# The Short Supply of Tall People revisited

Posted on 07/29/2010 by

This post started as a response to the two of the commenters on the previous post. As I neared 400 words and started to think about adding some tables I decided to make it it’s own post. Enjoy.

When I was first exposed to Wins Produced (see detail here), I did not immediately agree with the basic premise of how the model was built. The logic of using marginal value to account for wins and not absolute value did not immediately click in my head. I felt like big men would be undervalued by the model. As I typically do with this kind of thing, I examined and re-examined the logic behind the model. My conclusion was that there were valid and logical reasons why it’s set up this way. I’ll attempt to explain and in deference to requests,  I’ll try to keep this fairly math neutral.

As I turned the model around in my head, I tried to examine the facts:

1. Basketball more than any other sport is a sport about marginal value.
2. Wins are a direct result of the marginal absolute productivity of the players on the court as measured in point differential (margin of victory).
3. Wins produced uses regression to build a causal model for wins based on the statistics available in the standard boxscore.
4. There are multiple factors and contributions ( let’s call this player productivity) that go into scoring a point and the boxscore reflects a significant portion of these factors.
5. Wins are a function of Point differential
6. Point differential is a function of Player Productivity as measure in the boxscore stats and actually it’s a function of marginal player productivity (i.e. how much better your player’s on the court  are than your opponent’s )
7. Wins can thus be modeled as a function marginal player productivity
8. Wins Produced uses regression to build that model and can be shown through correlation to be successful.

So Wins Produced is based on the marginal productivity for each team. If I tweak the equations for Wins Produced to look at the math in a slightly different way:

Wins Produced Team=      Sum_for_all_your_Players (Prod_by_min*Minutes_Played) – Sum_for_all_oppn_Players (Prod_by_min*Minutes_Played) +

41 games

And we substitute the Production for the Average opponent for the second term for a reasonable approximation. So for an NBA team, much like a fantasy football team,  a player’s true value is really a function on their net productivity (i.e how much more they can produce than their opponent).

Wins Produced Player=     Players _Prod_by_min*Minutes_Played –

Avg.Oppnent_Prod_by_min*Minutes_Played +

.100*Minutes Played

The .100 term means that if you break even on average you’ll win half your games.

Another way to think about this is as follows, the average productivity of opponents in the calculation is fixed and for 2010 it’s something like this:

Now here’s the rub. Big Men (F/C) are on average more productive than everyone else . They in fact account for 50% of all productivity.  This makes it harder for a center to be better than the average and thus accumulate wins in our model but this is not out of step with the reality of the situation.  Teams also have a lot more at risk with their big men. It’s also much easier for a team to accumulate negative value at center and power forward because there is much more at risk. So a bad point guard performance will hurt your team, but a bad center will ruin your team. This is why you need at least an average big man to be successful in the NBA. Much like with your typical fantasy football team and the running back position, you need at least to break even at that center or you’re in for a long season.

At the end of the day, the idea that convinced me is the short supply of tall people. Over the history, it is the teams that have length that succeed. The final pieces was that a lot of the exceptional players in league history were tall for their position or played and produced like big men (Magic, Barkley, Rodman, Jordan, Garnett and Lebron are six examples that come quickly to mind).