Vikings defensive coordinator Alan Williams home schools his three young sons, ages 11, 9 and 6. Actually, his wife, Lisa, handles most of the teaching because her husband's job doesn't allow him much time to grade tests, read papers or explain algebra.

"I'm the administrator," Williams said, smiling.

He's comfortable and effective in that capacity in football, too. In his first season managing the Vikings defense, Williams has quietly resurrected a unit that displayed historic ineptitude defending the pass last season and finished the season in shambles.

The Vikings defense has improved in nearly every statistical category -- dramatically in some cases -- and ranks second behind Adrian Peterson on the list of reasons outlining why this team could secure a playoff berth Sunday in a supposed rebuilding season.

Their defense certainly isn't perfect, and it doesn't rank among the NFL's elite. But it's vastly improved, occasionally opportunistic and, judging by last week's stout performance at Houston, it's capable of carrying the offense on days when Peterson appears human.

"We're playing good ball right now," Pro Bowl defensive end Jared Allen said.

It's been a while since they could utter that declaration. The 2011 defense triggered a collective gag reflex, particularly whenever an opposing quarterback dropped back to pass. The team ranked 31st in scoring defense (28.1 points per game) and 26th in pass defense (251 yards per game) as quarterbacks, on average, completed 68 percent of their passes while posting a 107.6 rating.

"Last year was horrible," defensive end Brian Robison said.

Overall, they've been competent this season. The defense has forced more turnovers and scored three touchdowns. Their number of pass breakups has jumped from 64 last season to 103 this season, an undeniable byproduct of having better personnel and thus being in position to make plays.

Their defense has endured some rough patches and still is limited in a few areas. But the scoreboard reveals the true marker in measuring its improvement.

The Vikings rank 11th in the NFL in scoring defense at 20.9 points per game. That 7.2 points per game improvement represents the fourth-best season-to-season differential in team history and the largest margin since 1987-88.

The Vikings have allowed only 42 points during a three-game winning streak that created a win-and-in playoff scenario against the Green Bay Packers on Sunday.

"When everybody is confident in the game plan, this is exactly how we can play and I feel like this is our potential," Allen said. "I still think we can get even better."

Williams insists he expected this turnaround after replacing Fred Pagac last offseason. In evaluating his new defense, Williams felt its problems stemmed from depleted personnel more than anything else. Injuries forced the Vikings to rely on players who belonged as backups, at best.

"I think people think you just go and get another first-round guy or starter," Williams said. "That's not the case. This year the biggest thing is our guys are healthy."

Williams deserves credit, too. His impact has been obscured by the spotlight on Peterson's pursuit of history, but Williams has struck a nice balance between adhering to Leslie Frazier's defensive principles while also remaining unpredictable. He's adjusted his approach according to the opponent's strengths.

Williams did not call a single blitz in a victory against the Arizona Cardinals on Oct. 21. Only five other teams in the past five seasons went an entire game without blitzing, according to ESPN research. However, Williams also has formulated game plans heavy on blitzes, including last week against Houston.

"You want to be flexible and be able to take away what a team does best and make them play lefthanded," Williams said.

Like Frazier, Williams is a product of the Tony Dungy coaching tree and his personality fits that mold.

"You can tell they all worked together," cornerback Antoine Winfield said. "Same message, the way they talk, their demeanor. All soft-spoken, straight to the point."

Occasionally too direct. Williams angered his players after a loss to Seattle by publicly accusing some of them of loafing. Williams said Thursday that he shouldn't have voiced his frustration in that forum.

"An overreaction on my part to say we had loafs," he said. "Mistake on my part."

Well, it worked. His defense played inspired, maybe even angry, the following week against Detroit. Whether a mistake or clever ploy, Williams achieved his desired goal as the Vikings won an important game.

He needn't apologize for that.

Chip Scoggins • ascoggins@startribune.com