[mclellan36]

Originally Posted by Threnodas

The variability is actually even greater than the previous comment suggests. For a proportion P such as a batting average, the standard deviation after N observations (at-bats) is sqrt(P * (1-P) / N), and a 95% confidence interval is P +/- 2 * SD. So, for a .300 hitter, P = 0.3, 1-P = 0.7, and after 525 at-bats, the standard deviation is sqrt(0.3 * 0.7 / 525) = sqrt(21 / 100 / 525) = sqrt(1/2500) = 1/50 = 0.020. Thus, after 525 at-bats, you can only be 95% confident that a truly .300 hitter will have a season batting average anywhere between .260 and .340. The standard deviation only scales with the square root of N, too, so even after 4 seasons and 2100 at-bats, the .300 hitter's 95% confidence interval for their career batting average is still .280 to .320. The point is, baseball stats being displayed to 3 significant figures makes them seem much more authoritative than they really are, but outcomes are random, so relax.

Holy cow...I started reading this and I sprained my brain. I need to dust off my statistical analysis for dummies book!!