## Turnover "Efficiency"

The numbers show fairly conclusively that the best measures of passing and running proficiency are efficiency stats, i.e. yards per attempt. Efficiency stats correlate best with winning and "gross" stats such as total yards do not correlate well or at all.

But, as far as I know, no one has ever devised a turnover efficiency stat. Take David Carr, formerly of the Texans, for example. Everyone agrees that he threw a lot of interceptions, but why? Is it because he is a poor quarterback or is it because his team was very often behind and he was forced to throw very often to predictable routes? An interception rate stat can help answer that question.

Just like 'yards per pass attempt' is a better measure of passing proficiency than 'total passing yards,' so is 'interceptions per attempt' better than gross interceptions.

If I include gross interceptions in a regressing model, there is a strong inverse correlation between interceptions and winning. But we then run into the classic "correlation does not equal causation" fallacy. Because of the David Carr Effect, losing a game 'causes' interceptions to some degree.

In general, pass attempts are higher for losing teams than for winning teams. The team that is behind in a game will typically have a signficantly higher number of pass attempts than the winning team. In fact, pass attempts correlates negatively with wins at a weak but significant 0.17 coefficient.

Using interceptions per pass attempt instead of gross interceptions, therefore, helps reduce the backflow of causation in the correlation between wins and interceptions. Unfortunately, it also reduces the explanatory power of the model, but this is expected and actually good. It may not explain past game outcomes as well as using gross interceptions, but it may predict future outcomes better. Plus, turnover efficiency also helps prevent the causation backflow mentioned above as well as isolate the explanatory power of the other variables in the model.

Here is how the win-correlations break down for gross interceptions and interception efficiency:

Gross Int Thrown -0.51
Int/Pass Att -0.45

Gross Int Taken 0. 47
Int Taken/Pass Att 0.39