We certainly need to distinguish rookie UDFA's from those UDFA's who have eventually made an NFL team and have been contributors.
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1) The hope is that we sign ONE UDFA who can contribute as a backup (usually after injuries) in his rookie year. The expectation is that one or two make the 53 and have few reps as a rookie. Ponder was a fine success last year.
2) The hope is that 1-3 of our rookie UDFA's make the Practice Squad. These players might even be elevated later in the year or even be permanently promoted to the roster. Swinson is an example.
3) Hopefully, some of the UDFA's who are developed on the Practice Squad (and not poached) make the team in their 2nd or 3rd and become contributors or even end of the roster emergency players. One or two seem to make the 53 each year.
4) Successful teams pick up UDFA's who have not succeeded elsewhere. A successful example is Durden.
5) Finally, teams can pick up UDFA's who have played regularly, perhaps with some success, for several years in the league. A successful example here is Spillane.
6) As an aside, there is a 6th category: UDFA's who spend their rookie years on IR. Theoretically, they might make the 53 and become contributor in their 2nd year. I don't think that we have this situation on the patriots, certainly no this century.