Who was the all-time greatest hitter?
A lot depends on how much weight you give to batting average versus power hitting. But it would be hard to consider someone for the title of the all-time greatest hitter if someone else had both a higher lifetime batting average and a higher lifetime slugging average. That narrows down the list considerably.
The highest lifetime batting average was Ty Cobb's .367. But Rogers Hornsby hit .358 and, being far more of a home-run hitter, Hornsby had a higher lifetime slugging average than Cobb. No one had both a higher lifetime batting average and a higher lifetime slugging average than Cobb or Hornsby. Both of them therefore belong on the short list of candidates.
Babe Ruth had by far the highest lifetime slugging average -- .690. Batting averages count how many hits there are in how many official times at bat. Slugging averages count how many total bases there are from these hits -- counting a single as one base and a home run as four, for example.
If you get two singles and a double every 10 times at bat, then your batting average is .300, and your four total bases mean that your slugging average is .400. If you get two singles and a home run, then your six bases give you a slugging average of .600.
Babe Ruth's lifetime slugging average of .690 means that he averaged nearly 7 total bases every 10 times at bat. That would mean something like a single, a double and a home run every 10 times at bat -- over a span of 22 years.
Some great sluggers, in their best seasons, have had slugging averages of .700 or more, usually once or twice in a lifetime. Only two players -- Babe Ruth and Barry Bonds -- ever had a slugging average over .800 in a season. That's equivalent to two singles, a double and a home run every 10 times at bat, all season long.
But if we are talking about the all-time greatest hitters, we usually mean over the course of a career, not just in a particular season when a batter was hot.
To put the Babe's .690 lifetime slugging average in perspective, even such great sluggers as Hank Aaron, Willie Mays, Joe DiMaggio and Hank Greenberg, in their greatest seasons, never had a slugging average as high as the .690 that Babe Ruth had for his whole career. So the Babe makes the short list.