This one will be short. I've discussed how on base percentage (OBP) is more closely linked to run production than batting average, and how slugging percentage (SLG) is more closely linked to run production than batting average. The conclusion is that if you want to evaluate a batter, his batting average is OK, but his on base percentage and slugging percentage are better indicators of how good he is. The slash line--batting average/on base percentage/slugging percentage, like .319/.391/.534 for Yasiel Puig--combines all three.
But there's an even better measure. The correlation between OBP and runs is .88, which is good. The correlation between SLG and runs is .90, which is better. But if you combine the two, adding on base percentage and slugging percentage, you get a new measure, on base plus slugging, or OPS. The correlation between OPS and runs since 1995 is 0.94. That's really, really high. It means that OPS alone can explain 88% of run scoring.
OPS is not an esoteric stat. Watch ballgames, or read baseball articles, or watch Baseball Tonight, and you'll probably hear OPS mentioned. And when you do, you're hearing a single number that does a great job of describing a batter's skill.
What's a good OPS? There were 24 major leaguers who batted .300 last year. The 24th-ranked OPS was .845, Giancarlo Stanton. So let's say that an .850 OPS is like a .300 batting average.