The NFL free agency period started on Friday, and all weekend the signings came fast and furious. San Francisco made Nate Clements the highest-paid defensive player in league history. The Patriots filled their hole at outside linebacker with highly regarded Adalius Thomas. The Jaguars filled their hole at right tackle with underrated Tony Pashos.

Meanwhile, the Giants, a team with a multitude of holes, did nothing.

The Giants went into the off-season needing help on the offensive line, depth in the defensive front seven, and a replacement for retired running back Tiki Barber. The best players at the first two positions are now all off the market. The best available running backs are still out there, but of the three holes, running back is the one where a draft pick or trade makes more sense than a free agent.

The one free agent who most interested the Giants was former Arizona left tackle Leonard Davis. The underachieving one-time fourth overall pick was one of the most popular players in free agency despite never making a Pro Bowl. The Giants offered plenty of money but lost out to the division rival Cowboys, who will pay Davis a seven-year, $50 million contract — the kind of contract that just two years ago was reserved for only the top handful of linemen in the NFL.

Davis wasn’t the only offensive lineman signed for big money. Guards Eric Steinbach, Kris Dielman, and Dennis Dockery all signed huge contracts, getting paid between $6 million and $7 million a season.

All this makes it even harder to figure out why the Giants released Luke Petitgout, their starter at left tackle since the middle of the 1999 season. Despite his tendency to draw false start penalties, his performance was in the top half of starting NFL left tackles. The move was supposed to be salary cap-related, but the Giants only saved $1.4 million on their 2007 cap; Petitgout was scheduled to make $5 million, and instead the Giants are carrying a dead-money cap charge of $3.6 million.

Petitgout missed the second half of last year with a broken leg, but that can’t be the reason for the release either; unlike an ACL tear or a shoulder problem, a broken bone is not an injury with long-lasting ramifications.

To make matters worse, Petitgout’s backup, 36-year-old Bob Whitfield, retired. That leaves David Diehl at the top of the depth chart at left tackle. The versatile Diehl has been a utility player on the Giants line the last four years, starting at both guard positions as well as right tackle. But left and right tackle are very different positions, and Diehl’s only NFL start at left tackle came in the recent playoff loss to Philadelphia.

Behind Diehl is Guy Whimper, a fourth-round pick in last year’s draft. But Whimper is a project player, and that project is far from completion. As for this year’s draft, top prospects Joe Thomas and Levi Brown will be long gone by the time the Giants pick at number 20, and none of the other players at the position is seen as someone who can start in the NFL right away.

The left tackle hole also creates a domino effect across the offense. A subpar left tackle means more pressure on quarterback Eli Manning, and more pressure on Manning means more overthrows and more interceptions. And if the Giants are stuck with Diehl as the starter, that opens another hole at left guard, where Diehl started most of last season. The Giants might have tried to fill that hole with Steinbach or Dielman, but now all the top guards are off the market.

The same is true for the top outside linebackers, which is a problem after the Giants cut LaVar Arrington and Carlos Emmons. Joey Porter, released by Pittsburgh, doesn’t fit into New York’s 4–3 scheme. Cato June of the Colts is still out there but has problems tackling and will end up a disappointment without safety Bob Sanders to clean up after his mistakes.

What’s left is for the Giants to sign a running back like Dominic Rhodes, a player who could replace Barber and partner with Brandon Jacobs. But why sign one of these players when the Giants could trade for Buffalo’s talented but disgruntled veteran Willis McGahee, or better yet, use the draft? Rookie running backs have an easier transition to the NFL than players at any other position.

A lot of mock drafts have the Giants taking California’s Marshawn Lynch at no. 20, but they don’t even need to pick that early. This year’s draft is filled with smaller, shiftier backs who can catch the ball out of the backfield and offer an alternative to Jacobs’s downhill running style. Lorenzo Booker of Florida State is a particularly intriguing prospect, the top blue chip high school prospect four years ago who never matched his potential. Booker was held back, in part, because the Florida State program has generally been in decline — and could prosper in the NFL, just like his old backfield mate, Leon Washington of the Jets.

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