Wisconsin's best years have been under head coach Barry Alvarez, followed up by Bret Bielema, Barry Alvarez's hand-picked successor, working under athletics director Barry Alvarez. Bret Bielema left to Arkansas where he finished with a sub .500 overall record and took last place in his division 3 times in 5 years.
He was replaced at Wisconsin by Gary Andersen for two years, after which it seems many Wisconsin fans were happy to be rid of him because his coaching philosophy differed too much from the style of football that Barry Alvarez established. He went 7-23 in two and a half seasons at Oregon State, far worse results than the 19-7 record he earned while working under Barry Alvarez at Wisconsin.
Barry Alvarez then hired Paul Chryst, the offensive coordinator under Bret Bielema, who at the time was 19-19 overall after 3 years at Pitt. Working under Barry Alvarez, however, he has won 10 games or more 4 times in 6 seasons.
Combined records of Bret Bielema, Gary Andersen, and Paul Chryst as division 1 FBS head coaches:
Working for Barry Alvarez: 143-50 (.741)
Working for Not Barry Alvarez: 88-109 (.447)
The last 30 years of Wisconsin football have been coached by Barry Alvarez or someone that Barry Alvarez hired. It seems to me that Barry Alvarez is a substantial factor in Wisconsin's football success, and he isn't there anymore, granted maybe Chryst is similar enough of a coach to Alvarez to keep the train running awhile longer. Also Wisconsin seems like they recruit better than Iowa most years.