Using the Four Factors (and Pace and FT%) to Estimate Point Margin/Efficiency Margin!

The 'Four Factors' are the keys to success in winning a basketball game. They are, generally put, how often you make your baskets, how often you get offensive rebounds, how often you get to the free throw line, and how often you turn the ball over (similarly, how often you let your opponents do the same things). The better these four areas are, the better your team will be. Kenpom.com lists them for each team on their game plan page (example here).

The total number of possessions, Free Throw Percent, and Field Goal Percent are also needed to calculate the actual score, and therefore are also important to winning a game, but we are only given Possessions from Kenpom's four factors data. (Free Throw Percent can be estimated by each teams' average).

My equations are CLOSE, but require a bit of alteration by viewing the regression lines between actual and predicted numbers....but check out the huge formula!

Here's a quick primer of definitions:

Poss=Possessions

FTR=Free throw Rate (FTA/FGA)
eFG%=Effective Field Goal Percentage
(FG%=Field Goal Percent)
OR%=Offensive Rebound percentage
TO%=Turnover percent

(TO=Turnovers)

The first thing we need to find is Free Throws Attempted! We can estimate it thusly:

FTA=(Poss-TO%*Poss)/((1/FTR)*(eFG%+(1-eFG%)*(1-OR%)+.475))

From this we can get:

FGA=FTA/FTR

I'll explain where this comes from later -- but now we have the estimated number of free throws attempted and field goals attempted.

Then you just calculate the final score in the following way:

Final Score=FTA*FT%+FGA*eFG%

After doing this for both teams, you can predict a point margin (or estimate one from a previous game).

To find the efficiency of a team, simply divide the final score by possessions played!

Now for the really nerdy part: WHY DOES THIS WORK??

Algebra!

No seriously, check it out:

Premises:
1) Possession change (the calculation for total possessions) can only happen in the following ways: when a team gets a defensive rebound, when the ball is turned over, when the ball goes in the hoop. Also, we estimate that .475 percent of the time a free throw is attempted, a possession ends.
2) We can represent Field Goal Attempt possession changes in the following way: FGA*(FG%+(1-FG%)*(1-OR%))

That is to say, when you make a shot (FG% means when the ball goes in) and when you miss it (1-FG%) and don't get an offensive rebound, (1-OR%) the other team gets the ball next.

3) We can therefore estimate possessions in the following way:

Possessions=FGA*(FG%+(1-FG%)*(1-OR%))+.475*FTA+TO

4) Unfortunately, the four factors do not offer us FG%, but a close number, eFG%, so we can turn the formula into this:

Possessions=FGA*(eFG%+(1-eFG%)*(1-OR%))+.475*FTA+(TO%*Poss)

5) Since we don't have FTA or FGA, we need to use FTR to get rid of one of these two variables to solve for the other. Let's try FGA.

SINCE FTR=FTA/FGA..........FGA=FTA/FTR

This gives us:

Possessions=FTA/FTR*(eFG%+(1-eFG%)*(1-OR%))+.475*FTA+(TO%*Poss)

6) Factor it and use algebra!

Possessions-(TO%*Poss)=FTA*((1/FTR)*(eFG%+(1-eFG%)*(1-OR%))+.475)

=>
(Possessions-(TO%*Poss))/((1/FTR)*(eFG%+(1-eFG%)*(1-OR%))+.475)=FTA

7) Hooray!

Now, why is this important??
For me, it helps us predict the final score MORE accurately. Kenpom only keeps adjusted stats for offensive and defensive efficiencies....however, this might not be a very accurate representation of how a team works. For example, if one team REALLY relies on not fouling teams (like Uconn did this season) to make up for a stinky factor (like Uconn did with not forcing turnovers), they are more likely to fare poorly against good teams that are good at drawing fouls (like Georgetown, Syracuse, and Michigan St.).

And so we move forward!