Wednesday, April 1, 2009

Ain't Too Proud To Beg

An article in today’s Wall Street Journal ably outlines why “assists” is often a piece of data prone to enormous measurement error. Each team’s statisticians has total discretion over when to assign assists for both the home and visiting team, and the league-wide standard — “the last pass leading directly to a field goal, only if the player scoring the goal responds by demonstrating immediate reaction to the basket”— is maddeningly fuzzy. Could it be that the PGs often perceived as best in the league, due in large part to their outsized assist numbers, could benefit from measurement bias?

My first thought upon reading this is that each team faces the same biases, averaged over the season, right? Even if there is a home bias for assist tallies, each team has 42 home games and 42 road games. Every team gets a diverse sampling of different arenas around the league. … But that’s not quite right.

Each team in the league has a different mix of opposing teams on its schedule. For example, an Eastern conference team, say Miami, plays 52 games against Eastern conference opponents and 30 games (two per Western team) against Western opponents. Of the 52 games against Eastern opponents, Miami plays four times against each of its four Southeast Division rivals (Atlanta, Orlando, Charlotte, Washington), and three or four times against all other Eastern teams. Now consider Atlanta. Atlanta’s schedule mix is roughly the same, except that they play Miami four times, and they don’t play Atlanta! Next, consider Detroit’s schedule vs. Miami’s. Detroit plays each of the other Central Division teams four times, which is pretty similar to Miami, which plays each Central Division team (including Detroit) three or four times. Detroit plays the Atlantic teams three or four times each, just like Miami does. Detroit plays each Southeast team (including Miami) three or four times, whereas Miami played all the non-Southeast teams four times. Also, Detroit plays each Western team twice, just like Miami does.

But a Western team, say Utah, plays each Eastern team only twice, and each Western team three or four times (each Northwest Division team, four times for sure). So the greatest discrepancy of schedule is between Eastern vs. Western teams, rather than any discrepancy for teams of different divisions within the same conference.

We can assume that the home statisticians of each team will be roughly equally friendly (i.e. very) to home-team point guards in assigning assists. The real variation, I would hypothesize, comes in how friendly the home statistician is to the visiting team’s point guard. Some may have a strong sense of fairness, while some may just say “Screw it.”

It is notable that of the top seven players on the league assists leaders list (or equivalently, the players averaging 8.0 assists per game or above), five play in the Western Conference. Now, perhaps this limited sample is not fair; ten of the top twenty players come from the East. Still, it is instructive to consider the gaudy end of the distribution. If there are more arenas in the West where the statisticians happen to be unusually friendly to visiting PGs like Paul, Williams, or Nash, then they could have an advantage in amassing assist stats compared to guys like Rondo or Calderon who spend more of their time in the East.

The obvious solution, not mentioned by the WSJ writer, is for the NBA to assign official statisticians to each game. Really, I don’t understand why this isn’t done. Teams could still track and collect their own stats privately, but why not have a neutral, central, better-trained body take charge of the statistics? We trust the federal government to collect unemployment data; we don’t ask a local Chamber of Commerce or the National Association of Homebuilders to do it for us.

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