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February 25, 2009
Battier and the Box Score
Learning More About the Game

by Kevin Pelton


Michael Lewis packed plenty into his feature on the NBA's new math in New York Times Magazine over All-Star Weekend, which spanned eight pages online. The famed author of Moneyball discussed how growing interest in basketball statistical analysis led the Houston Rockets to hire Daryl Morey as their general manager, as well as why Shane Battier's background made him an ideal fit to become the Rockets' first big addition after hiring Morey.

Yet in terms of what fans can take from the piece, I think it all starts with one quote:

"Someone created the box score," Morey tells Lewis, "and he should be shot."

Imagine There's No Box Scores. It's Easy if You Try.

What if Morey's imagined dystopia sprang to life and anyone trying to record player stats was shot on sight? How then would we evaluate players? Obviously, subjective scouting would be paramount, but people whose minds work like mine would probably try to find some way to quantify player contributions. We would have no choice but to start with the effectiveness of teams, tying it back to players.

We could look at the win-loss record by player, but that would do nothing to separate teammates from each other. A next step might be looking at the performance of the team strictly when a given player was on the court, but this would still be highly dependent on his four teammates, not to mention the opposition. Eventually, we might try to find a way to control for these other factors to isolate a player's bottom-line impact on the game.

The rating system I've just described is what has come to be known as adjusted plus-minus, and in some form it is the primary measure proffered by Morey to help explain Battier's value to the Rockets. According to the specific flavor of adjusted plus-minus used by the Houston front office, Battier is apparently a "plus six" over the course of his career, presumably meaning his presence on the floor is worth six points per 48 minutes.

Let's take a look at how that compares to the publicly-available numbers for Battier, compiled from a variety of sources. Dan Rosenbaum was the first person to report adjusted plus-minus, combining the 2002-03 and 2003-04 seasons. David Lewin, who now works with Rosenbaum in Cleveland, contributed numbers for 2004-05 and 2005-06. More recently, Steven Ilardi reported 2006-07 numbers; he's since teamed with Aaron Barzilai to offer daily updates the last season-plus at BasketballValue.com, and I got 2008-09 numbers from Barzilai. Lastly, the 2007-08 figures came from Eli Witus, who subsequently was hired by the Rockets as part of their team of analysts. (Note that these are all per 100 possessions, not per 48 minutes. I converted one of Ilardi's numbers to make it consistent.)

Year     APM

0304    +2.2*
0405    +9.8
0506    +6.0
0607    +1.8^
0708    +4.8
0809    +5.1

* Includes both 2002-03 and 2003-04 seasons
^ Includes postseason and 2005-06 numbers at lower weights

All of these individuals used slightly different methods, but that doesn't explain the variation we see in the year-to-year numbers. The fluctuation is a natural result of the adjusted plus-minus process. Because each player plays with relatively few different lineups over the course of a single season, it's hard to precisely estimate their impact. Therefore, looking at a player's adjusted plus-minus number for any given season is dangerous. In one noteworthy example that has inspired more than 125 posts in a recent thread at the APBRmetrics board, Chris Paul's dismal defensive adjusted plus-minus in 2007-08 was used to argue that he was hurting his team defensively and did not belong in the MVP discussion. This year, Paul rates as one of the league's best defenders by adjusted plus-minus.

Over time, adjusted plus-minus becomes more useful as patterns start to emerge. In this case, the numbers show Battier to consistently have a positive impact, on average about five points per 100 possessions. That's along the same lines as indicated by Morey.

Critics of Lewis' article have taken him to task for giving Battier credit for Houston's turnaround between 2005-06 and 2006-07, when he was new to the team, given the Rockets were much better in 2004-05 before being plagued by injury the following season. They've also been dubious of Battier's role in the Grizzlies' development into a playoff contender, and in Houston's 22-game winning streak last season. In truth, Lewis' description of Battier--"every team he has ever played on has acquired some magical ability to win"--was surely hyperbole. However, Lewis could have said, equally poetically and entirely accurately, that Battier's teams have possessed a magical tendency to play better when he is on the floor.

We Value What We Count

All in all, the box score seems fairly innocuous. So why does it trouble Morey so? Without presuming to speak for him, I suspect Morey's disdain starts with this simple but crucial reality: What is tracked, what can be counted, tends to be valued. For years, the easiest things to count in basketball were points, rebounds and assists. As recently as the early 1970s, they along with shooting statistics and personal fouls were the only things tracked by the NBA for individual players. Inevitably, points, rebounds and assists emerged as basketball's version of baseball's "triple crown" stats.

One irony Lewis never specifically pointed out in his piece was that his description of Battier sounds, in many respects, like the ideal role player. He knows what his team needs him to do, happily accepts it without complaint and by any measure executes it effectively. Battier's former coaches--three of whom (Hubie Brown, Mike Fratello and Jeff Van Gundy) happen to be prominent television analysts--rave about him as a player and a teammate. This is not a case of statistical analysis invalidating conventional wisdom. If anything, with Battier the numbers are amplifying the old maxims about the value of defense and team play.

A point made effectively and repeatedly by True Hoop's Henry Abbott is that, especially in basketball, the statistical "revolution" is not so much about using numbers as it is about using the right numbers. As it turns out, points, rebounds and assists don't tell the entire story. That's certainly true for Battier, whose career numbers (10.1 points per game, 5.1 rebounds per game, 1.8 assists per game) are eerily similar but slightly worse than those of the immortal Darius Miles (10.4 ppg, 5.1 rpg, 1.9 apg).

Rockets owner Leslie Alexander sums this position up well, telling Lewis, "All I knew was Shane's stats, and obviously they weren't great. He [Morey] had to sell me. It was hard for me to see it."

We'd like to believe that these statistics are meaningful only to fantasy players and not to the people in charge, but studies have shown otherwise. "Teams pay for little more than the glory statistics," Rosenbaum argued in a New York Times column, and my research has found a strong link between scoring and player salaries even when playing time is removed from the equation. The lure of impressive per-game statistics is strong, and when general managers pay players based on stats that don't translate into wins, they reinforce the stat padding Morey rails against in Lewis' piece.

The Right Numbers Have Their Say

Thanks to the development of APBRmetrics, box-score stats need not mean merely per-game averages in the triple crown stats. All manner of player statistics exist that better reflect the relationship between individual performance and team success. The question, then, is this: Do better box-score stats explain Battier's value? That's the argument Carl Bialik of the Wall Street Journal made in a post last week his "The Numbers Guy" blog.

Bialik relied on two prominent statistics--Dave Berri's Win Score and the Win Shares method developed by Justin Kubatko of Basketball-Reference.com, building on the work of Dean Oliver--which have Battier rated along the same lines as adjusted plus-minus. I'm a little more cynical on this point. My own WARP rating system certainly considers Battier a useful player--he rated as worth about seven Wins Above Replacement Player in 2005-06, his best season by this measure--but not an impact performer as suggested by adjusted plus-minus.

Why the discrepancy? The two systems, different in many respects, share two important features in common: Neither places a heavy weight on shot creation, and both make use of a team adjustment to credit a team's defensive performance to its players. Both these factors work to Battier's benefit, since he is an efficient shooter who uses few of his team's possessions (and would have a hard time increasing his role in the offense, as Morey tells Lewis) and has played on top defensive teams throughout his career.

Looking through the prism of my system, which adjusts a player's individual efficiency based on his possession usage, tells a different story about Battier's offense. Only in his best offensive season (2004-05) does he rate as even an average player at that end of the floor. In Battier's case, the success of his teams' defenses does reflect his own defensive ability. However, this is not true for every player, making team adjustments a crude measure of defense. Weaker individual defenders like Battier's Rockets teammate Brent Barry get credited just the same as players like Battier carrying a heavier load. So while the team adjustment gets Battier's defense right (he ranked 10th in total defensive Win Shares from 2005-06 and 2007-08), it doesn't do the same for everyone.

Certainly, using advanced metrics based on box-score stats gets us a lot closer to Battier's true value than looking at his per-game numbers, but it doesn't get us all the way there. This makes sense, since so much of what Battier does in terms of making shots more difficult for players like Kobe Bryant and drawing charges isn't reflected in the box score. We know this in part because these numbers are occasionally tracked, and Battier's are impressive indeed.

When 82games.com ranked players in charges drawn in 2005-06 and 2006-07, Battier ranked in the league's top 10 both years. Lewis used Battier's defense on Kobe Bryant to illustrate his effectiveness, and looking at a larger sample of Lakers/Rockets matchups, Bryant has a 49.1 percent True Shooting Percentage in head-to-head meetings over the last three seasons, when his TS% against the rest of the league has been nearly 58 percent. More generally speaking, Battier's counterpart numbers as tracked by my BP colleague Bradford Doolittle (and available for each player this season on their statistics page) have been "off the charts good," showing opposing wing players to lose nearly 20 percent of their per-possession efficiency against Battier's teams over the last four years.

Even the ability to have this discussion represents the advance of APBRmetrics. When Battier entered the league seven years ago, no one had even conceived of adjusted plus-minus. No matter what Morey thinks of it, the box score is here to stay. However, it is misleading people less and less as we devise better ways to tease value out of it, track more things that once went uncounted and advance methods like adjusted plus-minus that operate entirely independent of individual statistics. The ultimate beneficiaries have been the world's Shane Battiers, and deservedly so.

Kevin Pelton is an author of Basketball Prospectus. You can contact Kevin by clicking here or click here to see Kevin's other articles.

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Conference Check (02/24)
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Life After Rose (02/26)

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