When you go to, say, Basketball-Reference.com to look up statistics. Have you ever wondered what the Four Factors are and why they are so significant?
Originally the Four Factors come from Dean Oliver‘s (statistician, ESPN stat guy and former front office executive for the Seattle SuperSonics and Denver Nuggets) book “Basketball on Paper.” A delightful read that tries to answer into many interesting aspects of the of basketball such including; Understanding the value of coaching, whether defense wins championships and possession based analysis.
The Four Factors are actually the Eight Factors, since there are four of them for both offense and defense (Oliver’s relative weighted values in parentheses).
- Effective Field Goal % (40%)
- Turnover % (25%)
- Rebounding (20%)
- Free Throws per Field Goal Attempt (15%)
Oliver chose these factors and weighted values based on the fact that the combination of excellence in these four elements has a high correlation with winning. Shooting, taking care of the ball, rebounding and getting to the foul line are all skills that are mainly independent of each other.
Understanding those skills in Oliver’s words can bring “strategic advantages that can be gained with a thorough understanding of these factors.” And that the Four Factors can “start allowing a strategic understanding of the game.”
If you want to nerd out I suggest reading a paper written by Oliver here.
Let’s do the math and figure out how good the Four Factors are at predicting wins.
First I built a model based on the last five seasons in the NBA and ran them through a multiple linear regression which produced this function:
y = 144.75 x1 – 1.47 x2 + 4.28·10-1 x3 + 32.03 x4 – 150.85 x5 + 1.33 x6 + 4.12·10-1 x7 – 30.13 x8 – 37.19
Where R^2 = 0.993 (Basically the function should have a very high correlation with expected results), and x1…x8 are the Four Factors. Y = Expected wins.
Then we test this model and compare the expected results to what teams actually produced based on last season’s net ratings as shown below:
San Antonio Spurs Net Rating: +8.1. Expected Result: +6.8, Difference: 1.3
The final results are shown on the chart below for every team in the NBA:
The R^2 between the Four Factors and Net Rating is 96.2 percent, which means that based on this model about that much of net rating can be discovered just by knowing the Four Factors, which is an incredible insight. There’s some statistical uncertainty in this but the answer is with a large likelihood between 94 and 98 percent in any case.
If you type into the equation above exactly the league averages for each category, you should get a 41-win team. This model doesn’t do exactly that and produces something more equivalent to a 40.7 win squad. So it’s pretty close.
Based on working with the data I would disagree a bit with Oliver’s weighted values which I mentioned earlier; shooting efficiency is probably underrated and should be around or more than 50 percent. I didn’t calculate the exact figures but it’s definitely higher than Oliver’s estimation. I’m not sure of the method he used to determine those values. The others I don’t have a quarrel with.
In any case, it’s really interesting that just by knowing four numbers about the game, we can predict net team’s expected net ratings down to a few percentage points.
Stats are great! A better understanding of what correlates with winning and produces value can help us and give insights into what sort of strategies we should employ. Stats are often used to show how well players are doing in areas of the game we value; How many points they scored, how efficiently and how many passes did a player make.
What’s just as important as measuring those things is understanding what we ought to value. And stats can help with that.
You can go a lot deeper into this type of analysis but just based on the regression model I used you can already start finding tangible answers to questions like: Are we better off spending our time improving defense or offense? And, are we valuing rebounding appropriately?