Total Productivity Versus Marginal Productivity

Stacey Brook at the University of Iowa writes about the difference between total productivity and marginal productivity, using the 2009 WNBA Dispersal Draft as an example.

Brook's argument is that a team picking in the dispersal draft choose the player - center, power forward, point guard, whatever - whose value most exceeds the value of the player currently holding the postion. For example, if you have a great center, and the best player available is also a great center, you really don't gain much by drafting that available center. On the other hand, if you have a crappy shooting guard, and there is an average-to-good shooting guard available in the dispersal draft, it makes more sense to pick that average-to-good guard than the great center.

(It's hard to explain this without recourse to math. The math is in the link.)

With the Houston Comets folding, the Atlanta Dream got first pick in the draft. This was a long time before the arrival of Chamique Holdsclaw and Angel McCoughtry. The Dream was significiantly lacking in the post department, and Erika de Souza had been injured for a large part of the 2008 season. It wasn't just that Sancho Lyttle was a great post, it was that we didn't really have a great post otherwise. Picking Lyttle made sense.

Of course, the link provides a simplified example and doesn't take into account contract negotations, future draft needs or address any of the intricacies of providing a WNBA team. However, I've always been a big believer in increasing marginal value, so the link appealed to me. I think marginal value also provides an explanation for many of those mysterious trades in sports. "Yes, we're acquiring a sucky player. But that sucky player sucks marginally less than the player we're letting go, so the whole team gets better."

It's also great to see the WNBA be turned into a math problem. "A drink of alcohol increases blood alcohol content by 0.3% per drink per 150 pounds of weight at an inverse ratio. Assume that a player from the Phoenix Mercury enters the bar...."