If a variable has a weak correlation can you take the inverse of that variable to mean strong correlation?

Question

I'm doing a feature selection to determine what variable correlate most with NFL teams covering the spread. If I have a variable that represents the number of people who have bet on one side of the spread that is weakly correlated with the outcome can I use the inverse to say going against whatever number I have is strongly correlated?

Example:

I have team A playing. They have a spread of -3.5 ( which means they are projected to win by 3.5 points) and 65% of all public bets are on team A to cover said spread (win by 3.5 or more points) and the feature selection tells me that spread percentage has a 17% correlation to teams covering the spread. Can I say that going against the public and betting the other side would have a 83% correlation to winning?

Answer 1

No.

If you find a correlation between a continuous variable and some event has some value r, the correlation between that variable and the negation of that event is not 1-r, but -r. If the spread percentage has a correlation of 0.17 with the team winning, it has a correlation of -0.17 with the team losing.

Think of it this way - the positive correlation of the original comparison shows that the public is generally correct. The more people that bet on Team A to cover the spread, the more likely they are to win (positive correlation). You can't do better than a strategy that already works by doing the opposite.

As another example, imagine a completely uninformative variable, with zero correlation between the variable and the outcome. Taking some transformation of the uninformative variable does not somehow imbue it with perfect predictive power that is 100% correlated with the target.