KANSAS CITY, Mo. — The joke running through Jacksonville these days carries the same punch line as the one in Kansas City:

“Our team is so bad it can’t even stink in the right year.”

The Chiefs and Jaguars will vie for the top pick in the NFL draft in separate games Sunday. But the value of “winning” the race to the NFL’s worst record is debatable in a year without a clear, franchise-changing prospect.

There’s no Andrew Luck in this unlucky draft.

No Robert Griffin III, either.

Just a collection of talented young players who could fill holes at left tackle or linebacker or defensive end, but hardly push the needle for teams in desperate need of massive overhauls.

The Chiefs and Jaguars are both 2-13, but the Chiefs hold the tiebreaker for the No. 1 spot because of their weakness of schedule. The only way Jacksonville can jump them is if they lose to the Tennessee Titans and Kansas City beats the Denver Broncos, who are playing for an opportunity to secure home-field advantage throughout the playoffs.

That would give the Jaguars the worst overall record by themselves.

“You don’t want to be in this position,” Jaguars coach Mike Mularkey said. “Just like we didn’t want to be in that position in Atlanta when we drafted Matt Ryan (in 2008). But if you pick up the right guy, it can make a huge difference for you and get you out of that position.”

The Jaguars have never drafted first overall. They had the second choice in their expansion year of 1995 and again the following season.