A look at Brian Hoyer’s numbers from last season should have 49ers fans optimistic about what he could do as the team’s starter in 2017.

Hoyer in six games for the lowly Bears completed 67 percent of his throws, averaged 240 yards per game and had six touchdown passes to no interceptions. He logged 300-yard games in his first four starts.

His 98.0 passer rating was a career high and would have ranked seventh among NFL starters for the entire season, just ahead of Kirk Cousins (97.2).

But six games, of course, is a small sample. Hoyer, 31, would have likely regressed as defenses learned his tendencies within Chicago’s offense. His season ended prematurely after he broke his left, non-throwing arm in October against the Packers.

Now Hoyer finds himself as the likely starter for Kyle Shanahan, his offensive coordinator with the Browns back in 2014. Hoyer that year started 13 games, helping win seven of his first 11, before falling apart down the stretch.

So what’s fair to expect from Hoyer in San Francisco as the presumed stop-gap starter?

His 7.2 yards per attempt for his career is around the league average – after 49ers starters Blaine Gabbert and Colin Kaepernick in 2016 and 2015 averaged 6.4 and 6.9, respectively. San Francisco’s passing attack never cracked out of the bottom three under Jim Tomsula and Chip Kelly.

The best case for Hoyer in 2017 starts with staying healthy. He tore his ACL in 2013, dealt with concussions in 2015 with Houston and fractured his arm last season.

Hoyer will have to avoid taking sacks, which falls on his ability to get rid of the ball quickly paired with the offensive line in front of him. The veteran last season was sacked a career-low 2 percent of his attempts, in stark contrast to 49ers signal callers that were dropped on 8.7 percent of theirs.

With Shanahan’s reliance on play action and moving the pocket with bootlegs, San Francisco’s sacks allowed should more closely resemble Hoyer’s career rate of 5.1 percent, which would be a dramatic improvement over last season’s struggles for the 49ers.

One benefit Hoyer will have is a philosophy and roster catered to Shanahan’s system, to which Hoyer fits.

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With Hoyer will be wideout Pierre Garçon, who led the NFL with 113 receptions when Shanahan was his coordinator in 2013 with Washington. Hoyer should have a versatile running attack that might be the most talented he’s worked with, starting with Carlos Hyde and including Utah speedster Joe Williams, Tim Hightower, Kapri Bibbs and undrafted rookie Matt Breida.

If all goes right, meaning Shanahan hits the right notes and the 49ers have good injury luck, Hoyer could put together the best season of his career in just his second as a full-time starter.

That had to be the appeal of San Francisco in free agency for the career backup. Hoyer gets to reunite with Shanahan to build upon last season, play in a system that maximizes his lackluster physical tools and potentially start for two years while the team finds a long-term solution at the position.

Playing well could lead to another contract with San Francisco or elsewhere by the time his deal is up in 2019, when he’ll start the year at age 33. That’s a better foundation for another pay day than he could have set somewhere else.

The reasonable expectation for Hoyer in 2017 lands around his career averages. If he can complete 60 percent of his throws, average at least 7.2 yards per attempt and keep a 2-to-1 touchdown-to-interception ratio, the 49ers should feel good about their decision to bring him in for two seasons and $12 million.

Those numbers are about average for NFL starters, which would be an upgrade for the 49ers over their quarterback play from the last two seasons.