I would assume his responsibilities are to construct a scheme for coverages of punts and kicks as well as blocking responsibilities for the kick off, punt and FG units. I don't see how he can't be the main guy who chooses those players to be in those schemes...he should be the guy who chooses his kickers and the HC would sign off....So long winded short he is /should be responsible for the problems.
If he chooses a kicker with problems he should have the means to teach, mentor, coach the guy out of those issues....It's obvious he did squat with the 1st kid, or the kid would not take to coaching, if it was the later then the coach has to have some responsibility there as well if he picking uncoachable players.
I think the issue with this unit is to the extreme.....never seen kickers that seem to be so lacking in even basic efficiency....end zone kick offs or kicks inside a 50 yard distance....so far they have all been very bad.....The only common denominator is the ST Coach....I feel the same with his coverage teams.
