One of the nice things about projection systems is that they are able to sift through a large amount of data and very quickly give out an objective, baseline estimate. I frequently disagree with my own projections, simply because a human has different strengths and weaknesses than a computer. But not everyone has quick access to a projection system and, given the lack of desirability of having everyone who wants to see a projection come hang out with me in my office, some eyeballing is generally required.
One of the terms you see a lot in talking about different statistics is whether something has "predictive value." To put it in simple terms, it means what numbers do the best job at predicting future numbers. When you're looking at a player's stats, especially players who have a great deal of performance change in a season, just knowing which stats have predictive value and which do not gets you a lot of the way towards making an estimated projection of your own.
For each stat, I'm quoting the coefficient of determination, most commonly expressed as r^2, for each of the statistics in question. If you see something with an r^2 of 0.60, that simply means, in this case, that the stat in the first year explained 60 percent of the variance of the stat in the second year. Now, modeling is a lot more complex than simply r^2, but as a rough measure of which statistics are most predictive, it's quite useful.
Let's start with the hitters.