# 15

###### July , 2018

#### NBA Dollars per Bucket

- NBA superstars are typically worth every penny.
- Teams spend about $13,000 per point, but this varies widely.
- Karl-Anthony Towns and Louis Williams deserve a raise.

Professional athletes are well-compensated. In the NBA, the median 2018-2019 season contract salary is about $4 million. Moreover, teams are ready to pay well over that amount for top talent: more than 25 NBA players will make over $25 million this year alone. This isn't even including sponsorship money.

However, per NBA rules, each team is subject to a "salary cap", which is the total amount of money a particular NBA team is allowed to pay for their own players. Think of the "salary cap" as a hiring budget with teeth: teams must stay below this cap or face financial penalties. This forces teams to be as financially prudent as possible in creating a competitive team.

As a result, fans continually critique NBA front office salary cap strategy. Tune into any sports talk radio show and you'll hear this nuanced and passionate discussion daily, which often include the ubiquitous "overrated" and "underrated" descriptors. However, most of these debates fly right over my head since I only loosely follow the NBA (full disculore: go grizz).

Being an average fan, though, didn't stop me from doing a grossly oversimplified analysis evaluating teams and players from a return on investment perspective. I took a look at how much players/teams score in relation to how much they are paid/pay. Obviously this analysis isn't fair to every player since some players are valued for reasons other than scoring, but since the biggest contracts are given to the best scorers, it's worth at least a peek.

For team comparisons, I looked at aggregated stats and salary cap. For player comparisons, I only looked at roughly players with the 200 highest salaries. Check the notes section below for more information about how the analyses were done. Here are some findings:

**Superstars are typically worth every penny.**The highest paid players are scoring disproportionately more points per dollar when compared to the rest of the league. From a dollars per point perspective, superstars like Lebron James, Anthony Davis, and Kevin Durant are highly efficient. Even superstar Stephen Curry, the highest paid NBA player, was still reasonably efficient

*even when he only played 51 of the season's 82 games!*Yes, there are some busts (more on them later), but superstars tend to be positive outliers!

**Teams spend about $13,000 per point, but this varies widely among the teams.**Houston and Philadelphia got the biggest bang for their buck while Memphis and Sacramento had the worst. Houston and Philadelphia scored 400 more points than expected while Memphis and Sacramento scored 550 and 480 fewer points, respectively. (See Figure 2.)

**On average, Centers get paid the most.**The median salary for a Center is $12 million whie the median salaries for Forwards and Guards are about $10M. Additionally, Centers get paid about $23,000 per point while Forwards are paid $16,000 and Guards are paid $14,000. (For all players, a single player is paid about $16,000 per point.) (See Figure 1.)

**Karl-Anthony Towns (C), Louis Williams (G), and Joel Embiid (C) performed the best in terms of scoring per dollar in relation to their peers.**They each scored more than 1,000 points than expected in relation to their salary. Notably, Karl-Anthony Towns scored more than 1,300 points than would be expected. Pay the man. (See Figure 3.)

**Gordon Hayward (F), Mike Conley (G), and Luol Deng (F) performed the worst in terms of scoring per dollar in relation to their peers.**Each scored 1,000 points fewer than expected given their salary. Obviously these numbers are due to injuries. However, the point of this post is to highlight that salary cap money is spent regardless or not if the player plays, which is an opportunity cost for every team with injured players. (See Figure 3.)

**Some players were paid millions yet didn't play a single game.**From a salary cap perspective, these are nightmare scenarios:

- 1. Chris Bosh - $25M

- 2. Brandon Knight - $13M

- 3. Nikola Pekovic - $11M

- 4. Matt Barnes - $6M

- 5. Deron Williams - $5M

While there are some obvious flaws with this analysis, this can at least give NBA fans something to talk about. I will probably make another post eventually trying to gauge defense and the +/- stat in relation to salary.

Notes

- The analysis looked at the top 200 salaries, but this meant the analysis actually included 230 players. This is because some players literally had the exact same salary.
- Obviously, some teams tanked their record to jockey for a good lottery pick, which would skew the scoring statistics. However, my overall point still remains: teams are
*still*paying players no matter if they are winning, losing, or tanking. This goes the same for injuries: those players are still getting paid. - To be included in the descriptive statistics, a player had to play at least 1 game. So players like Chris Bosh and Matt Barnes were excluded from the overall analyses. I did this completely arbitrarily but mostly to lessen the skewness of a 0 inflated data distribution.
- In the comparison of actual/expected scores, the expected scores were derived from a very rudimentary linear model predicting season points based on season salary controlling for a player's position. That's why Mike Conley's residual (difference between actual and expected points) is similar to Gordon Hayward's residual even though they have roughly equal salaries but Mike Conley scored a lot more: Conley is a Guard while Hayward is a Forward.
- The descriptive statistics in Figure 1 were calculated at the individual level, not the aggregated level. That's why if you take the aggregated mean salary and divide it by the mean points, you may not get the displayed mean $ per point. If you do that, you're taking an average of an average which is usually incorrect ... click here for an explanation.
- It's interesting comparing model results of expected (prescriptive) points versus actual dollars per point (descriptive). This might go in a later blog post, but there are some cases where the expected points makes a player look majorly overrated, but then the $ per points is completely in line with the league average. For example, the most efficient player from a dollars per bucket perspective (non model) was actually Jamal Murray ($2,854 per point) even though he was ranked the #14 best outlier according to the model. Meanwhile, while Mike Conley had a terrible performance in terms of actual vs expected (with the model), he was ranked a little better (16th worst) in a dollars per point perspective (139,173 per point).

Extra Stuff

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