Fixing errors & improving accuracy

Much of my conjecture over my past few post has been flawed, but at least it's an attempt in growing.

Here, I will lay out the foundations of my current, modified EMA (or Efficiency Margin Added).
This shows each player's increase in the points per possession his team scores on the floor.

First, I gotta define a few things:

ON = PlusMinus (+/-) while a player is on the court
OFF = PlusMinus (+/-) while a player is off the court
Net = The points a player scores, minus the points his man scores
Min%=percent of game a player plays in, or percent of minutes played

here are two basic estimations for how much one player helps his teammates (which I call TMA, or Teammate Margin Added). This is a factor based on their substitution, i.e. how many points a team stands to benefit by a player being in (how good they are on the court minus how good they are off the court).

TMA1=2 x (Teammates' Net While On Court - Teammates' Average Net)
^for this one, we estimate that they add just as much as they do on the court as their team loses when they are off the court

and
TMA2=Teammates' Net While On Court - (4/5 x OFF)
^i.e. their four teammates make up roughly 4/5 of the point margin while a player is off the court



So we get our estimated Teammate Margin Added (eTMA) by averaging these two estimates.

now, we need to find out what a players' Net is, adjusted for how good his teammates are (adjusted Net, or aNet)

aNet=Net-(1/4) x (All Teammates' Total eTMA)x Min%

The 1/4 multiplier is because each player helps a sum total of four teammates while on the court.

Then, a players' overall Point Margin Added (PMA) simply adds our two estimates:

PMA=eTMA+aNet

and per possession, we calculate EMA as

EMA=PMA/(Team Possessions Played x Min%)

Top 25 NBA Players

	Nathan's Most Efficient Basketball Players
	THA/48=Teammate Help Added Every 48 Minutes Played
	PHA/48=Personal Help Added Every 48 Minutes Played
	Player #	Player	THA/48	PHA/48	THA+PHA/48
1	MIA	Wade	1.49	23.19	24.68
2	CLE	James	2.00	22.59	24.59
3	BOS	Garnett	1.36	20.76	22.13
4	NOH	Paul	3.98	12.85	16.83
5	PHO	Nash	1.95	14.33	16.28
6	UTA	Kirilenko	-1.26	16.25	14.99
7	LAL	Odom	8.55	4.81	13.36
8	PHO	Stoudemire	-5.81	18.53	12.72
9	PHO	O'Neal	-2.88	15.10	12.22
10	HOU	Yao	2.48	9.19	11.67
11	CHI	Gordon	0.59	10.97	11.56
12	ORL	Howard	-2.23	13.58	11.36
13	CLE	Ilgauskas	6.98	3.80	10.78
14	PHO	Hill	2.52	8.22	10.74
15	DET	Hamilton	-2.79	13.48	10.69
16	LAL	Bryant	0.21	9.99	10.21
17	DET	Wallace	6.69	3.25	9.95
18	BOS	R.Allen	1.99	6.98	8.97
19	CHI	Noah	5.34	3.58	8.92
20	LAL	Bynum	-1.07	9.66	8.59
21	POR	Roy	0.33	8.14	8.47
22	IND	Granger	-1.82	10.29	8.47
23	UTA	Millsap	2.49	5.69	8.19
24	PHI	Iguodala	4.90	3.19	8.09
25	MIL	Sessions	-4.55	12.38	7.83

Point Margin Above Replacement Player, or PMARP, and its adjusted counterpart, EMARP


FM=Final Margin (of your team)
Net=points scored - points scored by your man
Min%=percent of minutes played
+/-=PlusMinus=point margin change while you're on the floor
OFF=point margin change while you're off the floor

2 categories:

1) Teammate Help Added=THA
THA=(1-Min%)x(FM-Net)-(4/5)x(OFF)
TS THA=Team Sum THA=Combined THA of entire team

2) Personal Help Added=PHA
PHA=Net-(TS THA-THA)*Min%

SHA=Sum Help Added=THA+PHA

SHAPP=Sum Help Added Per Possession=(THA+PHA)/(Team Possessions Played x Minute%)

GameAdjusted SHAPP=SHAPP-(Team Efficiency Margin/5)

Player's Efficiency Margin, Explained

Here's the formula, with an explanation of what it is and how it works.

What it is:

This represents how many points a player is worth (how much they boost the point margin by) when they are on the floor for one possession per team (i.e. -- your team gets the ball, and your opponents' team get's the ball).

How it works:

This is the representation of two measures: the first is how many points a player scores, minus how many points their man scores (The NetTangibles value). This is an obvious good measure for how good a player might be overall (if they can score 20 points, they aren't worth much if they let their man score 50 every game).

The second is the more complicated one: it estimates how much they help their teammates (their intangibles). We take the expected help based on how many points their teammates and man's teammates scored (times the % of minutes the player played) combined with their NetTangibles, and subtract this from how much help the player actually gave (their PlusMinus value). This helps to accurately record how much a player's presence on the court actually benefitted their teammates above when they were off the court. This value will be higher for good point guards, worse for players that turn the ball over a lot, etcetera.

Then we simply estimate how many possessions the player was on the court for (a fairly accurate measure, Google 'estimating possessions played') and divide.

Edit: BUT ALAS, there is one problem with this formula. As a players' minute% reach 100%, the only value that comes into question is their Net Points (that is to say, their intangibles become zero). So our BEST GUESS for how much a player helps a team that also plays every minute of the game is simply their Actual Plus/Minus (PMa). So our best guess is a weight between the prior formula and their amount of minutes played: