Kevin Seifert did an interesting study ranking NFL teams in order of the most original draft picks still on their rosters. The Green Bay Packers lead the way with 33. The Chicago Bears are last on the list with 15. The New York Giants rank a little below the middle of the pack with 23, tied with the Rams and the Chiefs for 18th. Of the 12 teams with fewer original picks still on the roster, all but the Cowboys and Saints have undergone a somewhat recent change in the front office that would help explain the phenomenon.
Of those 23 for the Giants, only eight project as starters, and numbers like these surely provide grist for the theory that the Giants haven't been drafting very well since Jerry Reese became their GM. That theory has some evidence behind it, for sure, but I'd like to point out a couple of mitigating factors here:
Eli Manning isn't counted as one of the 23 original picks still on the roster (or as one of the eight starters), because this is a computer-generated list and the Chargers technically picked Manning in 2004 before trading him to the Giants. So to be fair and accurate, you have to move the Giants up to 24, tied with the Bills and Dolphins for 16th, right in the middle of the NFL pack. Manning cost the Giants two picks in the 2004 draft and two picks in the 2005 draft, so that's a total of four picks that don't count toward this list but did produce their 10-year starting quarterback and two-time Super Bowl MVP.
Had this list been generated just three months ago, the Giants would have had 31 original picks still on the roster. Andre Brown, Hakeem Nicks, Linval Joseph, Justin Tuck, Corey Webster and Terrell Thomas all were free agents who didn't re-sign, and David Diehl and Brandon Jacobs retired. So this list catches the Giants at a period of unusual transition in their history -- a time when the core of a two-time Super Bowl championship roster was aging and in need of replacement.
Of course, to counter that last point, you could say that the evidence of poor drafting is that the Giants weren't able to replace those players with their own draft picks and instead found themselves having to sign 16 outside free agents. (One of whom, Mario Manningham, actually helped bring the number back up.)
The larger point here isn't necessarily about hitting on picks as much as it is maximizing the value of picks. The Giants haven't played the draft well enough in recent years to allow them to build and maintain a deep roster, and they paid the price for it with the free-agent roster turnover this offseason.