The Giants will attempt this weekend to accomplish the rare feat of going on the road in the playoffs and beating a team that swept them during the regular season. But there’s one big difference between the Giants team that lost to the Dallas Cowboys twice in 2007 and the team will take the field at Texas Stadium on Sunday: Ahmad Bradshaw.

Actually, since Bradshaw, the Giants’ rookie running back, is generously listed at 5 feet, 9 inches and weighs less than 200 pounds, he probably can’t be called a “big” difference. But the impact Bradshaw has on the Giants’ offense is huge.

The first two times the Giants played the Dallas Cowboys this NFL season, they didn’t know what they had in Bradshaw, a seventh-round pick in the 2007 draft. Bradshaw played in both games, but only on special teams, as he was buried on the running back depth chart behind Brandon Jacobs, Derrick Ward and Reuben Droughns.

It wasn’t until Week 16 of the NFL season, against the Buffalo Bills, when the Giants found out what kind of offensive threat Bradshaw can be. Injuries to the other running backs gave the Giants no choice but to give Bradshaw the bulk of the workload. He responded with 17 carries for 151 yards in a victory that would clinch a playoff spot.

In Sunday’s playoff victory against the Tampa Bay Buccaneers, Bradshaw’s role in the offense was even more important, even if his statistics weren’t as impressive. Bradshaw had 66 yards on 17 carries, but several of those runs carried the Giants to victory in the fourth quarter. Of the Giants’ first 11 plays in the fourth quarter, seven were handoffs to Bradshaw. Those seven went for gains of seven, eight, six, six, six, one and four yards, and they kept alive a 15-play, 92-yard touchdown drive.

The first run of the fourth quarter showed how tough Bradshaw can be: He took a handoff and was hit at the line of scrimmage by Tampa Bay defensive end Gaines Adams. He then bounced to the outside, where three more Buccaneers hit him. At that point he had his helmet knocked off, but he lunged forward for five more yards with his bare head exposed. It was that tough running that put the Giants in complete control of the game and set them up for their playoff rematch in Dallas, where Giants offensive coordinator Kevin Gilbride needs to give the Cowboys a healthy dose of Bradshaw. Although Jacobs has earned the starting job this season, Bradshaw was more effective than Jacobs in the two games they split carries, against the Buccaneers and Bills, and that means Bradshaw needs to get the ball against the Cowboys, even if that means fewer carries than usual for Jacobs.

What makes Bradshaw a special runner is the way he slashes through holes in the line of scrimmage. Most running backs who are small and fast, like Bradshaw, have a tendency to dance around behind the line of scrimmage and avoid contact as they look to break long runs. Bradshaw doesn’t do that. He lowers his shoulders and explodes through holes the way a bigger runner would. Once he gets past the line, however, he has the speed to outrun opposing linebackers and defensive backs, as he did on the 88-yard touchdown run that broke open the Buffalo game. The Giants drafted Bradshaw in 2007 mostly as an afterthought. He hadn’t done anything in college that would make him stand out to NFL scouts; he first enrolled at Virginia but coach Al Groh (the former Jets coach) kicked him off the team before he ever played a game because of an arrest for underage drinking. He then transferred to Marshall and played well, although nowhere near well enough in the eyes of most observers to justify his decision to leave school early and enter the draft.

But Bradshaw earned a spot on the regular-season roster as the Giants’ kickoff returner, and that’s where he opened the year in Week 1 against the Cowboys. The only noteworthy thing he did in that game, however, was fumble. He fumbled again the next week, and as a marginal player just trying to stick on the roster, he’s lucky those fumbles didn’t cost him his job.

But he hasn’t fumbled since then, and it’s more than just luck that Bradshaw is on the Giants’ roster: It’s a credit to Giants general manager Jerry Reese that he saw something in Bradshaw and took a shot on him in the seventh round. In fact, the Giants appear to have had one of the best 2007 drafts of any team in the NFL. All eight members of the Giants’ 2007 draft class were on the field for the Giants against Tampa Bay, which is a good sign that the Giants have stocked their roster with a lot of young talent.

It now appears that the most talented of the eight was Bradshaw, the last one drafted, and the Cowboys haven’t yet seen what the Giants’ offense looks like with him in the lineup.

Mr. Smith is a writer for FootballOutsiders.com.