How important is run defense when it comes to winning in the NFL? It’s hard to sit through a game without hearing about the importance of stopping the run. Coaches will emphasize it in every interview.

Since conventional wisdom states that run defense is the most important part of building a winning team, it would make sense that the most well-regarded defensive players would be the ones who excel at stopping the run.

Yet the opposite is true. The most famous defensive players are known for their play against the pass and their gaudy sack totals. They’re cornerbacks who can shut down star receivers and linemen or linebackers who can invade the backfield.

This misperception exists not only among fans. Despite the fact that two thirds of the Pro Bowl vote belongs to players and coaches, this year’s Pro Bowl defenses show a marked bias against players who are known for stopping the run. Instead, nearly all the defensive linemen and linebackers chosen for the game have made their names as pass rushers with hefty sack stats.

In the NFC, for example, Pro Bowl defensive ends include Arizona’s Bertrand Berry, who leads the conference in sacks, Atlanta’s Patrick Kerney, who is tied for second, and Carolina’s Julius Peppers, tied for sixth. Few defensive tackles rank among the conference leaders in sacks, but the ones that do were voted to the Pro Bowl: Minnesota’s Kevin Williams leads NFC defensive tackles in the statistic, while Dallas’s La’Roi Glover is third.

Of the six defensive linemen on the NFC roster, only Detroit’s Shaun Rogers is known for his run-stopping ability he’s also the only one without a high sack total. Berry and the Arizona defense were at the bottom of the NFL in run prevention, and Williams and the Minnesota defense were ranked 30th. Meanwhile, only outside linebacker Marcus Washington represents a Redskins’ defense that leads the league in preventing yards per carry.

The problem is even more pronounced with the AFC Pro Bowl rosters, in part because of the differences between the 3-4 and 4-3 defensive alignments. All six teams that use the 3-4 as their basic defense play in the AFC, including three division winners: the Patriots, Steelers, and Chargers, as well as the defense-oriented Ravens.

In a standard 4-3 alignment – four defensive linemen, three linebackers – defensive ends generally try to get around the offensive tackles so they can make the plays. The scheme favors pass rushers in particular, and most of the NFL sack leaders are 4-3 ends. Even the defensive tackles will make more plays, because a blocking mistake by the offensive line leaves a 4-3 tackle with a gap right in front of him.

But in a 3-4 alignment, the main responsibility of the three linemen is to tie up blockers, allowing the linebackers to penetrate the backfield. The sack leaders among 3-4 players are not defensive ends but linebackers: Steve Foley of the Chargers, Terrell Suggs of the Ravens, and Willie McGinest of the Patriots.

As a result, the AFC Pro Bowl defense exhibits a strange dichotomy between the defensive line and the linebackers. Five of the six defensive linemen chosen for the team play primarily in the 4-3 alignment. That includes all three defensive ends, and it is no surprise that these three players include the league leader in sacks, Indianapolis’s Dwight Freeney, and pass rush specialist John Abraham of the Jets.

Freeney, in particular, is out-muscled on most running plays and sometimes takes himself out of the play entirely with an undisciplined pass rush. Of the three chosen defensive ends, only Jason Taylor of Miami plays a balanced game, equally strong against the pass and the run. But even Taylor is famous for his sack total – he was second in the AFC last season, fourth this season – and not for stopping the ground game.

The only 3-4 lineman chosen for the Pro Bowl was New England’s Richard Seymour, and he was chosen at the wrong position – he’s primarily a defensive end, not an interior lineman.

Move on to the linebacker section of the AFC roster, however, and the situation is reversed, thanks in part to the fact that the 3-4 is designed for linebackers to make big plays. Buffalo’s Takeo Spikes is the only linebacker from a 4-3 team to make the roster. The other four AFC linebackers come from teams playing the 3-4: Pittsburgh’s Joey Porter and James Farrior, and Baltimore’s Ray Lewis and Terrell Suggs.

Suggs is a pass rush specialist who is recognized for his high sack total. He gets the glory and the trip to Hawaii while nose tackle Kelly Gregg, who does the dirty work that makes Baltimore’s defensive strength possible, goes overlooked.

A better selection of Pro Bowl defenders would feature primarily balanced players who excel against both the run and the pass. It would also try to make up for a problem that exists in the all-star selections for every sport: the election of declining players based on past reputation rather than recent performance.

Our ideal NFC roster removes Glover, whose numbers were down on a Dallas defense that collapsed this season, and replaces him with Cornelius Griffin, whose move from the Giants to the Redskins helped Washington become this season’s top run defense.

At linebacker, Jeremiah Trotter has keyed Philadelphia’s improved run defense, but he missed most of the season’s first half with injuries. For performance over the entire season, Washington’s Antonio Pierce is more deserving of recognition.

In the AFC, a better choice than Abraham would be Pittsburgh defensive end Aaron Smith. Voters missed Smith despite his eight sacks, an incredible number considering that 3-4 ends are supposed to be tying up blockers, not rushing the quarterback. But Smith does such a good job collapsing the pocket that he can get sacks on his own, and he’s stronger against the run than Abraham or Freeney.

Our team also switches one Raven for one Patriot. When so many strong AFC defenses play 3-4, it is absurd for the league’s best nose tackle to be left off the team. Baltimore’s Gregg replaces New England’s Seymour, who is a great player but wasn’t as dominant early in the year (partly because he was dealing with his father’s death).

Instead, it’s time to recognize one of the many Patriots defenders who has never made a Pro Bowl: outside linebacker Tedy Bruschi. He is strong in two areas where overall NFL performance has been faltering, pursuit and tackling, and he is a steadier performer than the sack-focused Suggs.

Finally, this was the season that Ray Lewis was not only trumped as the best defensive player in football – probably by his own teammate, safety Ed Reed – but also as the best inside linebacker in football. While Lewis still makes a lot of noise, teams are no longer afraid to run at him, so long as they can double-team Gregg first. A bigger impact was made by San Diego’s Donnie Edwards, a strong tackler who also has a knack for the game-turning interception.

The inclusion of Edwards would help rectify the dubious omission of any San Diego defenders from the Pro Bowl. The Chargers’ surprise season was driven just as much by their defense as their offense. The Chargers ranked sixth in the NFL in fewest opposing yards per carry. While their pass defense was league-average when it came to net yards per pass, the Chargers were particularly strong preventing third down conversions.

Why did people have a hard time recognizing their improvement on defense? Because they were 27th in sacking opposing quarterbacks. For teams, as much as players, sacks make the headlines while a balanced defense wins games.

Mr. Schatz is the editor-in-chief of FootballOutsiders.com.