The first 5 games were marred by poor personnel decisions (LJ Shelton at Left Tackle), and too much complexity in the play-calling.
The o-line had lots of strange-looking double teams and stunts, which were not working for unathletic linemen.
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I'm sure at some point Nick Saban decided to step-in, and help, and reduce the complexity. Early in the year, we saw Dante rollout right to avoid being sacked by Shelton's guy. Also, there was talk of going no-huddle to help the o-line. I'm sure these were Saban's ideas. I don't think that he's actually calling plays though. Maybe saying "No" to some plays... but probably not actucally calling them.
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Against the Chiefs, this offensive game-plan looked a lot like earlier in the year. It looked complex again. With 9 weeks under their belt, and better personnel on the o-line (MacIntosh), it looked like we were able to execute these same complex running plays that we could not run earlier in the year.
The commitment to the run, and the lack of turnovers and penalties were good to see in the Chiefs game.
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13 points is still not going to get Mike Mularkey an award for good play-calling, though. I would never bet money on a team that can't score 17-21 offensive points consistently.