If I might make a follow on comment in respect of PEI's post (and I do so cautiously, having a high regard for his background and experience), "normal" certification stuff is based on presumptions incorporated into the Design Standards (with a bit of fat here and there for mum and the kids and which serve us very well most of the time). However, if the conditions on the day vary significantly (and adversely) from those embodied in the presumptions, then things rapidly can get to the "all bets are off" stage.
Examples which come to mind include windshear and strong crosswind from the wrong side/OEI case on a min speed Vmcg-limited departure, and so forth. Either the Commander sticks with the trained protocol (windshear is a good case in question) or he/she may have to do something innovative eg with the strong crosswind/OEI situation. In the former, severely degraded performance capability may rapidly result in loss of control while, in the latter, there is high probability that control will be lost concurrent with the engine failure, albeit that the aircraft may well be somewhat above min V1.
Ergo, some days it just doesn't pay to get out of bed albeit folk such as Haynes, Sullenberger et al occasionally manage to pull it all together on the day. On other occasions, eg AF 4590, even though Marty (from what I could discern from available reading material) did everything he needed to do near perfectly, the aircraft just refused to sit up and perform the required tricks in its dreadfully degraded performance state.
As I am fond of observing, there are no guarantees, only probabilities and presumptions.