In 1941 Ted Williams hit .406. If he were in his prime today (say, the 2006 season), could he still hit around .400? Across the United States arguments similar to the following take place every day: Could Bill Russell dominate Shaq? Who was better: Peyton Manning or Joe Montana? Of course we can't know for sure the answers to these questions. We can, however, use mathematics to determine whether today's players are superior to players from an earlier time.

Let's examine how hitters from the 1940s through the 1980s compare to the hitters in 1941. We will define the level of pitching + defense (PD) in 1941 (PD1941 for short) to be average. If, for example, PD1990 = .10, that would mean a batter hitting against ...

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