Investor Sentiment and other Dumb Statistics

 I just read an interesting post on this weekend's Saints-Texans game (National Football League). The writer (Kerry J. Byrne) says

The 2010 Texans, for example, were dead last in Defensive Passer Rating (100.5), the best way to measure pass defenses because it consistently has a high correlation to wins and losses. Champions throughout history are almost always among the very best in the league at Defensive Passer Rating.

But, do teams win because they have good passing defenses? Or, do teams get ahead, then sit back in a "prevent defense" (5 or 6 defensive backs), against which it is more difficult to throw the ball? Also: the defensive linemen can "pin their ears back" and go after the passer, knowing that their hapless opponents are trailing late in the game and don't have time for a long, time-consuming drive.

To test Mr. Byrne's theory, we need to look at the data in a slightly different way. Does Defensive Passer Rating in the First Quarter also have a high correlation with wins and losses? Presumably, the game is more likely to be competitive in the first quarter than in the fourth. Does DPR show a better correlation to success than other statistics? Obviously, a team with a good pass defense will win more than a team with a lousy pass defense, but is this stat really a superior predictor? I'd be really interested to see the data broken down this way.

My favorite dumb football statistic is the  relationship between having a 100-yard rusher and winning the game (not so common these days, as the NFL has become a passing-dominated league). It used to be that, when a back reached 100 yards rushing, a graphic would flash on the screen, like "Bears are 53-24 (.688) when Walter Payton rushed for at least 100 yards and 58-58 (.500) when he doesn't." Maybe the Bears won because Payton went for 100. Or, maybe they got ahead, then ran out the clock by giving "the rock" to one of the NFL's all-time greats.

Investor Sentiment numbers are a dumb stock market statistic. If you pay attention to these numbers, you will see that sentiment follows the market. Investors become fearful after the market goes down, and greedy after it goes up...sentiment is worthless as a predictor! This chart from wallstreetcourier.com illustrates this point perfectly.

So, when you find a correlation that seems too good to be true, ask yourself if A really causes B, or does B cause A, or maybe an external factor C causes both A and B.

The lesson, of course: Correlation does not mean causation. Tweet