Assist to Turnover ratio: Fool's gold?

In response to my last post, commenter Louis singles out the assist to turnover ratio as a statistic that is overvalued. I'm mostly in agreement with the point he makes, but I do want to quibble with it a little bit.

Louis says:

I would rather know a player’s steals-to-turnover ratio because stealing the ball is the opposite of giving it away.

I think he makes a good point here, and one that a number of statistical evaluation systems have taken into account. By comparing steals-to-turnovers you can see how many possessions a player gains for his team (i.e. steals) versus how many the player loses for his team (i.e. turnovers). Steals, like defensive rebounds, take a possession away from the other team and give it to your team. If anything, I think I'd want to broaden the category of "steals" to include other forced turnovers that do not get recorded as steals, such as charges taken and "over-the-backs" (is there a technical name for that violation?) drawn. A turnovers forced to turnovers committed ratio would identify the players that help a team win by creating additional possessions for their team. That said, I would point out that apart from their relationship to the number of possessions created/lost for a team, turnovers forced and turnovers committed have very little to do with one another. These measures involve very different skill-sets, and are unlikely (I would guess) to have much relationship to one another.

My quibble with Louis' point comes in here. Unlike Louis, I think that turnovers and assists are actually related to one another. Assist-to-turnover ratio is normally brought up when point guards are being evaluated, and I think there is a good reason for this relationship. The intuition is that the defense collapses when a point guard penetrates. The better the point guard, the more likely the point guard is going to be able to find the man that has been left open by the sagging defender. The worse the point guard, the more likely that his pass to the "open" man will be intercepted (either because he makes a physically bad pass or he was incorrect in believing that the man he was passing to was open). With this bit of intuition in hand, we can see that assist-to-turnover ratio can function as a proxy for a point guard's ability to drive and dish successfully.

Despite its ability to serve as a proxy for the ability to drive and dish, I still agree with Louis that assist-to-turnover ratio isn't a particularly useful statistic as currently used. I'll elaborate on my reasons for taking this position tomorrow. In the mean time, let me know what you think of my intuition regarding the assist-to-turnover ratio.