How many head coaches with a defensive background have won a Super Bowl and how many head coaches with an offensive background have won a Super Bowl?
I apologize for any confusion earlier. Here's a more direct answer to your question, but please note that these numbers reflect data from Super Bowl I (1967) through Super Bowl LIV (2020) for simplicity's sake:
Head Coaches with a Defensive Background that have won the Super Bowl - 15:
Vince Lombardi, Don Shula, Chuck Noll, Tom Landry, Bill Walsh, Joe Gibbs, Bill Parcells, George Seifert, Bill Belichick, Tony Dungy, Tom Coughlin, Mike Tomlin, Pete Carroll, and John Harbaugh.
Head Coaches with an Offensive Background that have won the Super Bowl - 22:
John Madden, Bud Grant, Bill Walsh, Joe Gibbs, Mike Ditka, Bill Parcells, George Seifert, Jimmy Johnson, Mike Holmgren, Dick Vermeil, Bill Belichick, Jon Gruden, Bill Cowher, Tony Dungy, Sean Payton, Mike Tomlin, Mike McCarthy, Jim Harbaugh, Pete Carroll, Gary Kubiak, Doug Pederson, and Andy Reid.
Note that some coaches like Bill Belichick, Bill Walsh, and Joe Gibbs are mentioned in both categories due to their diverse coaching background, having significant experience and impact on both sides of the ball.
Also, please note that the list above includes coaches who've won multiple Super Bowls, so the total count of Super Bowl victories is more than the number of individual coaches listed.