I'm a student, so I can't really answer the OP's question, but I thought it was interesting so started thinking about it.
For everything below, I'm going to define success in terms of on-field success (i.e. how well a team's robot works). Not necessarily winning the event, but having a competitive robot and the potential to win. Similarly, I define failure not as being a finalist or making a few mistakes at competition, but not being a competitor at all.
Inspiration
We've all heard it: FIRST is about inspiration. For some students, failure will be inspiring. They prefer to just try things out and see from themselves what comes out of it. However, I believe that for most, success will be more so. Telling someone "you can do this" versus "you might be able to do this" sends a stronger message. It really varies by person though--I have friends on all sides of this issue.
But I think there is a danger with failure. If you're successful, at worst students will be indifferent. If you're not, they might learn that "this is hard" or "I can't do this" and no longer want to go into engineering / STEM / etc.
There's also the possibility of a greater impact with success. Successful teams have the power to inspire not only their own students, but students around the world. I've been pushed by what I've designed and built to do better next time, but seeing other teams' robots has inspired me more than anything else, and given me a goal to push towards.
There is definitely a power in failure. I just don't think competition is the place to do so. And not to the extent that I've defined it as. Learning from mistakes, testing out ideas that don't work, and "failing" during prototyping is great. Just keep it all in context. Failure as a motivation to do better helps; failure as an end does not.
Learning
I think the question was more focused on whether you learn more from success or failure. Again, I think it's both. If you never lose, you never learn why you need to try hard. If you never win, you never learn why you
are trying hard.
For more specific lessons, such as the original example about developing a strategy, I think the lessons will be more ingrained if they come from failure. A couple of friends and I came up with a list of "things we are never putting on our robot again." (Mainly rope, especially when used to move stuff.) Had we not used them in the first place, and just been told it wouldn't work, we might never have understood why not to. But the lesson came with a price. Here it was just that we had to deal with rope for one season. It could have been much more, and seriously affected points above.
This may not be the best example because the rope wasn't something we were warned against, but the only solution anyone could come up with. There were mentors who helped with it.
I believe the strongest lesson a mentor can teach is
how to succeed. It can come by guiding students through the process, letting them experiment themselves, or some combination of the two. It will really depend on the team, and what the mentors / students believe.
In the end
I think I've rambled on enough...in the end, what I'd say is to show students how to succeed, but make sure they understand why. Use the offseason and prototyping as a time to try out all sorts of ideas and see what does and doesn't work. Don't let it come at the price of failure at competition, but that doesn't mean to not experiment.
And it'd vary by teams. What mentors are / are not able or willing to do, what students want / don't want to do, and everything else. The best balance is what both groups compromise on and believe is best for the team as a whole.
Random thoughts
Quote:
Originally Posted by Ginger Power
Meanwhile many other teams who resent mentor-built-robots [...]
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This is an interesting point. There are many people who don't believe in mentor-run, but who are fine with other teams doing whatever they think is best. (i.e. "you inspire your way.") I've always believed that people who actually resent mentor-built robots / mentor-run teams are those who are jealous of their success or frustrated with their own failure. I guess that's another danger of failing: putting down those who are more successful in order to make yourself feel better. It's another lesson I think mentors should be teaching students: how to avoid that thinking, and how to cope with failure because at some point, everyone will experience it.
(I'm not trying to get into a mentor-run/built debate; I just wanted to respond to that.)
Wow, that was long...