Beyond the box score: Part II

Friday March 12, 2010 9:37 AM

Beyond The Box Score: Part II

An introduction into the world of advanced basketball analytics

Jason Friedman Staff Writer

HOUSTON - If you missed yesterday’s column, click here to read Part I of our introduction to advanced basketball analytics.


One of the more underrated statistics, usage rate measures the percentage of possessions used by a player during his time on the floor, taking into account field goal attempts, free throws, assists and turnovers.

As you’d expect, the league’s elite players typically possess the highest usage rates, with Dwyane Wade, Carmelo Anthony, LeBron James, Kobe Bryant and Kevin Durant currently constituting the NBA’s top-5. These players have the ball in their hands all the time and assume a lion’s share of the responsibility for ensuring their respective team’s offense runs smoothly. As such, they typically use more than 30 percent of their club’s possessions while they’re on the floor, a figure which places them about 10 percent above the league average.

Of course, that high number only makes sense given the fact teams typically want the ball in their stars’ hands as much as possible (although interesting theories have been presented about how a more equitable and balanced approach could end up being better for teams in the long run. Read more about one such theory here – it’s well worth your time).

It’s a generally accepted – and rather intuitive – rule that, at a certain point, a player’s efficiency decreases as his usage rate increases (for example, just imagine an otherwise efficient role player being asked to assume the offensive responsibilities of someone like James or Bryant. Odds are that player’s efficiency will rapidly plummet). The league’s cream of the crop, then, consists of those who witness the least amount of drop-off despite the increased workload.

Exploring this from a Houston Rockets’ perspective, fans should derive optimism from the case of Aaron Brooks, a player who has seen his usage increase by more than 15 percent this season – his first as a full-time starter – while simultaneously experiencing a nearly 25 percent uptick in efficiency (as measured by PER, John Hollinger’s player efficiency rating). Similarly, Kyle Lowry and Luis Scola have also effectively shouldered more responsibility this year while losing none of – and actually adding to – their overall efficiency.


These are also known as “The Four Factors of Basketball,” a term coined by Dean Oliver, one of the godfathers of hoops analytics and now a member of the Denver Nuggets’ front office.

Oliver broke down the keys to success on the hardwood into four categories: shooting, turnovers, rebounding and free throws, with shooting being the most significant aspect of the game by a large margin. That in and of itself isn’t groundbreaking, of course; most fans would come to the same conclusion about the nuts and bolts of the game whether or not they are analytically inclined.

What set Oliver apart, however, was the way he went about measuring the game’s key components. Effective field goal percentage is similar to true shooting percentage in that it is weighted to properly take into account the added significance of the 3-point shot; the primary difference between the two is that TS%, you’ll recall, also factors in free throw shooting. The formula for eFG%: (FG + 0.5 * 3P) / FGA

Why use eFG% as opposed to traditional field goal percentage? Again, it’s all about utilizing a better method to determine what truly impacts winning and losing. If Team X is shooting 50% from the field after 10 shots and all of its made baskets are of the 2-point variety, that’s good. But if Team Y is shooting 40% on its 10 shots but all of its makes came from beyond the arc, that’s even better given that they would be leading this hypothetical game 12-10. Effective field goal percentage recognizes the difference and provides a better gauge of what’s taking place on the court, listing Team X’s eFG% at 50 percent and Team Y’s eFG% at 60 percent.

One last note on eFG%: there’s no need to worry about learning a new baseline for what’s considered a good percentage. The average NBA player sports an eFG% of 50 percent so anything above that number is positive.

As for the other three factors, Oliver measured them thusly: turnover rate calculates the percentage of possessions which ended in a turnover; rebound rate measures the percentage of available rebounds grabbed by a team; and free throw rate accounts for the number of free throws taken per field goal attempt.

You see the pattern: as with all of the statistics we’ve introduced over the last two days, the common denominator is a shift of focus away from the raw numbers since those tend to be so drastically impacted by things like pace and usage. By instead examining the data using ratios or differentials, it evens out the playing field so to speak and allows us to obtain a much clearer view of a team’s strengths and weaknesses. It’s like looking through a microscope with a lens that magnifies the object 100x instead of 10x.


Quite possibly the most controversial of the “new” numbers, plus/minus has long been a part of hockey as a way to quantify each player’s impact based upon the number of goals his team scores and allows while he’s on the ice. The same method is now being used in basketball as even the majority of today’s box scores list each player’s +/- for the game.

Much of the hullaballoo over +/- seems to stem from misunderstanding more than anything else. As with any statistic, sample size is key as is a basic understanding of the figure’s limitations. Plus/minus is not the end-all and be-all of a player’s value and it was never intended to serve as such. There are, of course, so many variables in play and so many considerations to be made when sussing out the true importance of the +/- data. For instance: which teammates shared the floor with Player X, was he going against the opposing team’s starters of reserves, was he on the floor in a close game or a blowout, etc.

All that having been said, there is plenty of value to be found within the realm of +/- when applied properly. Teams can cull invaluable insight into certain lineup combinations in addition to getting a glimpse at certain players who, despite their limited box score totals, simply help their club consistently win while they’re on the floor (Houston’s Shane Battier and Chuck Hayes being prime examples of this phenomenon).

As with all statistics both new and old, +/- is but one shade occupying the color palette. Use it and it alone and you’ll no doubt be left with a picture dull and devoid of true substance. Apply it along with a host of others, however, and the portrait suddenly has the potential to capture an image of the world in a way we’ve never before seen.

That, in essence, is what these numbers are all about: they are the continuation of a journey designed to cut to the core of basketball while unearthing its myriad mysteries along the way. They can be used for team building or simply as a way to settle water cooler debates about the most clutch player in the game. But always, always, always they should bring you a deeper appreciation and understanding of this beautiful game.

So dig deep, do your research and keep asking questions. There remain a host of unsolved problems out there on topics like injury prevention and how a player’s numbers in international play may or may not correlate to NBA success. Should you stumble upon a possible solution, feel free to pass it along to the Rockets’ front office at

In the interim, be sure to utilize all the colors at your disposal. Your own personal basketball canvas awaits.

Got a question for Send it to Jason Friedman. And for up to the second news and injury updates follow the Rockets and Jason on Twitter.