To do one's best at rock climbing and remain safe, one should prepare for the worst, and think the best, and when deciding whether to climb a particular face under given circumstances, make an objective judgment of the difficulty and risk.
a. Prepare for the worst — when making preparations, assume the worst case scenario. If you can do something to increase safety in the event of a problem (e.g., a runner unexpectedly comes out), assume the problem will arise, and take action to ensure safety nonetheless.
b. Think the best — focus on the goal, rather than a potential fall. Being well prepared and attentive, so that you climb with care and will react rightly and quickly to any incidents, will help you climb well and increase your safety. But being afraid of falling won't help you climb well. Having done all you can to increase safety and decrease the risk of falling, and being attentive so that you can react quickly if a piece of stone breaks off, a runner comes out, a climbing starts falling, etc., it's better to focus on the intended goal of climbing successfully than the possibility of a failure and fall.
c. When deciding whether to make a climb, it's best to make an objective assessment of it. One shouldn't ignore the risks (assuming the best), but there is also no need to pretend they are worse than they are (assuming the worst).
I find these three ways of relating to risk in rock climbing a good analogy to three ways St. Thomas Aquinas gives of making judgment about things or persons. In a Summa article on whether doubtful matters should be decided in the more favorable/more charitable fashion, ST II-II, q. 60, a. 4, he makes a threefold distinction:
a. When making an assessment about a possible evil of a person in order to remedy it, one should in doubtful matters incline towards assuming the worst. (E.g., if you see signs of someone abusing alcohol, and if you can act in such a way as to help him if your suspicions are accurate (without harming him if your suspicions turn out to be inaccurate), than you should do so, rather than assuming the best, and failing to act.) (ad 3)
b. When making an assessment about a fault or vice of a person in himself, one should in doubtful matters assume the best, even if it is objectively less likely — it's much better to be wrong in assuming the best of someone, than to be wrong in assuming the worst of someone. (Again, in the situation where you see signs of someone abusing alcohol, you should, as regards your attitude toward that person, assume the best — should not think less of his character or virtue due to this suspicion) (ad 3)
c. When making an assessment about things, one should make a judgment according to what is most probable.
As in rock climbing, to the extent that you can hinder an evil by assuming the worst and preparing for it, you should do so, so also, to the extent that you can hinder a potential vice of someone by assuming the worst and acting to hinder it, you should do so.
Yet as, in regards to the possibility of falling, having taking all the steps to increase safety, and avoiding entering into an excessively risky situation, you should climb with confidence rather than fear, so also, in regards to the person's own character, your attitude should be positive, looking to the virtue you hope he has, rather than to a vice that he might have.