I was in Europe, on Eurex and Euronext from 2002-2010... no pit experience unfortunately... would've loved that.
Obviously, the only way you could TELL in advance that anything is mispriced is if it's an arbritrage. What I mean when I say "you think that X is mispriced" is that one makes a prediction of some sort (relative value, absolute value etc) and makes a bet on this prediction being correct. If your prediction methodology is good, you will be correct more frequently in dollar-weighted terms. Simply identifying that X is rich or cheap vs history (even a 100 years of history) is not good enough. A good monkey knows whose banana he's stealing - e.g. if I am making a prediction that something is over/under priced, I usually try to identify why. There are no free lunches, there are only cheap lunches, so before biting into it check for rocks and broken glass. Trading as a prop trader is vastly different from trading as a market maker (I have done both). In case of being an MM you serve as a provider of liquidity in exchange for the vig and most of your risk is due to informational asymmetry. You have the stiatistical edge by definition, the more you trade the better off you are. As a propster, you are willing to pay vig to take advantage of informational asymmetry (in whatever form, be it statistical analysis, inside knowledge or synthetic understanding of expected supply and demand).
I'll add one more thing. Every monetary decision you'll ever make will be a tug of war between your goals, your emotions and the self-interest of any middle men involved. It is very useful to break down every situation using these three "principal components". It is definitely true in the context of proprietary trading, but just as true in car shopping, selling your home or buying a Gucci bag for your girlfriend.
Statistical analysis being a proprietary model that identifies a statistical anomaly which can be exploited with a positive expected return. Inside knowledge being knowing something the market does not. Synthetic understanding of expected supply and demand being something along the lines of order flow access. Would you say these are apt elaborations of your description of informational asymmetries?
Yes. In some cases it's a combination of a few of these - e.g. if you have a good knowledge of the structured product issueance, it combines expectations of supply and demand with some insider knowledge (if you know that something is coming due or being issued).