Thursday, February 19, 2009

Traditional Statistics

A really good set of statistics should tell us something. They great thing about baseball statistics, for example, is that they are simple to understand - a .300 batting average means that the player gets three hits for every ten hitting chances - and translate into something meaningful. To be a .300 hitter is to be a great hitter; to say "so-and-so hits .300" is meaningful shorthand equivalent to "great hitter".

Baseball has good statistics, in part, because it's a game of individual vs. individual. Baseball is a great sport to break down into pieces like that.

Team sports, on the other hand, aren't as meaningful because you can't look at them outside of context. Football really only has a few meaningful stats. A running back's total rushing yards. A quarterback's pass completion percentage. There have been some coined stats like quarterback efficiency rating but those numbers don't have much meaning.

As for basketball, the traditional stats are "points per game", "rebounds per game" and "assists per game". They're the stats that are used for the "abbreviation line" to sum up a player's total contribution. All of them are context dependent. For example, "points per game" might depend on what sort of scoring role is assigned to the shooter. All of them depend not just on position played, but on total minutes played.

What sorts of relative value due these three stats have?

Let's take an example: Suppose you're a GM and you get a shot at three players (A, B, and C). This is all you know about them:

Player A: 20 ppg, 0 rpg, 0 apg
Player B: 0 ppg, 20 rpg, 0 apg
Player C: 0 ppg, 0 rpg, 20 apg

Which one do you want? A, B, or C?

Well, how do you win in basketball? You win by scoring more points than the other team. Therefore, the Iron Law of Basketball Worth is "a player's worth is dependent on how many points she helps her team score". Note that the definition says nothing about scoring points - you can help someone else score points and still have value.

I imagine that Player A must be some kind of shooting guard or shooting forward, a #2 or #3. Clearly, she has value to the team: she scores 20 points a game, and brings the team 20 points closer to victory on the average. However, she doesn't pull down any boards - at all - and doesn't assist either. She's probably a shoot-first-ask-questions-later ballhog with no strength or size. But she will give you 20 points a night.

Player C also has some value, too. She doesn't score 20 points a game, but she contributed to 20 field goals scored by other players. Of course, the definition of "contribution" is rather weak in the United States, since the definition requires that the pass to other player actually "assisted" the scoring player, and sometimes scorers are so liberal that they virtually award an assist to the player touching the ball before the scorer touched it.

In order to assess C's value, we'd have to determine how many of those assists were "real" assists. Undoubtedly, however, C has value. How many players do you know who average 20 assists per game? Magic Johnson didn't even do that well.

Player B's case is more problematic. There's a difference between an offensive rebound and a defensive rebound. One gives you the chance to shoot again, the other takes away the opponent's chance to shoot again. Unfortunately, rebounds do not necessarily lead to scores. If they were all offensive rebounds, then why wasn't player B able to score with any of them. Still, Player B's rebounding rate is almost that of a Bill Russell or Wilt Chamberlain. What's surprising is that if Player B is a center - which I suspect - then why wasn't Player B able to dish out at least once and score an assist?

So who is more valuable? A, B, or C.

I'm actually leaning towards Player C due to the rarity of her accomplishment. However, I'd think that Player A might be more valuable than Player C, with Player B being of (relatively) lesser value.
All are good players, but each is astonishingly one-dimensional.


a) does an assist equal a field goal? Or just part of one? Half a field goal? Or more?
b) is a rebound equal to some fractional part of a field goal?

The fact that traditional basketball stats might not tell you much has led to some stat mavens creating their own basketball stats to determine a player's true worth. I'll talk about the simplest kind of coined stat - the "linear metric" - next.

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