Introducing Two New NBA Stats Called FLW and APV

Baseball has Runs Created, Base Runs, Extrapolated Runs, et al, to estimate the number of runs a player scored using only stats such as singles, doubles, triples, etc. To my knowledge, football has no touchdown estimators, and basketball has no point estimators. (Basketball, however, does have a few "Points Created" statistics, but those use players' points scored in their formulas.)

The following formula is what I call "Faux Linear Weights." Like linear weights formulas for baseball, Faux Linear Weights attempts to estimate a player's points scored by giving different weights to various factors. Those factors for FLW are simple—two-pointers attempted (or FGA minus 3PTA), free throws attempted, and three-pointers attempted.

According to FLW, Points/Game = ~ (0.944 * TWA/G) + (0.906 * FTA/G) + (1.08 * THA/G) - 0.36, where TWA is two-pointers attempted and THA is three-pointers attempted.

A more complicated variation of FLW, which includes assists, rebounds, steals, blocks, and turnovers, is as follows:

Points/Game = ~ (0.007 * REB/G) - (0.02 * AST/G) - (0.204 * STL/G) + (0.028 * BLK/G) + (0.178 * TOV/G) + (0.955 * TWA) + (0.85 * FTA) + (1.096 * THA/G) - 0.4

The latter formula yields a lower RMSE than the former, but I'll choose to use the first, as it doesn't add for turnovers and subtract for assists like the second.

Using a group of just more than 1,200 players (who all played at least 164 games, or two seasons' worth, and played at least one year, 1979 or later, when the league started tracking turnovers), the simple FLW yields a RMSE of 0.518 and the complicated FLW has a RMSE of 0.509, when the estimated points-per-game are compared to actual points-per-game.

[Note: Using totals instead of per-game averages in both formulas produces an RMSE higher than the standard formulas; to find total estimated points, just calculate the formula as usual and multiply the estimated PPG by games played. ]

The second stat is what I like to call APV, or Approximate Player Value. It attempts to bring all player statistics into one number, but it is by no means all-powerful—point guards are overrated and big men are underrated by this system, an error I'm trying to fix. (Speak up if you have any suggestions on how to fix the formula, too.)

APV = (PTS * 0.6 + REB * 1.3 + AST * 1.8 + STL * 5 + BLK * 3 - TOV * 2.5 - FGA * 0.5 + FGM * 2 - FTA * 0.5 + FTM * 1.25 - 3PTA * 0.5 + 3PTM * 2.5) / GP

Here are last year's leaders in APV:

Player	APV
LeBron James	73.5
Chris Paul	71.4
Kobe Bryant	67.9
Dwyane Wade	65.0
Allen Iverson	65.0
Baron Davis	62.6
Carmelo Anthony	59.9
Deron Williams	59.8
Steve Nash	59.8
Caron Butler	58.7

As I mentioned before, point guards are severely overrated by this system, and big men are undervalued. And I have no idea why this is, either, but both LeBron James' and Chris Paul's 2007-08 seasons were better than Michael Jordan's best season, and they were both better than every single player season since the merger through 1999.

APV looks like a fine measurement for the present (the PG-C error notwithstanding), but is not a great tool to compare players to those of past generations.