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May 14, 2003

Lies, Damned Lies

Randomness: Catch the Fever!

by Nate Silver

Your favorite player hit .360 last season. If you know nothing else, what can you expect him to hit this season?

This isn't meant to be a trick question; let's assume the guy had at least 500 at bats in the previous season. Gates Brown and Shane Spencer need not apply. What's your best guess? .350? .340? Not likely.

The evidence is overwhelming. Let's look at all hitters since WWII who hit .350 or better in at least 500 at bats; the only other requirement is that they had at least 250 at bats in the year following.

Name			Year	BA (n) BA (n+1) Delta
-----------------------------------------------------
Aaron, Hank		1959	.355	.292	-.063
Boggs, Wade		1983	.361	.325	-.036
Boggs, Wade		1985	.368	.357	-.011
Boggs, Wade		1986	.357	.363	+.006
Boggs, Wade		1987	.363	.366	+.003
Boggs, Wade		1988	.366	.330	-.036
Boudreau, Lou		1948	.355	.284	-.071
Carew, Rod		1974	.364	.359	-.005
Carew, Rod		1975	.359	.331	-.028
Carew, Rod		1977	.388	.333	-.055
Cash, Norm		1961	.361	.243	-.118
Clemente, Roberto	1961	.351	.312	-.039
Clemente, Roberto	1967	.357	.291	-.066
Cooper, Cecil		1980	.352	.320	-.032
Erstad, Darin		2000	.355	.258	-.097
Garciaparra, Nomar	1999	.357	.372	+.015
Garr, Ralph		1974	.353	.278	-.075
Gwynn, Tony		1984	.351	.317	-.035
Gwynn, Tony		1987	.370	.313	-.057
Gwynn, Tony		1995	.368	.353	-.016
Gwynn, Tony		1997	.372	.321	-.051
Helton, Todd		2000	.372	.336	-.037
Kuenn, Harvey		1959	.353	.308	-.045
Madlock, Bill		1975	.354	.339	-.016
Mantle, Mickey		1956	.353	.365	+.012
Martinez, Edgar		1995	.356	.327	-.030
Mattingly, Don		1986	.352	.327	-.025
McGee, Willie		1985	.353	.256	-.097
Musial, Stan		1946	.365	.312	-.054
Musial, Stan		1948	.376	.338	-.038
Musial, Stan		1951	.355	.336	-.019
Musial, Stan		1957	.351	.337	-.014
Olerud, John		1993	.363	.297	-.066
Olerud, John		1998	.354	.298	-.056
Piazza, Mike		1997	.362	.328	-.034
Puckett, Kirby		1988	.356	.339	-.018
Rodriguez, Alex		1996	.358	.300	-.058
Torre, Joe		1971	.363	.289	-.074
Vernon, Mickey		1946	.353	.265	-.088
Walker, Harry		1947	.363	.292	-.070
Walker, Larry		1997	.366	.363	-.003
Williams, Ted		1948	.369	.343	-.027
-----------------------------------------------------
AVERAGE				.360	.319	-.041
MEDIAN				.358	.326	-.040

There were 42 hitters that met the criteria; on the average, they hit about .360 in the year in question. The next year?

• 38 of the 42 hitters (90%) saw a decline in their batting average;
• 13 of 42 (31%) failed to hit .300;
• The average drop-off in batting average was 41 points; the median drop-off in batting average was 40 points.

We don't need to whip this horse too much, since the data pretty much speaks for itself. It's a commonly stated stathead credo that batting average is subject to a higher degree of random fluctuation than most other components of offensive performance, and numbers like this are the reason why.