I thought this was an interesting observation from a Duke fan re their coaching change ... the last lines sum it up:
A lot, and I can speak from experience here. Duke fired Ted Roof after the 2007 season and hired David Cutcliffe. For context, Roof went 6-45. The coach before him, Carl Franks, went 7-45. We'd won 4 games in the 4 years before Cutcliffe was hired, including one conference win (thank you, 2004 Clemson). David Cutcliffe won 4 games in his first year and 5 in his second (our most wins in a 2-year period since 1994-95). That part of the improvement came from just being a better in-game coach than we'd had in a long time.
We won 3 games each in his 3rd and 4th seasons. They were transition years of sorts, but in year 4 we caught a few bad breaks (some self-inflicted) that cost us. But Year 5, the 2012 season, was the breakthrough. We won 6 games and went to our first bowl game in 18 years--and that sixth win was a last-minute win over Carolina for the first time since 2003. At this point, virtually all of the players in the system were Cutcliffe recruits and guys who'd never been coached by Ted Roof. This is part 2 of what a good coach does: Better recruiting over time.
Between Year 5 and Year 6 (last year), Duke announced a capital campaign for the university as a whole, with significant funding for improvements to the athletic facilities. Part of that was the biggest improvements to Wallace Wade Stadium in its 84-year history. Some of the bleachers are being replaced with seats, the track is being taken out, the field is going to be lowered, and the final stage is to eventually close the horseshoe into a bowl.
That is the hidden third part of what a good coach can do for a program. A good coach revitalizes a program and makes it worth spending money on. Before we hired Coach Cutcliffe, the athletic department didn't care all that much about the football program and kind of let it rot. They read the tea leaves and saw that football was becoming more and more important, and that it might not be a viable option for a major athletic department to have a useless football program. Cutcliffe was actually the program's first outside hire for head football coach since Fred Goldsmith in 1994. They provided Coach Cut with a lot of investments just to get the program up to par--replacing the 80-yard practice field with a full-length one, for example. We gave him the resources he needed to improve the program, and he's given us a program worth making bigger investments in.
Not every coach can take these resources and do what Coach Cutcliffe has done with them. He's gone beyond our wildest dreams in such a short amount of time. But what Coach Cutcliffe has done for us is dramatically improve our win-loss record, improve our recruiting, improve our facilities, re-engage the fans in a program that may as well have been dead just seven years ago.
That's what a good coach can do for a bad program.