Nylon Calculus: Balancing the value of volume scoring with efficiency

By any measure, Russell Westbrook had an historic season with the Oklahoma City Thunder in 2016-17.  He broke the Big O’s long-standing triple-double record; he won the Most Valuable Player Award; and he dragged an undermanned Thunder squad into the Playoffs.  BUT, he also used a larger percentage (41.7 percent) of his team’s possessions — with field goal attempts, free throw attempts, and turnovers — than any other player in the modern era, making Kobe Bryant’s previous high mark for usage rate (38.7 percent) look downright egalitarian.

And just like Kobe in 2006, Westbrook wasn’t super efficient with all of those opportunities to score, shooting just 42.5 percent from the field.  In fact, he’s the first player since Bryant in 2005-06 to earn the ignominious distinction of MISSING over 1000 shots in a single season (Westbrook missed 1117 during his MVP campaign).  But also, just like Kobe in 2006, Westbrook’s teammates last year weren’t great, especially not on offense.  As such, I can’t really blame Russ for having borderline ball-hog tendencies; he was just doing his best to help his team win.  But, the question remains: was Westbrook more valuable to the Thunder than his more-efficient MVP competitors — James Harden, Kawhi Leonard, and LeBron James — were to their respective squads?

I’ve had trouble answering that question, so I tried to come up with a stat that would help balance the value of a player who carries the burden of offensive creativity for his team with the value of a player who helps his team score efficiently.  I did my best to keep things simple while still (hopefully) adding something new to the discussion.  The result is a not-so-advanced stat that measures how beneficial an individual’s playmaking is to his team.

The straw man, counting stats

In brainstorming ways to balance the value of volume and efficiency, my first thought was to try multiplying the two factors together so that the product would represent a little of both.  For example, what if I multiplied FGA by true shooting percentage? I got busy crunching the numbers and realized…I had just “invented” counting stats.

I felt good about that.

But, honestly, counting stats, like total points and total assists, aren’t a bad place to get started. Simply adding the number of points a player scored to the number of points he generated for teammates on assists gives us a reasonably good measure of which player did the most to carry his team’s offense in 2016-17:

We can think of these counting stats as a naive estimate of a player’s value to his team, we’ll treat this stat — the sum of points scored + assisted — as a straw man against which we can compare our new stat later on.

From here, we need to think about defining a “breakpoint” efficiency above which an individual’s playmaking volume is actually helping his team. This is a familiar concept for fans of advanced-stat equations, but it should be pretty intuitive for people who aren’t huge nerds, too. Basically, there is a minimum efficiency at which a player must convert his opportunities for him to be considered helpful to his team, otherwise his opportunities should be given to another player who could help the team score more efficiently. When calculating offensive Win Shares, the efficiency breakpoint is set to the league average, so that any points scored at above-average efficiency is counted towards the good (this is a player’s so-called “marginal offense”). Calculations for PER use an analogous breakpoint (set to 1 point per possession).

For this new stat, I chose to compare an individual’s playmaking efficiency to his teammates’ efficiency on plays where he wasn’t directly involved (as the scorer or assister). You can get a first glimpse at how some of the league’s best creators stack up by this measure of “efficiency added” in the chart above. Again, the idea is that any player who scores less efficiently than his teammates isn’t really helpful to his offense, because his opportunities would theoretically yield more points if they were re-allocated to others. The flaw in this logic is that a team’s best players are often tasked with taking the most difficult shots; late in possessions, against the opponent’s best defenders, etc. I hope you’ll agree that some of this bias is “washed out” when we consider playmaking holistically, with assist efficiency tallied alongside scoring efficiency.  You’ll see what I mean, if you just read on.

A new stat, MVP-Meter

So, now I’m going to show some equations. There will be plenty of charts and tables below which will help to explain how the formula adds up. So, if you hate math, go ahead and skip down a section.

I tried to keep the calculation as simple as possible. I think there is a natural tendency to distrust any stat that is too confusing to calculate easily and I’m doing my best to avoid confusing myself or anybody trying to follow along. If you get hung up, just remember the instruction hidden in the acronym MVP-Meter: Multiply the Volume of Play-Making by Efficiency, with Teammate Efficiency Removed.

Here are some finer points about the formula:

• Potential assists include passes that led immediately to a made or missed FGA, in other words, potential assists exclude passes that led immediately to a shooting foul.
• Assist points include 2-pointers, 3-pointers, and And-1 free throws made by teammates on a player’s assists, but they exclude points from shooting fouls (e.g., two-shot fouls).
• For consistency, MVP-Meter ignores free throws when calculating scoring efficiency; as such, it’s more analogous to effective field goal percent than true shooting percent.
• Teammate efficiency is calculated for any FGA when the player did not score or assist.
• MVP-Meter has units of points or “points added”.

Calculating 2016-17 MVP-Meter stats

Let’s apply MVP-Meter to the 2016-17 regular season and find out which players were most-valuable to their teams’ offenses. In the chart below, the width of each purple box represents an individual’s scoring volume (i.e., FGA) and the height of each purple box represents his scoring efficiency relative to his teammates, so that the area of each purple box represents the points that a player added to his team’s offense by scoring (above and beyond what his teammate’s might have otherwise mustered). Likewise, the width of each green box represents an individual’s assisting volume (i.e., potential assists) and the height of each green box represents his teammates’ scoring efficiency when he assisted relative to his teammates efficiency without his help, so that the area of each green box represents the points that a player added to his team’s offense by assisting. Adding the area of the purple and green boxes yields MVP-Meter.  Each gray box shows the counterweight provided by a player’s teammates, with taller gray boxes (e.g., GSW) representing highly efficient teammates.

MVP-Meter confirms that Russell Westbrook’s season was quite impressive.  As mentioned, in terms of individual scoring, he wasn’t super efficient (short purple box), but his playmaking made his teammates better (tall green box) and he carried a huge load on offense (wide purple and green boxes). His MVP-Meter was further enhanced by the relative ineptitude of his teammates — he had the lowest teammate efficiency of any qualified player (minimum 2,000 minutes played) at 0.93 points per possession. The Thunder had a lot of trouble scoring if Westbrook didn’t do it himself or, at least, facilitate his teammates with an assist.

But there was another player who appeared to help his team score even more than Westbrook. LeBron James was much more efficient than Westbrook with his individual scoring (taller purple box) and his playmaking for others (taller green box) with comparable, albeit slightly less onerous offensive responsibilities on his team. The Cavaliers were overall more efficient than the Thunder, but the key factor for MVP-Meter is the gap in scoring efficiency between the opportunities James facilitated (by scoring or assisting) and the alternative opportunities where James was not directly involved. By this measure, James made larger improvements to the Cavs offense than Westbrook made to the Thunder offense.

Here’s a more thorough look at the numbers that add up to MVP-Meter in tabular format:

You can see that just one of the Top-10 players added more points by scoring (Karl-Anthony Towns) than he did by assisting. On the other end of the spectrum, true point guards like John Wall and Ricky Rubio actually scored less efficiently than their teammates, but they were able to make up for their scoring deficiencies with effective, high-volume assisting (big green boxes above). From a nuts and bolts standpoint, the formula favors high-assist guys because assisted shots are consistently more efficient than unassisted shots, so it’s “easier” for a playmaker to add points to his team by assisting his teammates than by scoring himself (which would include a mix of assisted and unassisted shots). But again, I prefer to give the benefit of the doubt to offensive creators who are generally forced to take harder shots, so this effect is intentional. Consequently, most of the Top-10 are primary ball handlers in one form or another.

Here’s another chart which shows the league leaders for each component of MVP-Meter: points added by scoring (purple bars) and points added by assisting (green bars).  You can see just how far ahead of the pack we find James in MVP-Meter (purple + green bars):

It’s worth noting that each of the top-6 players as ranked by MVP-Meter did, in fact, receive a 2017 MVP vote of some kind.  So, the acronym is apparently pretty apt.

Comparing MVP-Meter to the straw man

Okay, hopefully you’re getting a sense for how the MVP-Meter is meant to work. Let’s turn back to our straw man and evaluate whether we’re better off or worse off than we when we started this exercise. The chart below compares player ranks for our full-throttle volume-based measure of player value (total points + total assists) to our MVP-Meter stat that blends playmaking volume and efficiency.  Players are sorted by color to represent positions: primary ball handlers (red), wings with heavy ball-handling responsibilities (orange), more traditional scoring wings (green), and bigs (blue).

The upper end of the diagram is pretty straightforward: the Top-6 from the counting stats list remained above the fray when ranked by MVP-Meter, with only minor re-shuffling between the two sets of leaders. From there, we see lots of movement in the Top-30.  The traditional wings (green) and bigs (blue) — who are asked to finish plays more often than they’re asked to create opportunities for others — are mostly downgraded by MVP-Meter. Score-first players who don’t shoot particularly efficiently (DeMar DeRozan, Andrew Wiggins, for example) get it the worst. Some players with fantastic teammates (like, Kyrie Irving, say) get dinged by MVP-Meter, too.  On the other hand, efficient playmakers (including Kyle Lowry, Mike Conley, and Goran Dragic) and hyper-efficient scorers (see Kevin Durant, Karl-Anthony Towns, and Bradley Beal) get a boost. Ever wonder how to compare DeMarcus Cousins’ heavier workload to Nikola Jokic’s more efficient, but less voluminous playmaking (Jokic was No. 40 in points + assists)?  Well, MVP-Meter prefers Jokic at No. 7 to Cousins at No. 20.

Whether you’re talking about Jokic vs. Cousins or any other NBA debate, it’s probably better to use more than one season of data to draw conclusions. So, below, we turn to the multiyear MVP-Meter. Because some of the formula’s terms (namely potential assists and assist points) are based on the NBA’s tracking data, we can calculate MVP-Meter starting in the 2013-14 season:

In the end, we find Steph Curry burying the MVP-Meter needle and edging LeBron James by just one extra point added to his offense over the past four regular seasons. Reassuringly, each of the Top-10 players as ranked by multiyear MVP-Meter garnered some MVP votes recently. Moreover, each of the five players who garnered more than 1.0 MVP Award share over the past four years — Curry, James, Harden, Durant, and Westbrook — was also in the Top-8 for multiyear MVP-Meter. The only conspicuous MVP-level player further down the list is Kawhi Leonard. Leonard’s MVP-Meter is dampened by his relatively modest playmaking volume as well as his highly efficient Spurs teammates. Finally, the last four MVP winners were ranked No. 2 (Durant, 2014), No. 1 (Curry, 2015), No. 1 (Curry, 2016), and No. 2 (Westbrook, 2017) in MVP-Meter.

Next: Nylon Calculus -- Offseason movement and offensive styles

I admit MVP-Meter is far from a perfect all-in-one stat, in fact, it’s very limited.  But it does seem to be a halfway decent barometer of recent MVP Award voting and, hopefully, it’s a new way to argue about the relative value of scoring volume vs. scoring efficiency.