Don't cry for me, Michael Tucker

Don't they get the picks BECAUSE he signed before the deadline? I thought the pre-deadline signing precluded any arbitration offer. Tucker wasn't offered arbitration, the Giants signed him early, thus they gave up the pick.

No, arbitration eligible FA MUST be offered arbitration by the deadline in order to receive their compensatory picks.  For FA who haven't signed elsewhere this can become a gamble for the offering team (a la Atlanta a few years back getting stuck with the huge arbitration award to Greg Maddux).  But, IF, the player has already signed with another team, the offer of arbitration is a no-risk way to accumulate compensatory draft picks.  The player can't accept the arbitration offer having already signed elsewhere, and the team offering arbitration is automatically awarded the signing team's appropriate pick and a sandwich pick.  In Tucker's case, had KC failed to offer him arbitration in the hours following his signing, the Giants would have kept their 1st round pick, thus foiling Sabean's master plan.  However, in that case, the offer of arbitration is typically de rigeur.  No team ever simply refuses to take the picks because their too cheap.  Hell, even Oakland took all those picks for the Moneyball draft even though they strained their budget and had to pick accordingly.  Florida's behavior in this last month is simply a mockery of sports franchise ownership.