KANSAS CITY, Mo. — Kansas City Chiefs head coach Andy Reid said Monday that quarterback Alex Smith suffered a sprained right shoulder in Sunday’s victory over the St. Louis Rams.

“It happened in the game and he was able to go through the game and everything worked out OK,” Reid said. “It’s a bit sore today, tender, but he’s upbeat about it. We are doing all the precautionary things in looking at it … it should be fine.”

But Reid did not express concern that Smith might not be available for this Sunday’s game against the New York Jets at Arrowhead Stadium.

“It’s more of a bruise than anything,” said Reid. “He’ll need some time to get the soreness out of there.”

In a season where the Chiefs have lost multiple players for multiple games and even the season, the only position group that had escaped the injury bug was quarterback. Smith has not been limited in any of the season’s practices or games, and still may not be if he can practice on Wednesday.

Reid indicated the sprain came late in the first half, on one of the back-to-back sacks where Smith was taken down by St. Louis defensive end Robert Quinn. On both of those plays, Smith’s right shoulder was the first thing that hit the turf. The second sack appeared the most violent when his shoulder hit the ground with the weight of Quinn on top of him.

After the game, Smith did not indicate he was in any pain and he did not stay in the training room for any extra treatment. That’s good news for a Chiefs offense that continues to grow and establish an identity with Smith at the controls. Against the Rams, Smith completed 24 of 28 passes and averaged 8.1 yards an attempt.

The offense is relying on balance, as they are getting production on the ground and through the air as Reid has split the play calls at almost 50-50 run-pass. When they do throw, the Chiefs are not taking the ball down the field in their pass scheme; in the past five games, Smith has thrown only one pass that traveled more than 20 yards. He has thrown 21 of his 214 passes more than 10 yards away from the line of scrimmage.

“I think it’s a matter of staying patient with it (the running game) as the game goes on,” said Smith. “It starts with the guys up front and they are wearing on them and our backs are running well … any time you have balance, the other guys can’t pin their ears back and rush. You’re going to help yourself keep it balanced.”

Since a poor performance in the season opener against Tennessee, Smith has been solid, if not spectacular. He has thrown just one interception since tossing three against the Titans. He has pushed his completion percentage to 66.8 percent and he now has nine touchdown passes.

With half a season left to play, the Chiefs need to believe they’ll have Smith on the field to manage the offense and give them a chance of returning to the playoffs.

MEDICAL WATCH: CB Jamell Fleming and OLB Josh Martin suffered hamstring injuries and will be reevaluated mid-week. … SS Eric Berry will continue to work on rehabbing his high ankle sprain and may have a good chance of being active Suunday. Berry has missed the last five games due to the injury he suffered on Sept. 14.

REPORT CARD VS. RAMS

PASSING OFFENSE: A – It was a good performance for the Chiefs offense throwing against the St. Louis defense. Quarterback Alex Smith was on fire, completing 85.7 percent of his passes and averaging 8.1 yards on his 28 passing attempts. Smith had no interceptions, was sacked twice and did a good job of distributing the ball, connecting with eight different receivers.

RUSHING OFFENSE: B – The Chiefs did not have great individual productivity in the run game against St. Louis; the only thing that came close was a 36-yard touchdown run in the second half by Jamaal Charles that was part of a 73-yard performance. That was the team’s longest scoring run of the season and the longest run of any kind for Charles in 2014.

PASS DEFENSE: A – The Chiefs defense took advantage of inexperienced Rams quarterback Austin Davis, along with an injury situation on the St. Louis offensive line that did not allow for continuity in pass protection. In the first Rams possession of the game, Davis hit a 43-yard pass to wide receiver Kenny Britt. After that play, Davis was 14 of 23 for only 117 yards. The K.C. defense gave him no room to breathe, sacking Davis seven times.

RUSH DEFENSE: B – The way the game unfolded, St. Louis did not have many opportunities in the second half to keep working on its running game. The young backs trio of Zac Stacy, Benny Cunningham and Tre Mason showed promise and hit a couple of nice runs, but overall the Kansas City defense stifled the Rams runners and got after the quarterback.

SPECIAL TEAMS: A – Until Sunday, the Chiefs kicking game struggled to make a contribution for the 2014 Chiefs. Big plays were expected on a weekly basis because that was something they provided last year. But the trickle-down effect from the team’s early injury situation this year shuffled the cards for the special teams and they are only now producing consistent effort. Against the Rams, the Chiefs produced a kickoff return touchdown from Knile Davis and rookie kicker Cairo Santos nailed a 53-yard field goal.

COACHING: A – Week by week, the profile of this team is being established by the play-calling and actions of head coach Andy Reid and his staff. The offense has shown success when Reid splits the opportunities 50-50 between run and pass. Defensively, the Chiefs are transitioning away from all press man-to-man coverage to more off-coverage and zones. It has helped limit the big plays against them. This team started 0-2 and was hampered by injuries. They have gone 4-1 in the last five games as injury replacements have been blended into the effort.