Uncertain Principles

Over at the World's Fair, Dave is asking people for their scientific eponyms, that is, the formula they would like to have named after themselves. These are, of course, entirely made up.

Here's my contribution, from the scientific study of pick-up basketball: the Orzel Teammate Desirability Factor (TDF):

The Factor ranges between positive and negative infinity and is a quantitative measure of how much I want to have a given player on my team. The components going into this are:

• P is the average number of points scored per game
• ρ is the player's career shooting percentage
• A is the average number of assists per game
• S is the average number of steals per game
• R is the average number of rebounds per game
• T is the average number of turnovers per game
• Y is the Yap Measure, the amount of time the player spends talking during a given game
• K is the Knowledge Factor, which measures the player's knowledge of the game of basketball.

The Teammate Desirability Factor consists of three terms:

1) The product of points per game and shooting percentage. If you score a lot of points, that increases my chances of winning, which is a positive factor. If, however, you take fifty shots a game to score five baskets, you're going to get on my nerves, so the scoring needs to be weighted down by the shooting percentage.

2) The product of assists, steals, and rebounds divided by turnovers. Obviously, assists are good, because that means you're likely to pass the ball to me in scoring position. Steals are a reasonable measure of defensive ability, and defense wins championships. Rebounds get us extra posessions, which means more chances for me to score.

Turnovers, on the other hand, are bad, and offset the positive effects of steals, assists, and rebounds.

3) The Yap to Knowledge Ratio. Trash-talking during the game is a negative factor, but is mitigated by general knowledge of the game. It's OK to talk smack if you know what you're talking about.

If however, you are a know-nothing pinhead with a big mouth, this ratio becomes extremely large and negative, indicating that you are not the sort of player I want on my team, because you're just going to piss me off.

As you can see from the formula, the best teammates are players who score well on efficient shooting, play defense, pass, and rebound without turning the ball over too much, and keep their mouth shut unless they have something useful to say. Such players are, sadly, rather rare.

Steals and rebounding can offset a poor assist-to-turnover ratio, provided there are at least some assists (if any of those factors are zero, the second term cancels completely). Some theorists suggest that the first term should be modified to reward "clutch" shots-- the so-called "Baum Criterion"-- but it is not clear that the net effect of the occasional game-winning bomb compensates for bricklaying during the main action. Some researchers argue for increasing the importance of steals (the Mahmood-Rice Conjecture), while others argue that steals obtained by deceptively calling for the outlet pass shouldn't count (the Bartell Correction).

Note that the only real way to end up with a negative TDF is through yapping without knowledge. Turnovers and poor shooting can reduce a player's TDF, but not send it into the negative range. Again, there are competing theories that reduce the negative impact of yapping provided that the trash-talking is amusing. This is the known as the Lanterman-Bodden Effect, but further experimental study is required to determine the magnitude of the effect.