There's not a huge range of values for established, healthy prime-age players like Dustin Pedroia or Robinson Cano. Maybe you get them for $1 cheaper than you thought, or someone pays $2 more, but for the most part, we know where they slot. The more interesting and variant players are ones whose past performance (as measured by their stats) made a sharp jump or decline last year, and also those who due to youth and inexperience, or injuries and age, might change dramatically. The question when evaluating these more difficult players is how to interpret their past performance. Or, put differently, how much to ignore it.
At the risk of making a point so obvious it insults one's intelligence, past performance does not have any causal effect on this year's stats. That is, a home run or 30 hit in 2011 does not cause a ball to carry over the fence in 2012. Past-season base hits exert no physical force on subsequent balls in the field of play. Previous seasons' numbers are merely indicators of future performance, but present skills and opportunity are what determine it. It's easy to confuse the two as past statistical performance is one of the major tools we use to evaluate present skills, and so sometimes one conflates them. In the case of established players for whom little has changed, this is often an inconsequential error. In the case of volatile ones, it can cost you a chance to win your league.
A few examples of difficult-to-value players are Adam Dunn, Chone Figgins, Francisco Liriano, Brian Matusz, Phil Hughes, Alex Rodriguez, Carl Crawford and Hanley Ramirez on the one hand, and Jacoby Ellsbury, Curtis Granderson and Brett Lawrie on the other. The numbers they put up last year aren't going to impact the numbers they put up this year except insofar as they affect playing time. But assuming all will play - which they will if they produce this year - how do evaluate them for 2012?
Dunn is hitting for power and displaying a strong batting eye this spring. He's apparently in better shape and not dealing with surgery to remove his appendix as he was last year. He's no longer adjusting to a new league, a new city and his first go-round as the DH. These are the relevant variables when deciding what Dunn will do this year. Not the historically putrid 2011 stats he put up.
You can do a similar analysis with each of these players. What are his skills? How is his health? How have his circumstances changed? Last year's stats only matter insofar as they help you discern a player's skills. In and of themselves, they mean nothing.
For that reason I tend to buy players with bad 2011 stats as long as they seem healthy and should continue to have opportunities. I'll buy younger players whose performances could take significant leaps given their increased experience. I'll also buy players coming off career years whose performances are supported by their skills and circumstances where the market doubts them. I'll even buy older players who seem to be in an age-related decline, so long as there was an extenuating circumstance, like a non-chronic injury.