Applying the standard stereotypes, you might think that your average role-playing group would have little to nothing in common with a group athletes.  You might also argue that role-players can learn nothing from athletic teams.  I would disagree, and I'd start by suggesting that role-players particularly look to a staple of team sports practices everywhere:  the post-game analysis.

I think there are two useful ways to approach the post-game analysis as an RPG player.  First and foremost, there's the group postgame.  As a "team" of sorts, you can always take a few minutes at the end of the night to talk through your favorite points of the session as well as one or two things that might have gone better.  Second, there's a sort of individual postgame that I like to call many worlds gaming.  I re-evaluate a few key moments from the session and look at other ways they could have gone, usually writing these down on my notes sheet during the session so I remember which moments I want to revisit afterward.

Team Postgaming Pitfalls

Let's address the team postgame first.  I think all GMs should encourage this, but it's a tricky thing to do properly.  There are a few common pitfalls - here are some that I have encountered in my time doing team postgaming.

First, there's always the problem of digressions and rambling.  This is just an extension of the problem of rambling and digressions during the session itself, and it can be handled in many of the same ways.  You can timebox players' responses, giving them only a minute or two each to note their favorite and least favorite parts.  You could also hand out sheets where the players could just jot down bullet points during the session - maybe 3-5 bullets of "loved it" and an equal number of "hated it."  There are other approaches; the key thing is to recognize that you might need to worry about this and address it up front.  I personally like to use a variant of the 3-5 bullet point approach.

Second, players might focus on problems that aren't precisely correctable (for example, an unlucky roll of the dice).  While these are easily dismissed as unfair, I think it's important for the GM to take the note anyway.  A little reflection on the GM's part might reveal a way that the situation could have been handled more smoothly.  Failing that, a short one-on-one with the player might also reveal a way to correct this type of problem in the future.  Perhaps, for example, the player whose character died as the result of a botch would have been satisfied had the character's death simply been described more "awesomely."

Finally, GMs can find it hard to handle honest criticism, especially if a player is angry at something that happened.  This is tricky in any case, of course.  I can't give any better advice for handling criticism than any of the multitude of business books on the subject.  What I can say, though, is that I view role-playing at its core as a team effort, and importantly, the GM and the players are on the same team.  Simply realizing this and building a rapport with your players early can go a long way toward making this criticism easier to take since the players will understand you're not out to get them, you're there to make sure everyone has fun.

Individual Postgaming

So there's the team postgame, but what about the many worlds postgame?  I'll give an example from my own role-playing experience.

In a recent game, I was trying out playing a character very unlike the character archetypes I normally play.  In doing so, I've been trying to put myself into the mindset of a person very different from myself.  In a session, the character came across a situation that he should have had little chance of understanding, at least not quickly.  I handled the situation in game as well as I could in the moment, but I recognized that my reactions were more my own than that character's.  I compromised partially in the interests of keeping the session moving along, and partially because I didn't think the situation was critical enough to the story that my flub would really have broken anything in the campaign.  However, I was disappointed in my handling of the situation for my own reasons; I felt that I really wasn't in the mind of my character and wasn't understanding his motivations and feelings.  Because I wanted to work on my gameplay for myself, I noted this situation.  Later, after the session was over, I ran through the scenario a few times on my own, thinking about other ways the character could have reacted.  I jotted down some quick notes on why he might have reacted in the different was and what he might have been feeling that would have driven him to those reactions.  None of this mattered for the campaign itself, but in doing this for myself, I feel more confident about playing this character for the rest of the campaign.

Final Notes

On a final note, I know that this might sound like a lot of work for just a game.  I want to emphasize that I don't think this postgaming should seem like work.  Postgaming can be quick and fun - 10 minutes after a session and/or 10-15 minutes thinking about your character on your own between sessions.  Perhaps it's my years of GMing influencing my playing style, but I find that I tend to think about gaming between sessions anyway because I enjoy doing so.  Postgaming like this just puts some minimal structure to how I think about gaming between sessions.  It also gives me the confidence to let myself be freer during the sessions, allowing me to be more in the moment and have more fun instead of worrying too much and over-thinking my character's actions.