KANSAS CITY, Mo. — The Kansas City Chiefs saw value in a trio of players that were essentially castoffs from what was one of the least-successful franchises in the NFL over the past 10 years, and their decision to pick them up when just about nobody else was calling is a big reason why they’re playing in the Super Bowl.

The biggest move was picking up Damien Williams, who has gone from journeyman running back to an integral part of one of the league’s best offenses. Backup quarterback Matt Moore filled in admirably when Pat Mahomes was hurt this season, and safety Jordan Lucas played on just about every Chiefs special teams unit.

All three once played for the Dolphins.

Now, all three are headed back to Miami.

“It’s a big stage and a big moment,” Williams said. “I’m a pride-type person. I like to take pride. At the end of the day, this could be your last run, your last play, so you have to go at it as such. I’m going hard every single day.”

Each of those three players know quite well that any game could be their last.

Williams spent his first four seasons with the Dolphins, playing in 58 games and even taking over the starting role for a four-game stretch in 2017. But when they no longer envisioned Williams in their future, he signed a one-year prove-it deal with Kansas City to be the backup to Kareem Hunt, who was just then emerging as a star.

Then last season, Hunt was kicked off the team following an ugly off-the-field incident, and Williams took over down the stretch. He ran for 129 yards and a touchdown while also catching a touchdown pass in a playoff win over Indianapolis, and he added two touchdowns receiving and another rushing in the Chiefs’ overtime AFC title game loss to New England.

That was enough to give Williams the No. 1 job entering this season. But injury trouble that has followed him throughout his career popped up again — it was a shoulder injury two years ago, a rib injury this year. He was sidelined for a long stretch in the middle of the season, and veteran LeSean McCoy and a host of others handled the majority of the reps.

The time off might have done Williams some good, though. He’s been healthy and fresh when Kansas City has needed him most, scoring four touchdowns the past two weeks to give him a franchise-record eight TDs in the postseason.

“He’s playing good football,” Chiefs coach Andy Reid said. “He was banged up and he worked through it. I think he’s done a nice job. Playing physical and running hard. Been impressed with his game right now, catching the ball well too.”

The Chiefs’ offense isn’t necessarily predicated on the run, especially with Mahomes under center. But Williams does just enough to keep defenses honest, and his ability to block and catch in the passing game has proven invaluable.