Each week, Washington Redskins Coach Joe Gibbs receives a package from his old buddy Dick Vermeil, detailing the bleak odds of winning NFL games when teams turn the ball over more often than they take it away. Much has changed since these grandfathers were in their coaching heyday 20 years ago, but this statistic still reigns supreme and was reinforced in the coaches' reunion today when Vermeil's Chiefs trumped Gibbs's Redskins, 28-21, at Arrowhead Stadium, largely because of turnover margin.

The Redskins have lived dangerously throughout this season, and after defying the football gods for three weeks by winning despite losing the turnover battle, they have dropped successive close games based on a failure to reverse that trend. Kansas City caused three fumbles, leading directly to 10 points, including a game-swinging 80-yard return, while Washington went without forcing a turnover for the fourth straight game. NFL teams entered this weekend 1-17 when going 0-3 on turnover differential, a fact that Gibbs and Vermeil can cite endlessly.

"I've got to do some creative thinking about it," Gibbs, 64, said of the lengthy turnover drought. "We do a lot of stuff to emphasize turnovers and taking the ball away in practice. I probably need to think long and hard about it myself."

His counterpart has it figured out. "We took the ball away and won the football game," said Vermeil, 68. "If we don't take it away, we don't win the game."

For the second straight week the Redskins outgained an opponent by more than 100 yards; quarterback Mark Brunell (25 of 41 for 331 yards, three touchdowns and a sparkling 110.9 rating) went over 300 yards in consecutive games for the first time since the start of the 2000 season (62 appearances), wide receiver Santana Moss had a career-best 173 yards receiving and the Chiefs' vaunted rushing attack was stifled (3.0 yards per carry). Still, Washington lost, sporting a minus-8 turnover differential through five games.

Kansas City's second-year end Jared Allen did what the Redskins' aggressive defense could not -- make big plays. Allen had three sacks -- Washington has five all season. He forced or helped cause all three fumbles and recovered two (Washington has two take-aways all season). He bettered both of the Redskins' powerful tackles at times, getting around Jon Jansen and Chris Samuels for sacks, and delivered a huge blow to reserve running back Rock Cartwright that dislodged the ball, leading to safety Sammy Knight's 80-yard return for a touchdown, giving the Chiefs a 21-14 lead in the third quarter.

"He's a player on the rise," Chiefs defensive end Eric Hicks said of Allen. "And I guess you could say he arrived today."

Knight's return was one of three plays of 60 yards or longer during a 13-minute second-half span when the teams combined for 36 points. Kansas City produced two of those plays, enough for the win. The Redskins led 7-6 at the half, and the Chiefs went ahead on Priest Holmes's six-yard run on the first drive of the third quarter. Quarterback Trent Green, a former Redskin, converted the two-point conversion with a lob that wide receiver Marc Boerigter out-leaped rookie cornerback Carlos Rogers to snag.

The Redskins tied the game at 14 with one perfectly scripted play. On second and 19, Moss lined up wide left, with tight end Robert Royal outside Samuels, the left tackle, and H-back Chris Cooley in motion to the right. In a flash, Moss took three steps inside to catch a screen pass, while Royal sprinted to the left sideline to block safety William Bartee, who read the screen correctly, out of bounds. Samuels kicked out left as well and pummeled defensive end Kendrell Bell, creating a huge vacuum down the left sideline. Moss, an explosive sprinter, never looked back, racing past Knight's dive and going 78 yards for the longest score of his career, and second touchdown of 70 yards or longer this season.

"I think it was one of the prettiest plays I've ever seen," Gibbs said.

Washington gave those points back on its next possession, however. Cartwright replaced Clinton Portis, who was beaten and bruised and unable to continue his past dominance over this franchise, on second and three from the Kansas City 25, when he raced right, was tackled by defensive end Carlos Hall and then finished off by Allen; the ball squirted free and Knight dashed down the right sideline for a 21-14 lead with just less than 21 minutes to play.

"There's no excuse," said Cartwright, who did not have a carry this season before Sunday. "I shouldn't have fumbled the ball, and it cost us seven points. It was a huge play. It was crucial."

Portis, tying a career worst with a seven-game touchdown slump, reentered the game during Washington's next drive, an illegal contact penalty negated Brunell's interception in the end zone, and Cooley caught an 11-yard touchdown pass to cap a 67-yard drive with 30 seconds remaining in the third quarter. Washington's offense was done for the afternoon, but the Chiefs had another huge play left in them.

Holmes caught a screen pass on the left side on the third play of the fourth quarter, and turned it into a 60-yard masterpiece, a patient and intuitive tango from one sideline to the other culminating in a well-balanced tiptoe inside the right pylon for a score. Strong-side linebacker Marcus Washington might have had a shot, but was blocked early, rendering his late sprint obsolete. As Holmes, a perennial Pro Bowler, navigated the interior of the field, Rogers fell and as he rounded the corner to the right sideline, cornerback Walt Harris dived in vain.

"Obviously, he made a heck of a play," defensive end Renaldo Wynn said. "But all I know is when we got to the sidelines the coaches were saying we have to tackle better. That's two weeks in a row that big plays and missed tackles have cost us."

The first half was not nearly as flashy. Allen reached beyond Samuels to strip Brunell at the Kansas City 18, then recovered it himself. Lawrence Tynes capped the ensuing 80-yard drive with a 20-yard field goal for a 3-0 lead. Brunell and Moss connected three times for 52 yards, including a four-yard touchdown, on the next drive to grab the lead, and Tynes was good from 38 yards to cut it to 7-6 in the second quarter. Any chance the Redskins had of padding the lead died late in the half when Allen nailed Brunell on a scramble. The quarterback bounced off safety Jerome Woods and Allen pounced on the loose ball.

Another game; another turnover misadventure (or three). "It's been the same story we've been singing all year long," Portis said. "Turnovers and penalties. Turnovers and penalties. Nothing's changed."

The tune is sweet music to Vermeil's ears, while his old friend in Washington still finds it haunting.

Kansas City Chiefs running back Priest Holmes remains a step ahead of Redskins linebacker Marcus Washington on his way to a 60-yard touchdown off a screen pass from quarterback Trent Green.Redskins quarterback Mark Brunell is sacked by Chiefs defensive tackle John Browning during the second quarter at Arrowhead Stadium.Redskins wide receiver Santana Moss leaves behind Kansas City defensive back Sammy Knight on a 78-yard touchdown reception in the third quarter.