KANSAS CITY, Mo. -- The four quarterbacks on the Kansas City Chiefs' roster have combined for 136 career NFL starts and almost 7,000 snaps, so the team has enough experience at a most important position.

The trouble is that all of it belongs to one player, Alex Smith. The Chiefs’ other three quarterbacks -- including this year’s first-round draft pick, Patrick Mahomes II -- have yet to take a snap in an NFL game.

But general manager John Dorsey said he thinks Smith's backup is on the roster now.

“I do," Dorsey said. “It will be a good, competitive battle for that position. You’ve just got to let that work itself out. We’ve got to see how training camp unfolds."

The first shot at the No. 2 quarterback spot will go to Mahomes. The Chiefs paid an impressive price, two No. 1 picks and a third-rounder, to move up 17 spots in the first round last week to draft Mahomes out of Texas Tech.

So much depends on the pace of his development. The other backup quarterbacks are Tyler Bray, who is entering his fifth season with the Chiefs but has yet to play, and Joel Stave, who spent part of last season on Kansas City’s practice squad.

“Let’s see when Patrick comes here how much he develops, [how much] he understands, [how much] he learns the system, how much he can advance with the quality of coaching that we have," Dorsey said. “That’s the whole thing we all want to see, is how fast he can accelerate his learning curve in that regard and see where he does wind up on the depth chart after playing four preseason games."

Mahomes played exclusively in the spread offense at Texas Tech, so he’s bound to need transition time to an NFL system. The Chiefs were careful to say when he was drafted that he isn’t ready to play, which would remove him from consideration to be the No. 2 quarterback if that doesn’t change during the summer.

Mahomes’ first practice with the Chiefs will be Saturday, when the Chiefs begin a three-day rookie camp. Full-squad practice begins May 23.

“We’ll get in and see how it goes," coach Andy Reid said. “The one nice thing is, we have a good quarterback [already] here. You look at what Dorsey went through with Aaron Rodgers [Dorsey was director of football operations and held other roles with the Green Bay Packers]. It took time. We’re OK.

“I’m just glad we got [Mahomes]. It’s kind of a neat deal. It’s a positive thing. It gives an opportunity for Kansas City to have that position in pretty good hands for a long period of time."

For his part, Mahomes said he didn’t think the transition to the Chiefs’ offense would be as difficult as others believe. Mahomes said that at Texas Tech, he called protections and routes and had the OK to change plays no matter the down, distance or game situation.

“I feel like a lot of [spread] quarterbacks haven’t had that before, so that’s definitely going to help the transition a little bit," Mahomes said. “The coaches that the Kansas City Chiefs have, with coach Reid and [quarterbacks coach Matt] Nagy and those guys, they’ll help me a lot and they’ll really push me to be the best quarterback that I can possibly be. That’s the biggest thing that’s going to help.”

Though it may not be the plan now, the Chiefs could acquire a veteran to be the primary backup for Smith, who has been remarkably durable since joining the Chiefs. He has missed two games because of injuries in four seasons.

The Chiefs have had a veteran backup for Smith the last four seasons: Chase Daniel from 2013 to 2015 and Nick Foles last season. The Chiefs acquired Foles after training camp started.

The Chiefs open the 2017 season on Sept. 7 against the Patriots in New England.