Broncos already taking off-season hits as Brock Osweiler signs with the Houston Texans

First, you hold the trophy. Then, you try to hold your team together.

That’s the formidable challenge facing every Super Bowl champion. Your newly-crowned players want to get paid, and 31 other teams are looking for some of that magic that got you so far — with the bonus of eroding the champ’s base of success.

The Denver Broncos are dealing with that headache at the moment. Two days after Peyton Manning announced his retirement, Brock Osweiler — the team’s presumed quarterback of the future — gave Denver a Heisman-like straight arm and signed with the Houston Texans on Wednesday, the first day of the free-agency period.

The Broncos were unwilling to pay the 6-foot-7 Osweiler the $18 million per year he was seeking — the Texans hit that number with a four-year deal worth $72 million — and Osweiler wasn’t happy about being benched in favor of Manning throughout the playoffs.

“We’ve stayed true to our philosophy of building a team with players who want to be Denver Broncos and want to be here,” John Elway, executive vice president of football operations, said on the team’s website. “That’s been a successful approach for us. While we did offer a very competitive and fair long-term contract to Brock, we ultimately had to remain disciplined while continuing to assemble a roster that can compete for championships.”

Although they wanted to keep Osweiler, the Broncos weren’t going to pay a stratospheric salary for a quarterback with seven career starts (five of which led to victories) who in their estimation was not worth more than $16 million per year.

The Broncos won’t be the first Super Bowl champion to begin its next season without the two top quarterbacks from the year before. Baltimore did that after winning the Super Bowl in the 2000 season, then parting ways with Trent Dilfer and Tony Banks.

Denver also lost a pair of defensive standouts, with defensive tackle Malik Jackson heading to Jacksonville, and linebacker Danny Trevathan going to Chicago and reuniting with former Broncos coach John Fox.

While “Shock & Osweiler” was still reverberating throughout the NFL, the New York Giants also made a big deal by signing defensive end Olivier Vernon, who became reasonably expendable in Miami after the Dolphins signed Mario Williams.

The Giants, who were last in total defense and 30th in sacks in 2015, are hoping the addition of Vernon, along with the re-signing of Jason Pierre-Paul, will pump some life into their pass rush.

As pass-rushing tandems go, it’s difficult to top Oakland’s, with the Raiders adding linebacker Bruce Irvin from Seattle as a bookend to budding superstar Khalil Mack.

It doesn’t hurt the Raiders’ cause that AFC West rival Denver is now in search of a quarterback, and that Kansas City was docked two draft picks for tampering; i.e. improper contact with wide receiver Jeremy Maclin during free agency last year. The Chiefs were stripped of their third-round pick in April’s draft, and a sixth-round pick next year. Additionally, there were fines of $250,000 for the club, $50,000 for Coach Andy Reid, and $25,000 for General Manager John Dorsey.

Philadelphia was extremely active on the first day of free agency, signing quarterback Chase Daniel, most recently a backup in Kansas City; signing former Rams safety Rodney McLeod, and swapping their No. 13 pick in the first round for Miami’s No. 8 as part of the deal that sent linebacker Kiko Alonso and cornerback Byron Maxwell to the Dolphins. The Eagles also completed a deal that sent 2014 NFL rushing champion DeMarco Murray to Tennessee, which gave up the second pick of the fourth round in this year’s draft for Philadelphia’s 15th pick in the round.

Carolina, which lost the Super Bowl, held on to All-Pro fullback Mike Tolbert and defensive end Charles Johnson, both of whom accepted pay cuts to stay with the Panthers.

Tampa Bay re-signed All-Pro running back Doug Martin, and former Cleveland center Alex Mack is headed for Atlanta. The Chiefs signed Browns tackle Mitchell Schwartz to a five-year deal.

Tight end Antonio Gates, 35, agreed to a two-year deal with San Diego that will allow him to retire with the team that signed him as an undrafted rookie in 2003.

Indianapolis parted ways with receiver Andre Johnson, who contributed a modest 41 catches for 503 yards and four touchdowns last season. He failed to make a catch in three games, something he hadn’t done once since 2005, his third of 12 seasons with Houston.

sam.farmer@latimes.com

Twitter: @LATimesfarmer