Beyond the Box Score

It is time to stop evaluating players based on statistical feats. The ubiquity of statistical data has brought with it a ready supply of historical comparisons. In today’s NBA, one can hardly turn around without running into a stat trumpeting a player as “the first player since MJ to have 18 consecutive games of 20-5-5”. Who can ignore the box score aggregators, with their perpetual lists of “top performances of the night” that are oriented mainly around points, rebounds, and assists? The basketball community is awash in counting stats-based evaluations, but it’s time to cut it out.

The comeuppance has been a long time coming, to be perfectly honest. Fans have long prized points, rebounds, and assists as basketball’s version of the “Triple Crown” – a trio of statistics that can combine to depict a player’s value. Such an outcome is to be expected, since those three statistics are usually the largest numbers in any box score; our eyes are drawn to big numbers. In The Book of Basketball, Bill Simmons concretized the method of measuring players by Points+Rebounds+Assists in constructing his all-time rankings, which certainly did nothing to cool the ardor of counting stat acolytes.

It Was Never a Good Idea

Adding together counting stats was a bad idea to begin with. Taking values that describe discrete events and adding them without modification is among the poorest methods of measuring a player’s impact. Every box score statistic (every statistic period, as a matter of fact) exists on a certain scale. While it is quite common for a player to score 10 points in a game, and somewhat common for a player to grab 10 rebounds in a game, it is decidedly uncommon for a player to register 10 steals in a game. The scale – or range of normal values – for steals is much smaller than the scale for points. Since points, rebounds, and assists each have their own scale, adding them is always going to privilege points above the other components.

It is possible to adjust for scale by taking the root of the numbers’ product and finding the geometric mean, but that is difficult to do in one’s head when looking at the box score. In addition, doing so only runs us into another reason why evaluating players by PTS+REB+AST is a bad idea: it tells us very little about a player’s defensive performance, and nothing about how efficiently the player registered his stat line.

Write your own caption starting with “Scoring efficiency is …”
Photo via Players’ Tribune

Okay, that’s two reasons. Let’s start with the second reason: we know how many points the player scored, but how many shots did it take him? Yes, we know how many rebounds he got, but how many rebounds did he lose to an opponent? Fine, we know how many assists a player recorded, but how many bad passes did he throw? How many good passes did not become assists because a teammate missed the shot? Taking the “add up counting stats” approach does not give us the context needed to affirm that the player had a good, bad, or average game. Opportunity and playing time heavily impact the distribution of counting stats on a team. As such, PTS+REB+AST is a better proxy for importance to a player’s team than for the player’s performance or value compared with his peers on other teams.

Box Score Feats Tell Us Nothing About Defense

In its most common form, the “Triple Crown” line ignores defense almost entirely. Only defensive rebounds factor into the PTS/REB/AST “slash line”. I have written at some length previously about how unreliable defensive rebounds are as indicators of defensive prowess. Even statistical feats that include steals and blocks (or “stocks,” the tagalong younger sibling of the counting stats brigade) only include a small amount of information about a player’s defensive performance.

Stocks legend
Jed Jacobsohn/Getty Images

The best shotblockers of all time only recorded blocks on 8-10% of opponent two-pointers at most. Only two players have ever recorded steals on 5% of the possessions they were in the game, and only 37 player-seasons have ever surpassed 4%. Thus, even a player who achieves the vaunted 5 x 5 in a game has only left a mark on 10 out of 60-80 defensive possessions during his time in the game. When we consider that steals can also be the result of harassing defense by a player’s teammate, and not a result of the player’s own contribution, it becomes even more difficult to trust “stocks” as an accurate measure of individual defense.  

Statistical Feats Are Less Valuable Now Than Ever Before

It has always been a bad idea to measure value by listing a player’s counting stats. Now, it’s even worse to do this type of “analysis” than ever before. As even a cursory perusal of NBA records will show, the modern era is more conducive to the accumulation of the three main counting stats by the same player than any era in history.

Let’s start with 30 point triple-doubles – Russell Westbrook’s average performance during his MVP campaign. There have been 474 such performances in league history; 167 of them have come since 2015. In other words, over 1/3 of the 30/10/10 games in league history have come during the last five years.

Upping the ante brings the distinction into sharper contrast. There have been 220 games where a player registered 35 points, 10 rebounds, and 10 assists – 160 before 2015, and 60 since then. 34 out of the 93 games in the league’s history with 40/10/10 have come in the past five years.

The same dynamic appears when we review smaller samples of games. There have been 58 games with 30 points, 10 rebounds and 15 assists; 16 of them have occurred since 2015. It works for non-triple doubles as well: 12 of 41 games with 50 points, 8 boards, and 8 dimes have come in the last five years. Leaving aside rebounds, 20 of 85 games with 45 points and 10 assists have come within the time frame, as have 26 of 73 games with 50 points and 8 assists. The examples are arbitrary, but the concept is pervasive. There are more “unique” performances now than there have ever been.

Visualizing the Change

The chart below shows the occurrence of each type of statistical feat over time. The drop down menu contains a checkbox that will allow you to view one game type at a time, which I recommend due to the differences in frequency among the different series.

This second chart has each class of games on its own page, which you can navigate using the arrows.

In both views, a trend clearly emerges. There is a definite spike in the 60’s when Oscar Robertson dominated a league playing at a staggeringly frantic pace. Outside of this unique set of circumstances, box score “feats” have been rare throughout NBA history aside from the past five years. Please note that neither of these charts are adjusted for pace, meaning that the effect is in reality even more pronounced. Despite a 45-year-long decline in pace (1960-2005), the convergence of box score stats increases.

You can also click on the data point for each season to view the tool tip, which includes the average minutes played for games fitting the criteria in that season. Stars play fewer minutes per game today than in previous eras, but are doing more damage in the box score than their predecessors. Does this fact reflect greater dominance by today’s stars, or a league uniquely suited to the aggregation of box score stats by a single player? Is it skill, or context?

The League Has Changed

At the beginning of NBA time, counting stats measured contributions made by very different groups of players. There was relatively little overlap in points, rebounds, and assists. Those numbers measured facets of the game that were primarily the domain of centers (points and rebounds) and point guards (assists).

Once the game crawled out of the primordial ooze and eliminated goaltending and camping out under the basket, the multitalented player emerged. Though it was still uncommon for players to achieve statistical feats involving points, rebounds, and assists, there was no longer a rigid distinction between big man stats and guard stats.

The first evolution of the jumbo-sized playmaker
Photo by Andrew D. Bernstein

Then, evolution leapt forward. Less than a decade after the beginning of the turnover era (1973-74), Magic Johnson and Larry Bird broke the NBA taxonomy by mastering both “big man” skills and perimeter skills. The two towered over other players with comparable ball handling skill and passing ability, yet easily slithered past peers who could jostle with them in the paint. Never before had it been so easy to recognize a player’s breadth of talent by combining his counting stats.

In the last five years, the NBA has made another leap forward. More and more frequently, teams rely on primary ball handlers who are far larger than the prototypical point guard’s physical profile. Simultaneously, big men have been pulled away from the basket and offensive rebounds have continued an historical downward trend. As a result, it is now oftentimes possible for a team’s primary ball handler to grab an uncontested defensive rebound and push the ball down the floor while the opposing team transitions from offense to defense.

We should note that this is good for teams. While the increasing concentration of box score stats into a single player’s line may seem like “stat padding” from the fan’s point of view, there is a strategic advantage for teams in having a do-it-all star. Taking another clip of Giannis Antetokounmpo, notice that the opponents’ primary rebounder (Clint Capela) partially turns his back on Giannis to run upcourt, and Giannis attacks from the wing before the defense is set.

How Much Has the League Changed?

When compared with previous eras, the current NBA is perfectly optimized for a single star to rack up points, rebounds, and assists. The modern star is a one-stop shop – a supermarket superstar. In order to determine that this is so, I found a pace-stabilized assist figure for every player-season in the turnover era. I then weighted each player’s assists by his scoring ability, captured by his points per 100 possessions in that season. Dividing the weighted total by the league total of pace-stabilized assists, we obtain a weighted average of the scoring output for assisters in a given season. Following the same steps for rebounds gives us the following results:

Both the average scoring output per rebound and the average scoring output per assist are at their highest levels ever. Comparing players across eras – the siren song that lures careless purveyors of statistics to their ruin – requires us to account for this fact. Just because a modern player accomplishes a statistical feat that has never happened before does not necessarily demonstrate that the player has truly surpassed all his predecessors. Statistical feats in and of themselves are more common now than in prior eras.

Counting Stats Won’t Work for Comparing Normal Players Either

The most common use for citing statistical feats is to compare legends across eras. Using counting stats is just as ineffective for comparing non-stars to one another, however. There have been 245 performances when a player recorded 10 rebounds and 10 assists, but scored 10 or fewer points. 49 of those games have come since 2015. The chart below shows the distribution of these games throughout the years, with guide lines to show how each season relates to other seasons in terms of frequency.

Even more significant than the prevalence of such performances, however, is the degree to which they are reflective of the value a supporting player brings to his team. Looking at the PPG/RPG/APG of a role player gives a highly distorted view of his value. Supporting players will usually not be their team’s primary distributor, nor will they take enough shots to score much.

Using the typical box score stat line ignores the things that complementary players need to do in order for their teams to win. Role players must defend their man well, make correct rotations, help when the scheme calls for it, set screens, make the “next pass,” make a pass ahead in transition, and do other dirty work. Trying to compare Maurice Harkless and Jae Crowder on the basis of PPG/RPG/APG is futile, and will lead you to the wrong conclusion more often than not. Counting stats do not adequately measure star players or normal players.

How Should We Evaluate Players?

Alright, so perusing the box score doesn’t give us enough information to know how well a player played. What else can we use instead? Waiting until season’s end for full-season data to evaluate players is not ideal, since it inherently prohibits the information from being actionable in-season. What we truly need is a new box score. We need to move beyond the box score.

I would now like to present the basketball community with my all-new Advanced Box Scores – a box score that provides information describing a player’s performance on both ends of the floor at the game level. The Advanced Box Score uses my models for measuring offense (Points Created) and defense (Points Saved) to describe each player’s impact in terms of the amount of points he contributed for his team in that game.

How would this box score be useful, and how would one use it? As a use case, take a look at one of the more memorable games from this season: Joel Embiid’s bagel:

Here is the link if you want to open the sheet in your browser:

Why did Joel Embiid score zero points in Toronto’s victory? The obvious answer, repeated across the league and the internet, is “Marc Gasol shut him down”. The traditional box score, however, provides scant evidence of this fact. In fact, with 3 points, 6 rebounds, and 9 assists in nearly 35 minutes, Gasol’s performance looks decidedly uninspiring using the normal method.

What the Advanced Box Score reveals, by contrast, is that Gasol saved 21.8 points with his defense, carrying a heavy defensive load and forcing 4.2 points’ worth of turnovers. In spite of an unimpressive line in the box score, Gasol also contributed 4.6 points from passing, 1.2 points from screens, and 0.6 points from offensive rebounds. Thus, even on a horrid shooting night, Gasol still managed to contribute 30.4 points to his team’s effort. He was the second- or third-best player on his team in the game, behind a strong two-way game from Rondae Hollis-Jefferson and equivalent to a solid scoring performance from Pascal Siakam.

In the near future, I plan to present a more detailed walkthrough of each of the items in the Advanced Box Score and what it means. For now, we can conclude by stating what should be obvious: there are better alternatives to the traditional box score available now. It was never a good idea to evaluate players by adding up their counting stats, and the changing shape of the league has made that method utterly unusable. It is time to move beyond the box score to the Advanced Box Score.


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