NBA Season Preview Part Two: Back Of The Basketball Card Stats Can Only Get Us So Far

With the start of the 2011-2012 NBA season only weeks away at this point, I wanted to take this opportunity to pass along a few general concepts and specific stats that can greatly enhance an NBA fan's appreciation of the finer points of the game. Back of the basketball card stats (Pts/gm, Reb/gm, Ast/gm, etc.) and standard game box scores undeniably represent a familiar and comfortable style of analysis deeply embedded in the lexicon of NBA fans everywhere, but it is important to know that intelligent efforts have been made to interpret and express the information provided in traditional box scores in more meaningful ways.

Part One of this season preview series is available here, just in case you missed it, and with that out of the way let's move on two Part Two...


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The first draft of this story focused on explaining the systematic biases and conceptual faults of a particular advanced basketball metric. It was a nice first draft, filled with phrases like "linear weights," "multiple linear regression analysis," "correlation to wins," and "retrodiction of team wins," but then a thought occurred to me...the metric itself wasn't really that important, but the ideas and approaches used to expose its flaws are something all basketball fans can appreciate and discuss without a specific love of detailed statistical analysis. You will no longer find the phrases listed above in this version of the article, and I have removed the discussion about the particular advanced metric almost completely, but the underlying conceptual complexity has most certainly been preserved in this final draft. The general topic of discussion? Approaches to reconciling the seemingly endless details of team basketball with the limited factual (read: statistical) record in meaningful ways. The specific topic of discussion? Rebounding.

The Fundamental Problem: The Limits of Box Scores

Basketball is not five games of one-on-one, it is a team game loaded with important contributions and lapses that go completely unrecorded but ultimately help to distinguish the winners from the losers. I don't think anyone would disagree. Then again, official scorers assign full credit for rebounds, assists, points, blocks, turnovers, etc. to a single player in the box score, so it is hard to deny that when we look at the back-of-the-basketball-card stats we all know so well and are deeply embedded in the lexicon of NBA discussions (Pts/Gm, Reb/Gm, Ast/Gm, Stl/Gm, etc.), that we are assenting to a certain degree of misinformation. The screens that lead to a made shot aren't recorded, the box outs that allow the rebound to be grabbed aren't recorded, and skip passes that lead to the assisting passes aren't recorded. Instead, the scorer, rebounder, and assister claim full (meaning undivided) credit for these events. As I pointed out in my breakdown of John Hollinger's PER metric, traditional box scores cannot give a truly comprehensive reporting of game events. Not only do they ignore the context in which all game events actually occur, they also fail to record important game details that elude simple classifications including, but not limited to, individual defense, help defense, timely rotations, successful box-outs, effective picks, specific locations of shot attempts, and when shot attempts occur within the context of the game.

The accounting provided by box scores is undoubtedly helpful when analyzing player performance, but the picture is also unquestionably incomplete. Should we just throw stats out the window and just watch the games and make subjective judgments without any factual points of reference? Of course not! Aside from the inherent flaws of human memory, reliance on unsubstantiated anecdotal evidence does nothing to advance the conversation or to advance our knowledge of basketball. We all get to have opinions, but we don't all get to be equally right, and there needs to be some acknowledgement of objective facts. To illustrate my point, I will relay one of my favorite quotes of all-time, spoken by Gene Siskel and retold via the brilliant Roger Ebert (taken from Roger Ebert's Movie Yearbook 2010):

When a so-called film critic defended a questionable review by saying, "After all, it's opinion," Gene told him: "There is a point when a personal opinion shades off into an error of fact. When you say The Valachi Papers is a better film than The Godfather, you are wrong." Quite true. We should respect differing opinions up to a certain point, and then it's time for the wise to blow the whistle...

In sports, I consider stats to be that whistle. Stats help to keep us honest by providing an accurate record of certain valuable on-court events. For example, if someone says Brandon Jennings is a good shooter, they are wrong. This is part of the reason why we need stats to evaluate talent and achievement. There will always be conceptual problems associated using traditional box score inputs as a basis for player evaluation, but intelligent efforts are being made to find better ways to break up and reassign credit for important on-court events to individual players. Although the ideas apply in some form to almost any recorded stat, for the sake of clarity the discussion will focus on rebounding.

The Specific Problem: Assigning Individuals Credit for Complex Team Events (The Rebound Problem)

Despite their familiarity and universal acceptance as a baseline reference for individual accomplishment on a basketball court, I don't believe that back-of-the-basketball-card-stats are particularly credible or accurate when assigning credit to individual players in a lot of situations. The decisions and evaluations for great players and terrible players are easy enough for anyone watching basketball, but deciding who is more valuable among players on the margins is especially important to a small-market team like the Bucks. How much do opportunities and positional assignments affect player performance? How well do we implicitly adjust for these issues in our conversations and evaluations? To explore these questions, let's take a closer look at rebounds.

Every basketball fan knows that grabbing rebounds is essential to victory, as rebounds are the primary method of securing additional possessions for each team, but every basketball fans also knows the anatomy of each rebound is both unique and complex. Allow me to illustrate my point with the following example: the Bucks defense forces a missed perimeter shot, and Andrew Bogut grabs the defensive rebound. There is no doubt that this outcome marks a successful defensive possession, because the Bucks defense forced a miss on the opponent's shot attempt and ultimately ended the opponent's possession without allowing any points. Maximizing efficiency while on offense and minimizing the opponent's efficiency while on defense is the indisputable key to victory, so the issue of how this credit is assigned on an individual level is of paramount importance to player evaluation. Possessions are the currency of basketball, and rebounds are worth possessions. The tricky part is that the only record a box score makes of this extremely valuable team event comes in the form of a defensive rebound credited to Andrew Bogut. However, assigning the full value of this event to Andrew Bogut because he actually secured the possession by grabbing the rebound seems a bit naive. For example, this game charting exercise provides some hard evidence to support the theory that roughly 30% of defensive rebounds go completely uncontested by the opposition. Is there truly nobody else deserving of recognition or credit in this situation?

To understand the logical fallacy underlying the assignment of full individual credit to the rebounder, let's revisit the hypothetical Bogut rebound in more detail. Every basketball fan not only knows the value of a rebound, but also that the anatomy of each rebound is both unique and undeniably complex. Although Bogut may actually grab the rebound (and of course somebody does have to actually grab the rebound to gain any value at all), this event is the product of a complex network of subtle strategic assignments left unrecorded by the box score. To properly assign credit for ending the opponent's possession, we would need more details in the hypothetical: who was defending the shooter, did team defense force a difficult shot attempt, how well did other defenders box out to allow Bogut to get the rebound, was another Bucks player in position to grab the rebound if Bogut had not done so, and did any players on the opposing team attempt to get the rebound or did they all retreat to prevent the Bucks from fastbreaking (or was it the end of a quarter and Bogut merely touched the ball to get credit)?

Furthermore, there are other implicit factors that influence the circumstances of the rebound. Andrew Bogut plays the position of Center, which is traditionally a position assigned to bigger and taller players that typically play interior defense (intuitively we know that interior areas closest to the basket represent the areas of highest likelihood for landing spots of missed shots) and are assigned the responsibility of grabbing the majority of rebounds for the team. If the missed shot came from a free throw, not would Andrew Bogut literally be assigned the premium position (on the block between the hoop and the closest opponent) and highest team responsibility for grabbing the miss, he would also be rebounding a type of shot that is grabbed by the defense at a much higher rate than a normal shot anyways (due to the positional advantage awarded to the defensive team on a free throw alignment). All of the factors listed above are important to consider when assigning individual credit for a rebound, and even though most of these details are not recorded as statistics, they provide an illustrative look at the reasons why most advanced stat analysts think it is patently incorrect to assign the full value of a rebound to the individual that grabs it.

The terrific sports analyst Phil Birnbaum has noted this problem of failing to contextualize opportunities:

Imagine that the NBA institutes a new rule: the offense is prohibited from touching a rebound until it has bounced three times on the floor.

...A defensive rebound still constitutes a change of possession, and is therefore still worth exactly the same [ ] as it was before. But, now, instead of 70% of rebounds going to the defense, the number is now 99%...

Given that there is now no skill at all, doesn't it overrate Rodman to give him credit for those rebounds? Obviously, any excess rebounds picked up by Rodman, instead of his teammates, are positioning, luck, or opportunities given him by his coach and team. Even a caveman could get them.

The argument for 99% also applies to 70%, but to a lesser extent. Some, but not all, of Rodman's rebounds are, in effect, his team "letting him" have the ball more. Those are perhaps better classified as team rebounds, rather than individual rebounds. Since they aren't, Rodman winds up overrated.
..That's opportunities.

We should know that some portion of rebounding is a matter of opportunities, rather than a difference in skill, so the issue should not be ignored or overlooked. Birnbaum illustrated how ignoring the impact of opportunities can create potentially misleading results. In his next example, he uses the rough assumption that 70% of opponent misses are grabbed as defensive rebounds and 30% of team misses are grabbed as offensive by an average team for his examples...just for reference, the averages this season were 73.6% and 26.4%, respectively, and always hover around the 70-30 marks he uses for estimates:

...[T]here's a second reason rebounds are overrated, a much more important reason...

...As [John] Hollinger writes here, "missed shots can be rebounded while turnovers can't, and ... a defensive rebound is merely the completing piece of a sequence that began by forcing a missed shot."

To get the opportunity for a defensive rebound [ ], the defense must first force the opposition to miss [ ]. The defensive rebound is a combination of the two acts: good defense for up to 24 seconds, and one grab of the ball. Crediting the rebounder with the full value of the defensive play is like crediting the kicker with all seven points of the touchdown.

Birnbaum goes on to point out that to get an opportunity for an offensive rebound, a shooter must have missed a field goal attempt. The two events should not be viewed superficially. A missed field goal is not as harmful as a turnover, because it creates an opportunity for recovery of the ball. The offensive rebound should not be treated like a steal back from the opposing team, because the event is a product of teamwork, opportunity, and on-court assignments. Yet in the box score, the shooter is charged with minus one possession (in the form of a missed FG), and the rebounder is credited with plus one possession (in the form of an offensive rebound). Let's allow Birnbaum to bring the whole thing home:

But that's the wrong weighting. Any field goal attempt has, intrinsically, built into it, the embedded feature that a missed shot results in a 30% chance of getting the ball back. The miss includes a consolation prize, a lottery ticket with a 30% chance of winning back the possession. The shooter figured that into his decision about whether to make the shot. That 30% chance belongs to the shooter. In effect, he hasn't wasted a whole possession with his miss, he's only wasted 70% of a possession. Remember Hollinger's point - a missed shot gives the team a chance to recover, but a turnover doesn't. Obviously, the shooter should be debited less for getting a shot away than for letting the shot clock expire.

These are the types of things that basketball analysts are dealing with when creating metrics to value player performance. The willingness and ability of analysts to think about a missed shot as losing only 70% of a possession, or 70% of a defensive rebound being the function of opportunity determined by a player's assignment/role, help to quietly incorporate complex team components into individual evaluations. These types of adjustments are things we simply cannot trust ourselves to do on a consistent basis, so it is important to understand how different stats approach these types of problems and then we can apply the stats to our own observations and ultimately produce more precise analysis.

You may not agree with the particular ratios used to reassign credit for rebounds, but committing to a particular reassignment of credit is not really the point of this piece. The point is to get you thinking about new and interesting ways to reconcile the endless list of inter-connected and unrecorded team assignments with the goal of evaluating individual skill and talent. I think it is pretty clear that a 70-30 division of credit for rebounds is closer to being correct than the 100-0 split imposed by traditional box scores. If you remain unconvinced that there is any problem with the 100-0 split, I want to take you through a few illustrative examples.

(1) David Lee - He's a scrappy PF/C with a history of high per game rebounding numbers, who grabbed nearly 10 rebounds per game this past season, which was good for the 11th highest average among all NBA players. You can't really argue with that level of performance. Well, actually you can, and in a pretty profound way.

Here are 2010-11 Golden State Warriors team rebounding rates relative to David Lee's court time.

On Court Off Court Net
Offensive Rebounding 27.60% 30.70% -3.00%
Defensive Rebounding 66.80% 67.70% -0.90%
Total Rebounding 47.20% 49.20% -2.00%


With David Lee on the court, the Warriors are the worst rebounding team in the entire NBA. Sure the high-pace systems Lee has played in have inflated his numbers, but would anyone have guessed his presence on the court would coincide with the Warriors grabbing a league-worst percentage of available rebounds? When Lee goes to the bench the Warriors jump all the way up to the equivalent of the 22nd ranked team in rebounding rate, and they also become the equivalent of the best offensive rebounding team in the entire NBA. Take away the NBA's 11th ranked per game rebounder and the team becomes a substantially better at rebounding. This is the type of stuff we are dealing with people. Let's do another player.

(2) Russell Westbrook - He is one of the top rebounding PGs in the league, ranking 4th among PGs with an average of 4.6 rebounds per game, and ranking first among PGs in average offensive rebounds per game and per minute offensive rebound rate. Any time you can get that type of rebounding production from your PG, you are gaining an advantage over your opponents, right?

Here are Oklahoma City team rebounding rates relative to Russell Westbrook's court time.

On Court Off Court Net
Offensive Rebounding 29.00% 30.20% -1.20%
Defensive Rebounding 70.80% 71.40% -0.50%
Total Rebounding 49.90% 50.80% -0.90%


The Thunder actually grabbed a lower percentage of available rebounds when Russell Westrbook was on the floor. Let that sink in for a minute. Now you might be thinking "a one percent difference in total rebounding isn't really a big difference," but in fact a one percent difference is a pretty big deal because there is a small standard of deviation for rebounding at the team level. For example, using these hoopdata numbers, a one percent drop in total rebounding percentage would knock the 6th ranked Thunder all the way down to the 14th ranked team. The team goes from well above-average to almost exactly average in rebounding when Russell Westbrook steps on the court. This isn't something you would guess by looking at the back of Russell's basketball card, or even by looking at the leaderboard for PG rebounding, but it is an important fact worth knowing and understanding. These are the types of things advanced stats can help to uncover. This is what actually happened.

When it comes to the reasons why the Thunder are a worse rebounding team with Westbrook on the court, the topic is open for discussion and debate. Maybe with Westrbook crashing defensive the boards, opposing teams did not have to commit players to transition defense and could use all of their players to pursue the offensive rebound. Maybe with Westbrook crashing the offensive boards, the counterpart defender became involved in rebounding when he otherwise would not have done so. Maybe Westbrook occupied premium space trying to grab rebounds that would otherwise have been occupied by a taller Thunder player with longer arms and a bigger body, leading to less rebounds being grabbed by his team. These are all possibilities, and I am sure we could brainstorm many other possibilities, but it would certainly give you something new to watch and observe the next time you take in a Thunder game, wouldn't it? This is how advanced stats can not only add new knowledge, but also make watching the game more enjoyable and ensure you are always sharpening your basketball sensibilities and always adding to your basketball acumen. Everybody wins.

One of the biggest complaints I hear about advanced statistical analysis is sports is that it sucks the fun out of the game. I understand that nobody wants an informal statistics course to break out in the middle of a basketball discussion, but statistics aren't meant to take the fun out of basketball, they are meant to enhance our knowledge and refine our level of observation and understanding. For being so simple, basketball is exceedingly complex; I encourage you to find ways to use advanced stats and the underlying concepts that inform them to find new ways to view the game and digest the story of what is happening on the court. Rather than find a few more creative ways to say I think an understanding of advanced stats is worth pursuing for every basketball fan, I want to leave you with a more eloquent and timeless message that Roger Ebert used to follow up the wonderful quote I included above:

What I believe is that all clear-minded people should remain two things throughout their lifetimes: curious and teachable. If someone I respect tells me I must take a cloer look at the films of Abbas Kiarostami, I will take that seriously...I will try to do what Pauline Kael said she did: Take everything you are, and all the films you've seen, into the theater. See the film and decide if anything has changed. The older you are and the more films you've seen, the more you take into the theater. When I had been a film critic for ten minutes, I treated Doris Day as a target for cheap shots. I have learned enough to say today that the woman was remarkably gifted.

Those who think Transformers is a great or even a good film are, may I tactfully suggest, not sufficiently evolved. Film by film, I hope they climb a personal ladder into the realm of better films, until their standards improve. These people contain multitudes. They deserve films that refresh parts others do not reach. They don't need to spend a lifetime with the water only up to their toes.

I guess the real point of this story is to encourage us all to remain curious and teachable when it comes to basketball, and to remind us that we never need to settle for spending a lifetime with the water only up to our toes. Beats the heck out of a story about the systematic biases and conceptual faults of a particular advanced basketball metric filled with phrases like "linear weights," "multiple linear regression analysis," "correlation to wins," and "retrodiction of team wins," right?

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