The draft is over, and free agents have been signed. Training camps are springing to life around the country. It’s the peak moment for a feeling often in short supply among N.F.L. fans: optimism. There’s no reason all 32 teams can’t overachieve this year, right?

Here’s a look at the league through the rose-colored glasses of late July by Victor Mather, and a somewhat more jaundiced view from Benjamin Hoffman:

A.F.C. West

Denver Broncos The Broncos are on top of the pile as Super Bowl champions, and Von Miller’s contract is locked up. The retirement of Peyton Manning should not be too big a blow, as his numbers were anemic most of last season.

Considering how limited Manning was in the Super Bowl, the Broncos essentially won a championship without a quarterback. If you liked that trick, you are going to love the team’s following it up by losing some significant players to free agency and replacing Manning with Mark Sanchez.

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Kansas City Chiefs The Chiefs looked as good as anyone, ripping off 10 straight wins to conclude last season. Running back Jamaal Charles is set to return from injury to make the team even better.

The N.F.L. has never been sentimental, but the Chiefs have become the anti-Hallmark card after Eric Berry fought his way all the way back from Hodgkin’s lymphoma to establish himself as one of the best defensive backs in the league and the team rewarded him with a protracted salary dispute that ended with his being franchise-tagged for the season.

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Oakland Raiders They went out and signed guard Kelechi Osemele plus a strong defensive crew. Sean Smith, Reggie Nelson and the rookie Karl Joseph could take the secondary from good to excellent.

With marked improvement last season, and several emerging stars, the Raiders appear to be on their way to legitimacy. Luckily, Mark Davis is providing plenty of distractions with talk of relocating the franchise, making things as difficult as possible for his players.

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