There's been a lot of noise here and on other boards about whether statistical analysis is the be-all end-all of baseball analysis or whether what you see with your eye trumps what some guy can produce on his excel spreadsheet. My personal take on the matter follows below. Hopefully we can have a productive discussion.
Statistics can tell us two things: what has already happened and what is likely to happen, with a certain degree of confidence. Statistics cannot guarantee that anything will happen -- only what is likely or unlikely to happen. Another important point to consider regarding statistics is the issue of "sample size", specificaly having enough "measurements" to fully capture the distribution of results. Baseball in my view is very amenable to statistical analysis, because there are a great number of results that can be catalogued, followed, and analyzed -- it is relatively easy to generate a large enough sample size for a large number of things.
Often, the debate with respect to statistics centers around outliers -- results that seem to be far away from what is viewed to be the average. If you believe that all the results in baseball are normally distributed, then it is reasonable to expect that results far away from the average are unlikely to occur. What people are arguing then, is whether an outlier is really an unlikely (often referred to as lucky / unlucky) event, or whether something has fundamentally changed the distribution of the results.
An example of an outlier could be McCann's eyesight as it relates to his offense -- at the start of the year, he struggled with the bat. His performance was below his career averages, and it was discovered that he could not see the baseball. Thus if nothing was done to correct the problem, then he probably would have had a terrible year. Fortunately, his problem was diagnosed and corrected, and now his performance is much closer to career averages, if not above.
In my view, when a discussion of statistics vs. "what I see" evolves, the only issue worth discussing is whether something has occurred that has changed the distribution of results. The problem with the "what I see" argument is that it is entirely subjective, and can only be evaluated by the observer. People often can look at the same situation and see different things -- whether a pitch is a ball or a strike for instance. Statistics have an advantage in this regard in that they are objective and can be evaluated by anyone. The disadvantage is that statistics often do not correlate perfectly with results and there is always room for debate to determine which statistic correlates better with the result of interest.
Finally, in my opinion, many of the "modern" statistics do a good job of predicting what will happen with a level of confidence that is adequate for me. At the same time, I acknowledge that it is entirely possible that KJ's suckiness and Raul Ibanez' awesomeness are results of some fundamental change in the way they are playing the game this year vs. previous years. Maybe KJ should have given Joe Boo a live chicken instead of the KFC, who knows. But I'll choose to believe stats more often than what someone sees, because as I argue above, I have no way to judge for myself how valid or not someone else's observation is.