By Maksim Horowitz (@) and Mohin Banker
A decade ago, the NBA was dominated by towering big men. Shaquille O’Neal, Tim Duncan, Kevin Garnett, and Dirk Nowitzki were giants who could post up at will. But now, they are fading into irrelevance as an era of elite guards begins. We term these perimeter players “the backcourt”. Players like Stephen Curry and Damian Lillard are examples of sharp-shooting guards who bring the game away from the basket. Even big men are evolving - Serge Ibaka and LaMarcus Aldridge are learning to translate their mid-range jumpers into 3-point shots. The NBA is shifting from an inside-out game to an outside-in game, and that makes the backcourt the two most important players on the court.
Before the start of the 2014-2015 season, Bradley Beal said he and John Wall were “definitely the best backcourt in the league.” (source) Dion Waiters responded to the quote, saying that Beal wasn’t “messing with me and Ky [Kyrie Irving]. I think me and Ky are the best backcourt, young backcourt.” (source) Stephen Curry appreciated Beal and Waiters’ confidence, but said, “We’re [Curry and Klay Thompson] the best backcourt in the NBA.” (source) That being said, Curry and Thompson seemed to be the consensus top backcourt for the 2014-2015 season, but what do the stats say? Now that the regular season has ended, we chose to evaluate the following – how did Curry and Thompson match up against the rest of the elite NBA backcourts in 2014-2015? We took it a step further, and asked - were Curry and Thompson in 2014-2015 the best NBA backcourt since 2000?
We chose eight metrics to measure the performance of a backcourt. Each metric collected accounts for times when both players are on the court and are recorded as team total statistics. Statistics were retrieved from Basketball Reference’s Lineup Finder (link), which outputs team stats while a certain lineup is on the floor. The metrics:
- Plus-minus - The difference in team points scored and opponent points scored
- Field goal % - The percentage of shots made out of shots attempted for the team
- Net effective field goal % - The difference in team effective field goal percentage and opponent effective field goal percentage (Effective FG%)
- Assists - Total team passes leading to a field goal
- Net steals - The difference between team steals and opponent steals
- Pace - The number of total possessions per 48 minutes
- Total rebounding % - The percentage of rebounds a team grabs out of the total rebounds in the game
- Team Total Plus Minus – Plus-minus including minutes the backcourt is off the floor
Each raw statistic (i.e. not percentages) is scaled per 100 possessions. We chose to scale our statistics for a team’s pace because a faster-playing team can put up more bloated stats. For example, a primary reason analysts voted Michael Carter-Williams over Victor Oladipo for Rookie of the Year was because Carter-Williams put up 16.7 PPG (points per game) to Oladipo’s 13.8 PPG. But, the Sixers were one of the fastest teams last year, and therefore had more possessions for Carter-Williams to make plays. When scaled to 100 possessions, Carter-Williams puts up 23.4 points compared Oladipo’s 22.8 points. Grantland’s Zach Lowe explained his vote for Oladipo over Carter-Williams: “Carter-Williams has better counting stats than Oladipo, but the gap is small, and mostly due to Carter-Williams logging a few more minutes and Philly piling up six more possessions per game than Orlando.” We adjust the statistics for pace to level the playing field for our sample backcourts.
When picking the different backcourts to compare, we looked at success and similarities in wins, stats, or skillsets. For example, while Jameer Nelson and Hedo Turkoglu were not known for being a skillful backcourt, they were integral to a historically great Orlando Magic team. Andre Miller and Corey Maggette played productive minutes for the Clippers, but the team struggled for wins that season. Mike Conley and Tony Allen are known to be lockdown defenders, but have offensive shortcomings. In total, we selected a sample of 35 different backcourt pairs to use in our analysis. You can take a look at them using the Shiny app we built and do some basic comparisons on your own: Shiny App!
Initial Exploration and Observations
To start our analysis, we looked at the distribution of each of our statistics. For each statistic, we marked Curry and Thompson’s scores with a vertical gold bar. From Figure 1 below, we can see that the duo’s scores are at the high end of each distribution excluding Total Rebounding Percentage (TBR) and Net Steals. However, we note that the correlations between Net Steals and the rest of our statistics are weak, leading us to believe that Net Steals may be representative of statistics that are less directly in the hands of each guard pair. The Splash Bros placement in the distribution of Total Rebounding Percentage shows that rebounding is not their strong suit, which makes sense due to Curry’s small frame.
Figure 1: Distributions of Statistics of Interest
Justification of Plus-Minus as Measure of Backcourt Influence
Throughout this article, we will continually look at the relationship between plus-minus and our other statistics. These comparisons were not done randomly or accidentally. We chose to use plus-minus because we feel that it explains the most about a backcourt’s impact on a team throughout a season. While field goal percentage, assists, and total rebounding percentage are important statistics to examine, scoring points wins games, and in expectation, teams that score more points will win more games (source: Basketball Pythagorean Theorem – Daryl Morey, General Manager Houston Rockets).
Below, in Figure 2, we display the difference between teams’ plus-minus while the duos are on the court, as well as the teams’ plus-minus across the entire season. (Yes, comparing to total team plus minus is flawed. Ideally we would compare to the teams plus-minus while the players weren’t on the court, but alas data collection limitations are real. Thus we proceed). From the plot below, we are able to directly visualize the influences each backcourt had on their respective teams’ scoring. We see that Curry/Thompson, Paul/Reddick, and Nelson/Turkoglu had the largest difference in team plus-minus while they were on the court. This means, across the season, each of these pairs increased their teams’ plus-minus while playing at seemingly an elite level. Looking to the left of the vertical red line drawn at a difference of 0 the threshold at which a backcourt contributes positively to their team’s point differential, we see there are 7 backcourt pairs. These pairs, headlined by Miller/Maggette and Miller/Iguodala, create fewer points for their teams when they were on the court compared to the team’s season total. We predicted that the 7 sub-par backcourts to the left of a plus-minus of 0 below will rank among the lowest backcourts in our sample.
Figure 2: Team Plus-Minus
We conducted a correlation test between each of our measurements, and found the strongest relationship was between net effective FG% and plus-minus, with a linear model explaining 86.3% of the variability in plus-minus around its mean. Intuitively, the strong relationship makes sense because net effective FG% measures how much better a team shoots compared to the opposing team, and plus-minus is the differential score between the teams. Since net effective FG% is controlled by appropriately weighting 3-pointers and pace, a lot of the noise in the data is mitigated. Most of the noise comes from free throw attempts. For example, the differential in a slow game with a lot of fouls depends on which team makes their free throws, not accounted for in effective field goal percentage. We like measuring backcourt performance in plus-minus because it shows that the team definitely scored more points than the other - that’s what really matters in basketball. And, net effective FG % is a good predictor of the metric. See Figure 3 below for a plot of this relationship:
Figure 3: Relationship between Net eFG% and Plus-Minus
We found a similar, but weaker relationship between assists and these two metrics. Since assists are associated with passing teams, it makes sense that more assists results in better relative FG% and a higher point differential because the team has better ball movement, and, as a result, better shot selection. The Golden State Warriors, with Curry and Thompson on the court, averaged 29.5 assists per 100 possession. This ranked the highest out of the backcourts we chose, barely edging out Stojakovic/Bibby and Paul/Redick who averaged 29.3 and 29.2 assists, respectively. And similarly, Curry/Thompson led in net effective field goal percentage and plus-minus. With an R2 of 0.496 for eFG% and 0.394 for plus-minus, the relationship is somewhat strong given basketball’s randomness and unpredictability.
Finally, we found that total rebounding percentage was moderately correlated with plus-minus with an R2 = 0.2751. Our initial thought was that larger and more physical guards who help secure possessions, like Jason Kidd or Russell Westbrook, should receive credit when we constructed rankings for our backcourts. The strong relationship between the team’s rebounding percentage and plus-minus which somewhat justified our above prediction.
Figure 5: Total Rebound vs. Plus-Minus
Fitting a Ranking Model
After examining the above bivariate relationships and our exploratory analysis, we decided to fit a model that would allow us to rank each of the guards. We chose to use all of our statistics except for Total Team Plus-Minus in our model as we saw that it had some multicollinearity issues with Pair Plus-Minus . Using a 1-factor model, we fit our statistics of interest and each was assigned a specific weight or “loading” to find our latent ranking. What these loadings determine is how much influence each of these variables have on the rankings. The loadings calculated were as follows:
Figure 6: Model Loadings
We see that each of our statistics have positive loadings except for Net Steals. The small negative loading associated with Net Steals suggests that the statistic doesn’t provide much value to our method of rankings. Interpreting the negative loading is a bit difficult, but we hypothesize that it may be associated with the idea that steals more often than not result from passes from the backcourt. This means that the passer (usually a guard) will be credited with a turnover, while the opposing team will be credited with a steal, which does not directly reflect on how the backcourts affect team play, rather it is a result of their position responsibilities. Moving on, we see that plus-minus and net eFG% have the highest weights in our model, which is what we expected from what we found in our bivariate analysis and initial EDA.
Before finalizing our rankings, we set to normalize the scores calculated by our model to a more interpretable scale. We did this by adding the minimum absolute value of the scores to each backcourt score then multiplying by 2. This allowed the normalized scores to range from 0 to slightly over 8. Below we display the rankings of our 35 pairs. Not surprisingly, the Splash Bros land in the number one spot as they had the highest score out of any of the backcourts in our sample, by a large margin. However, there are some surprises in the top 10, and even in the top 5! We hypothesized above that Miller/Maggette would be one of the lowest ranked pairs. Well, we were wrong as they are ranked 3rd. Another surprising placement is Miller/Iguodala ranking 8th. These two occurrences lead us to believe that these duos either made up for their lack of production in defense and assists, or they had extremely strong teams backing them. The latter seems less likely as these backcourt pairs were the leaders of their teams (that’s why we chose them!) and neither the 2008-2009 Sixers or 2002-2003 Clippers were particularly great teams. It’s interesting to see that James and Irving fall halfway through the rankings at 16th, and our dark horse duo of Nelson/Turkoglu let us down, ranking 23rd. Take these rankings with a grain of salt because they are by no means absolute, as we are only using one 9-statistic combination out of thousands of other combinations. But, using the statistics we collected, these are how our backcourts stack up against each other (pairs highlighted in blue are from the 2014-2015 season) :
|Rank||Backcourt Pair||Score||Rank||Backcourt Pair||Score|
|1||S. Curry | K. Thompson||8.08||19||D. Fisher | K. Bryant||3.64|
|2||S. Francis | C. Mobley||7.18||20||M. Bibby | D. Christie||3.38|
|3||A. Miller | C. Maggette||6.88||21||S. Nash | J. Johnson||3.08|
|4||A. Iverson | E. Snow||6.2||22||B. Davis | J. Richardson||3.06|
|5||J. Wall | B. Beal||5.88||23||J. Nelson | H. Turkoglu||3.02|
|6||C. Paul | J. Redick||5.82||24||J. Williams | D. Wade||2.72|
|7||G. Arenas | L. Hughes||5.66||25||J. Rose | R. Miller||2.54|
|8||A. Miller | A. Iguodala||5.5||26||M. Williams | L. James||2.5|
|9||T. Parker | M. Ginobili||5.28||27||S. Cassell | R. Allen||2.28|
|10||T. McGrady | R. Alston||5.26||28||G. Payton | K. Bryant||2.12|
|11||R. Westbrook | J. Harden||5.04||29||M. Bibby | J. Johnson||1.62|
|12||R. Rondo | R. Allen||4.78||30||D. Rose | K. Bogans||1.54|
|13||S. Nash | R. Bell||4.5||31||D. Lillard | W. Matthews||1.54|
|14||P. Beverly | J. Harden||4.38||32||K. Lowry | D. DeRozan||1.52|
|15||M. Williams | M. Redd||4.34||33||S. Nash | M. Finley||1.24|
|16||K. Irving | L. James||4.28||34||C. Billups | R. Hamilton||1|
|17||R. Felton | J. Richardson||4.24||35||G. Arenas | C. Butler||0|
|18||M. Bibby | P. Stojakovic||3.74|
From all measurements, Klay Thompson and Steph Curry cemented themselves as a historic backcourt. Their efficient shooting, coupled with their stifling defense and convincing win percentage, blows the Wizards’ and Trailblazers’ backcourts out of the water. Their numbers are also well ahead of any backcourt in the last fifteen years. Almost certainly, Curry and Thompson are the best backcourt we have seen in recent history!
However, some interesting things we noticed were that Chris Paul and J.J. Redick placed highly in many of the same measurements as the Splash Bros . One of the most telling statistics was the duo’s plus-minus relative to the team’s plus-minus, which Paul and Redick scored higher on than Curry and Thompson. Paul and Redick’s high relative plus-minus can be partially attributed to the Clippers’ weak backcourt bench in Austin Rivers and an injured Jamal Crawford, and the fact that Clippers’ starters play heavy minutes as a unit. According to Basketball Reference, the Clippers’ starting lineup played over 1200 minutes together over the season, but no other Clippers’ lineup played more than 250 minutes. Even so, Redick put up career high 16.4 points per game while shooting at a career high 47.7% from the field and 43.7% from three. Paul shot 48.5% from the field and 39.8% from three this year, which is better than any of his past years as a Clipper. It would be an uphill battle, but one could argue that Paul and Redick performed just as well as Curry and Thompson this year.
Jameer Nelson and Hedo Turkoglu from 2009 also fall in the upper echelon of backcourts, based on their large point differential and terrific shooting percentages. The Magic - with the duo playing - outscored their opponents by a much larger margin than the duo off the court. However, according to our factor model, the backcourt didn’t perform well in the statistics with larger weights such as assists or total rebounding percentage. The ranking model requires some fine-tuning, all else considered Nelson and Turkoglu still deserve consideration as one of the best backcourts since 2000.
From a statistical perspective, Curry and Thompson’s collective 2014-2015 season was absolutely dominant, akin to the likes of Isiah Thomas and Joe Dumars or Tim Duncan and David Robinson. In the last fifteen years, there have been numerous instances of great backcourts, but none put up numbers close to that of Curry and Thompson. At this point, their only legitimate criticism is their failure to win a championship -- something they intend to fix this year.