First the simple question: the gap between Phase I end and Phase II start is often quite long. There are other process and IP-related issues (with DoD, NSF mig

First the simple question: the gap between Phase I end and Phase II start is often quite long. There are other process and IP-related issues (with DoD, NSF might be different). Your estimate assumes that if you compete you have at least an average ability to win. This is very probably an inaccurate assumption. In my opinion, if you go in cold you are unlikely to have an average probability of winning on even a minority of the topics unless you are highly expert in the field of the topic and bring something utterly original yet reasonable to execute for the funding. Assuming you do know the topic at a far-above-average level - you might not know how to write a good proposal, or understand what the proposer is really asking for, or be seen to be able to execute successfully, or be able to commercialize the result of the effort (maybe not as important to NSF as of a few years back) to name a few; but you get the idea. Fundamentally, your odds depend on a fit with the topic and your personal ability to execute this type of process. That is why your odds go up after you successfully execute once. Lastly, do a lot of legwork before proposing - figure a generous amount of out-of-the-chair legwork into your expected value calculations. Look around for colleagues that have done this and pick their brains.