One of the D-backs who has missed Williams' presence the most is veteran second baseman Aaron Hill.
"I ran everything by him," Hill said of his relationship with Williams in Arizona. "Just about hitting and defense, I mean, he liked talking baseball. That's always fun."
The Nationals entered play Thursday with the best record in the National League at 72-53.
Gibson, who promoted Williams from first-base coach to third-base coach during his time as manager, participated in a joint interview with him for the D-backs pregame show Thursday.
"Matty is a new manager, new staff, they're just starting to gel," Gibson said. "Very strong club. They had a very good year last year. Continue to build off of that. They have a real opportunity ahead of them."
During his time as a player, Williams was known for his intensity, but as a coach and now manager, he has learned to temper it when needed.
"He's just such a welcoming person for everybody," Hill said. "Always got a smile, always positive, he's energetic, so it attracts good people and positiveness, so he's always fun to be around."
Gibson laughed when a reporter mentioned how relaxed Williams looked as a manager.
"When you win more games, it's much easier to relax," Gibson said. "I can tell you that from experience."
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.