More on the assist-to-turnover ratio

If I think the intuition behind using assist-to-turnover ratio to evaluate point guards is that it can be a proxy for the PG's ability to drive and dish, then why don't I think this ratio is particularly useful?

First, just because something can be a proxy doesn't mean that it is going to be a GOOD proxy. A point guard gets credit for assists (and the blame for turnovers) that occur off of set plays and other situations that do not involve him driving and dishing. Turnovers are still bad and assists are still good in these situations, but when these statistics are included in an assist-to-turnover ratio, then that ratio can no longer serve as a useful proxy for evaluating a PG's ability to drive and dish. If the powers-that-be decide to compile an assist-to-turnover ratio that only includes drives into the lane, then we'd have a useful proxy.

The second reason I think assist-to-turnover ratio is not particularly useful is because it treats all passes the same. A higher assist-to-turnover ratio is always considered better, but that just isn't the case. Let's say Steve Nash runs the pick-and-roll with Amare Stoudemire ten times, and all ten times he tries to thread the needle to Stoudemire. Six times he manages to get the pass to Amare (and from 3 feet away Amare almost always dunks it, so we can assume Amare hits all six of his shots after getting the passes from Nash), but four times his passes get intercepted. The Suns have had ten possessions, they've scored twelve points, and Nash has a 3:2 assist-to-turnover ratio. Now let's say Steve Nash runs a high pick-and-roll ten times with Kurt Thomas, gets into the lane each time, and then kicks the ball back out to one of the Suns' shooters when the defense collapses. There are a lot of long arms in the way, so two of his passes are picked-off, but he still gets eight of them to his shooters. Since the shooters are open, they knock down their shots at a 75% clip (six of eight). The Suns have had ten possessions, they've scored twelve points, and Nash has a 3:1 assist-to-turnover ratio. Does Nash's improved assist-to-turnover ratio in the second scenario make him a better point guard? From the standpoint of the Suns offense, the answer is clearly "No."

Why not? Despite what assist-to-turnover ratio tells us, not all passes are the same. The types of shots to which those passes lead matter a great deal--more specifically, the likelihood of players making the shots to which those passes lead makes a big difference. The higher percentage the shot created by a point guard's pass, the worse a PG's assist-to-turnover ratio can be and still be helpful to a team's chances to win a game.

A "perfect" PG could theoretically compute the chance of scoring based on each potential pass (evaluating both the likelihood of the pass being intercepted and the likelihood of the shot resulting from the pass being made if the pass is not intercepted) and always choose the pass with the highest expected scoring value. Making these decisions is complicated enough under our simple model, but becomes even more complicated once you take into account the fact that different teams are better at defending different shots. For instance, Amare Stoudemire might normally make 100% of his shots from in close, but the Spurs interior defense gives him problems so that he "only" makes 2/3 of his shots from in close. Now, it might no longer make sense for Nash to try and thread his passes inside to Stoudemire on the pick-and-roll. In practice, point guards make the decision where to pass based on "feel"--an intuitive, split-second thought process, based on years of playing, that helps them identify the pass that has "best" chance of resulting in a positive play. This feeling may or may not be right (after all, most point guards have been coached to protect the ball at all costs so they might be very risk-averse), but assist-to-turnover ratio by itself does not help us properly evaluate that decision in any useful way.

The situation gets complicated even further when we recognize that we are also generally making two further assumptions. First, we are assuming that the shot taken by the "open" man is likely to be made at a higher percentage than the shot the point guard could have taken once he had penetrated the lane, and that the open man's shot will be made at a higher enough percentage that the potential turnovers are worthwhile. Going back to our previous examples, if Steve Nash can hit his shots in the lane at a 60% clip, then him shooting the ball is just as good as either of the other two options. And with no assists and no turnovers, he won't have an assist-to-turnover ratio at all!

Second, and related to the previous point, we're assuming that we want an offense based around a point guard (or other player) penetrating and passing in the first place. Once the possibility of turnovers on passes is taken into account, a team's best offensive strategy might actually be to just let players create shots individually. A team's shooting percentage might be lower, but it could end up scoring more points because the lack of turnovers means it is taking more shots. The Dallas Mavericks are an example of a team that has gone this route. Using a steady diet of foul-line isolations (Dirk on a smaller guard after a switch is the favorite, but they also run this play for other other players), the Dallas Mavericks were 25th in assists per game in 2007, but were 2nd in offensive efficiency. (I couldn't find team assists adjusted for pace, but I think my point is still clear despite using these mismatched statistics)

Wow. My discussion of assist-to-turnover ratio certainly ballooned into something a bit more expansive, but I think it was all related. Wade through it all and (I think) my basic point is this: assist-to-turnover ratio can give us some useful information, but it falls short as a statistical measure because it unfairly punishes high-risk/high-reward passes that can be just as helpful to a team over the course of an entire game as the lower-risk/lower-reward passes that often result in a "better" assist-to-turnover ratio.