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.

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What is TPA?

by Alan Moghaddam

Chances are if you’re into sports you’ve seen the famed charts from @NBA_Math that feature overlapping pictures of NBA players in a conventional Cartesian plot with a line plotted on it (y=-x). Anything above the line is good, anything below is bad, and average values will tend to walk the line. The graph is a visual attempt to quantify some mystery statistic known as TPA.

This is a standard TPA graph from @NBA_Math

What is TPA?

This is something of a loaded question; the acronym TPA stands for “Total Points Added”. The basic idea behind it is that a player adds points on offense and defense. You then total these subsections to get TPA.

Unfortuantely, the definition above is rather incomplete. We now need to understand Offensive Points Added (OPA) and Defensive Points Saved (DPS), the components which make up TPA. The two subcategories are much more complex than TPA alone.

To get OPA and DPS, we need to use “Box Plus/Minus,” an all-in-one statistic created by Daniel Myers and hosted at basketball-reference.com. I promise we are almost at the bottom of the well here in terms of stat definitions. Box Plus/Minus is a relativistic stat that gauges a player’s impact on team performance when s/he is on the court. S/he again will have an impact on both defense and offense, so accordingly Box Plus/Minus can break down into two stats: Offensive Box Plus/Minus (OPBM) and Defensive Box Plus/Minus (DPBM). We can already see that TPA has the same structure as Box Plus Minus; both purport to measure a player’s impact on both ends of the floor. What is the difference between the two?

Equation 1. Calculation of TPA as a function of Defensive Points Saved and Offensive Points Awarded
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The Best Defensive Small Forwards in the NBA

In the last installment of this series, we evaluated the best defensive shooting guards. We noted that the shooting guard group is crucial in the modern NBA due to the advantages gained by employing versatile defenders capable of stopping opponents of different sizes and skill sets. The same rationale applies for the players in the “small forward” bin using basketball-reference.com’s play-by-play position designations. When compared with the previous group, the main difference is that the small forwards are larger. (perhaps we should start calling them “big wings”?)

Wings, whether they are categorized as “shooting guards” or “small forwards,” exhibit greater spread in the defensive load they carry than other position groups do.

While the median values are relatively consistent across positions, wings have a wider distribution than other positions. Raw defensive load for wings can range from very high (>15 ppg) to very low (<6 ppg). Other positions, especially interior defenders, have much more compressed distributions.

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Who Are the Best Defensive Shooting Guards in the League?

The NBA changes as rapidly as the seasons, and the league is heading toward a greater and greater reliance on versatile perimeter players. The prevalence of 3-pointers, combined with the emergence of bigger primary ball handlers replacing some of the smaller “point guards” of previous eras, has resulted in a single mandate for NBA defenses: to find defenders who are big enough and quick enough to guard anyone.

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Who are the Best Defensive Point Guards in the NBA?

Rankings are among the most popular exercises for most NBA fans, and also among the least efficient ways to evaluate data. The enduring appeal of rankings and lists owes to their relationship, however tangential, with the big questions: Who is the best? Which player is better? How much better or worse would a team be if they replaced this player with that one? Every fan, analyst, scout, coach, and executive needs to be able to answer these questions.

The problem with rankings is not the questions they address, but the biases implicit in ordinal numbering. Our brains are trained to think that the difference between 12 and 17 is the same as the difference between 18 and 23, and that all these values are on a different order of magnitude from single digit numbers. When we transfer these assumptions to rankings of the “Top 50 Players in the NBA” or something similar, we start with false presuppositions. There is not an identical difference in value between each pair of contiguous players on any player ranking. Even a hypothetically perfect, pie-in-the-sky ranking that ranked players in the exactly correct order would still need something besides the ranking to indicate the players’ true value relative to their peers. Our habit of using ordinal numbers to rank players blinds us to the shape of the data.

As a result, both league insiders and outsiders spend an inordinate amount of time debating questions such as “Is Kevin Durant the second-best player in the league or the eighth-best?” “Is Paul George a top 5 player, a top 10 player, or a top 15 player?” What really matters is how much a player contributes to wins by helping put points on the board (on offense) and keep points off the board (on defense). If the 6th ranked player in the league and the 16th ranked player are nearly identical in terms of their contribution to team success, it makes little sense to lay so much weight on their difference in the rankings.

What a valuable ranking system can tell us is how much value a player generates, relative to the rest of the population. In answering the question posed in the title of this article, I will attempt to provide enough context for the reader to be able to comprehend the shape of the data. As such, let’s start with refining the question itself:

Who are the best defensive point guards in the league?

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Steals Don’t Mean Squat

If there’s one thing we know about defensive statistics in the NBA, it’s that steals don’t mean squat. James Harden was second in the league in steals per game last year, and Andre Drummond was eighth. This was not merely an illusion created by the two playing lots of minutes, as both ranked within the top 20 in the league in steals per 36 minutes. In 2016-17, Manu Ginobili and T.J. McConnell were first and second in the league, respectively, in steals per 36 minutes. Steph Curry and Nerlens Noel were both in the top seven in the league in 2015-16, while the same two players along with Pablo Prigioni all ranked in the top eight in the league the previous season. Andray Blatche was eighth in the league in steals per 36 in 2012-13. The illusion extends back as far as steals go in the statistical record.

Jason Getz-USA TODAY Sports

The Real Reasons Why Steals Don’t Mean Squat

          These examples are merely anecdotal evidence, though; what really makes steals unreliable indicators of defensive performance are the many different chains of events which can lead to a player being credited with a steal in the box score. Many of those sequences involve plays made by teammates of the player who gets credit for the steal. Any observer can recognize these plays when they happen: tipped passes, saves on balls headed out of bounds, instances in which an on-ball defender pokes the ball away from the dribbler and another defender grabs the loose ball, traps, double teams, errant passes caused by pressure on the ballhandler, etc. Sometimes a steal is the result of a phenomenal play by one defender, but oftentimes a steal is the result of one player disrupting the offense and another player recovering the ball. Steals create an immediate problem of attribution; the player who gets credit for the steal is not always the player who truly created the turnover.

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Matchup-Based Defense

Defense is the unsolvable puzzle in NBA analytics. No matter how advanced the advanced stats get, defensive metrics continue to crash against the same conundrums. Better data often leads to better models, and recent years have seen a dramatic improvement in the quality of defensive data available for analysis. Tracking data, opponent shooting data, play-by-play data, and more have all played a hand in modern defensive analysis. In spite of the improvements, or perhaps in part because of the improvements, it is clear that defensive analysis is still not highly accurate.

Most defensive metrics which are currently extant are based on one of two schools of thought. In order to take stock of why defensive analysis is still frequently inaccurate, it will help to investigate the underlying assumptions behind most current models.

The Plus/Minus School of Thought

The most popular method by far is The Plus/Minus School, which counts BPM, RPM, RAPM, PIPM, and more among its adherents. The distinguishing precept of the Plus/Minus School is the belief that we can ascertain a player’s defensive value by evaluating the team’s performance with him on the court, if only we properly adjust for strength of opponent, the team’s talent level, the team’s performance with the player off the court, and the player’s performance level in seasons past. The adjustments made to raw plus/minus are attempts to extract reliable data by excising confounding variables.

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The Muses’ Notebook (Sep. 24)

by Baltej Parmar

For this series, I will be posting research that I’ve looked into and posted on my Twitter but wanted to expand and add some more thoughts about the data. Recently I looked into shot selection for all teams based on league average shooting talent. In other words, how good would each team’s offense be if they made a league average percentage of the shots they took, given the type of shots they took? I created two tables which you can see below. The first table accounts for whether or not three-point attempts were contested by the defense, as well as the location of the shot. Doing should tell us both how “good” or “bad” a shot is in terms of location as well as openness.

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The So-Called Disappearance of the Big Man, Part 2

In the first half of this study, I analyzed the conditions that would be necessary for a true “league without centers” – an ultimate small-ball paradise without any traditional big men. We found that the offensive value of high-efficiency finishers would be difficult to replace without an unimaginable increase in three-point shooting accuracy.

To this point, we haven’t yet analyzed the point at which most teams would not use a traditional big man for defensive purposes. While the foregoing analysis has laid out what I see as the necessary conditions for a big man to have no purpose on offense, the question remains as to what shape such conditions might take on the defensive end. When would it not make sense to have a big man on the defensive end?

Photo by Scott G Winterton, Deseret News
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Top 25 Rebounding Guards in the NBA

Rebounding has traditionally been the domain of big men throughout NBA history. As perimeter players have grown larger and more athletic, however, it has become more and more important for outside players to help out on the boards. Indeed, the last three seasons have even featured a guard (Russell Westbrook) averaging over 10 rebounds per game on his way to averaging a triple double.

(AP Photo/Sue Ogrocki)

Who are the best-rebounding guards in the league? To answer this question, I evaluated the relative difficulty of acquiring each rebound based on whether the rebound was contested or uncontested. By finding the success rates for the offense and the defense on each type of rebound and comparing the expected value with the observed value in each case, I was able to assign an appropriate value for each type of rebound – contested defensive rebounds, uncontested defensive rebounds, contested offensive rebounds, and uncontested defensive rebounds. The result gives us the total rebounding value added by each player. (For a more detailed description of the method for evaluating rebounds, consult The Basketball Bible)

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