Turning 4-factors into efficiency (and vice versa) - Part I

I used the definitions of the 4 factors (and other statistics) to derive a formula that gives us Points and Points Per Possession from only the following stats:

-eFG%
-OR%
-TO%
-FTR(%)
-FT%*
-FG%*

I like to just use the 4 factors (as they're found on the game plan page of Ken Pomeroy's team pages) -- we can estimate FT% and FG% depending on how far we are into the season. FT% would be estimated by the team's average FT% (or the league's FT%), and FG% would be estimated by: [the team (or league) ratio of average FG%/average eFG%] x [Game eFG%].

So here's the formula otherwise:





To get points, you simply add FT points and FG points. To get efficiency of course, we add the two and divide by possessions played.

In the upcoming weeks, I'll be using Ken Pomeroy's estimates for efficiency to predict 4-factors according to this method. Later, I'll reverse the process (in hopes to get a better picture at how teams control one another's four factors to get the resultant efficiency).



In case you were wondering: the large bracketed term equals Field Goals Attempted.
In the first formula, we simply multiply FGA by (eFG% x 2), as eFG%=Points per Field Goal Attempted/2.

In the second formula, we simply multiply FTR (FTA/FGA) by the FGA term to cancel the FGAs out to give us FTA.Then FTA are multiplied by FT% to give us total Points from Free Throws.



The large bracketed term was derived like so:

Possessions=FGA-OR+.44*FTA+TO
Poss= FGA-FGA*(1-FG%)*OR%+.44*(FGA*FTR%)
(Poss-TO)=FGA*(1-(1-FG%)*OR%+.44*FTR%)

then divided to give us:

FGA=(Poss-TO)/(.44*FTR%+1-(1-FG%)*OR%)