Refining field-goal percentage

I'm going to begin with a few definitions and explanations of stats. The stats mentioned here and the ideas behind them are in no way original. They've been explained before, and better, by Ken Pomeroy and by John Gasaway and by Dean Oliver.

I include an explanation here mostly so that I can easily refer potentially confused readers to it when I invoke these stats later.

I'll start with shooting stats.

The problem is that "field goal percentage" is, in many ways, an inadequate stat. And by "inadequate," I mean "meaningless."

For instance, suppose Player A shoots 100 2-point shots, and makes 40 of them; and suppose Player B shoots 100 3-point shots, and makes 30 of them. Then Player A's field goal percentage is 40%, and Player B's is 30%. Yet Player B scored 10 more points from the field than Player A did, because 3-point shots count more than 2-point shots do.

There is an easy fix for this problem. Simply count threes half-again as much as twos when calculating field goal percentage. This stat is commonly called "effective field goal percentage" (eFG), and is calculated as

eFG = 100 * (2FG + (.5 * 3FG))/FGA.

Another problem comes in when a player shoots a lot of free-throws. To fix this we use another stat (borrowed from John Gasaway, who in turn borrowed it from John Hollinger), points per weighted shot (PPWS):

PPWS = (points)/(FGA + (.475 * FTA))

[The .475 is because Ken Pomeroy analyzed a large sample of college games and found that, between 2-shot fouls, one-shot fouls, and 1+1 bonus fouls, in the end approximately 47.5% of free-throws end a possession that wasn't already counted by a FGA.]