Chryst was hired away from Pitt in December to replace Gary Andersen. The Madison native had previous experience at Wisconsin, most recently from 2005-11 as offensive coordinator and quarterbacks coach.
Though Alvarez hasn't had the opportunity to watch a huge portion of spring practice, he said he admires Chryst's talent. Chryst and the Badgers spring practice session culminates Saturday with the annual spring game at Camp Randall Stadium.
"I felt when Paul was here as an assistant and a coordinator, that he was one of the best play callers and quarterback developers that I've ever been around," Alvarez said.
"I like what I've seen, how he manages his vision for a program; how he deals with his assistant coaches, and how he delegates. I love my conversations with him about his vision, what he sees with the players and how he wants to bring them along."
Alvarez, who spent 16 years as Wisconsin's football coach before taking the athletic director position, said he doesn't feel anything is missing with the lack of a big crowd at the Badgers spring game.
In the past few weeks, fans have shown up in big numbers to watch Big Ten spring games at Ohio State (99,391), Nebraska (76,881), Penn State (68,000) and Michigan (66,000).
According to Alvarez, 10,000 to 20,000 fans have attended Wisconsin's spring game each season over the past 25 years.
"It's not a measuring stick because we've tried since 1990 to generate interest in a spring game," Alvarez said. "I just think there are too many things to do in Madison that we have not been able, through a number of coaches, to generate that type of interest.
"We've promoted it and done a lot of different things — we've drafted teams and had guest coaches. For the most part, that's kind of been the numbers that we'll get. We've never been able to crack through and have the numbers like those schools."
Wisconsin had 12,316 at its 2014 spring football game and 12,050 in 2013.