Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football

By Wayne Winston | Go to book overview

15
WOULD TED WILLIAMS HIT .406 TODAY?

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 PD1990 would hit 0.10 (or 100 points) higher than a batter hitting against PD1941. If PD1990 = —.10, that would mean a batter hitting against PD1990 would hit 0.10 (or 100 points) lower than a batter hitting against PD1941.

Since PD1941 = 0, simple algebra shows that

How can we estimate PD1942 — PD1941? Let's assume that the ability of all the 1941 hitters who were still playing in 1942 did not change from 1941 to 1942. Since young players tend to improve with experience and older players tend to lose ability over time, it seems reasonable to assume that the ability of a given cohort of players will not change much from year to year. Given this assumption, suppose the 1941 players who played in 1942 had a batting average (BA) of .260 in 1941 and .258 in 1942. This

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