A broad rule of thumb: for every 20 possible data sets you cover in your trawl, you should expect to find about 1 "statistically significant" correlation that'

A broad rule of thumb: for every 20 possible data sets you cover in your trawl, you should expect to find about 1 "statistically significant" correlation that's actually a fluke (at 95% confidence, using naive statistics). If you're digging through a massive data set looking for correlations, you need to account for that, and use more advanced statistical methods. Sportscasters often do exactly the opposite -- they quote results that aren't even particularly statistically significant (say, a 30% shooter making 3-of-4) and act as though it shows a player is "playing well" and should be trusted to continue the trend.