement saying his withdrawal was a "family decision."
"My wife and two daughters are together in the same state for the first time in three years and words cannot describe my happiness," Maddux said. "The game of baseball has many sacrifices but being apart from family is the toughest. I feel there is too much distance between the Dallas-Fort Worth Metroplex and Boston to see my family as much as I'd enjoy.
"Again, I thank Ben Cherington and the Boston Red Sox for the flattery, honor, and compliment of considering me for their position."
Maddux has not withdrawn from the Chicago Cubs search, however. The Cubs confirmed Monday night that Maddux will still interview on Wednesday.Late last week, Maddux called it "unbelievable to hear those two teams have interest." Maddux, 50, the older brother of former Cubs and Braves great Greg Maddux, pitched for 10 teams in a 15-year career in the majors. He was the Brewers' pitching coach for six seasons and has been in the same role with the Rangers the last three seasons. Maddux's withdrawal leaves Cleveland Indians bench coach Sandy Alomar Jr. next up to interview for the Red Sox job. He is scheduled to visit Fenway to meet with Red Sox brass on Wednesday. Phillies bench coach Pete Mackanin and Milwaukee Brewers hitting coach Dale Sveum have already been interviewed for the position. Maddux would have been perhaps the most intriguing candidate on Boston's list and the one who might best fulfill the needs of a team whose pitching could most benefit from a strong, expert voice. No less of an authority than Rangers president Nolan Ryan has called Maddux the hardest-working pitching coach he has ever been around, and Maddux brings a reputation for toughness and a demand that his charges be in top condition, attributes that would appear exactly in line with what the Sox require. In Texas, a graveyard for pitchers ever since the Ballpark in Arlington opened in 1994, the Rangers posted their best staff ERA (3.79) since 1983. In 2008, the season before Maddux came over from the Brewers, the staff ERA was 5.37. By the next season, he had shaved nearly a full run (4.38) and it went to sub-4.00 in 2010 (3.93) before dropping again this past season. Five Rangers starters made 29 or more starts in 2011, and four starters made 19 or more quality starts, led by C.J. Wilson's 23. The Sox had two pitchers with 19 or better: Josh Beckett (20) and Jon Lester (19). It was on Maddux's watch that Wilson converted from reliever to starter with spectacular results. All five members of the rotation won 13 or more games, and it was Maddux, responding to a directive from Ryan, who impressed upon his starters that they were expected to pitch deep into games. That doesn't mean the same as abusing pitch counts -- Wilson ranked 15th in the league with 105.6 pitches per start, and all five starters made it through the season healthy, which admittedly takes luck but also reflects the kind of conditioning Maddux expected. Instead of taking a step back when ace Cliff Lee left as a free agent for Philadelphia last winter, the Rangers got better, Ryan calling Maddux one of the team's best-ever free-agent signings. ESPNBoston.com's Gordon Edes contributed to this report.