Who is the Clutchest? Evaluating improvements in scoring efficiency from the regular to the post-season from the 2010 to 2020 NBA playoffs.
Kiran Krishnamurthi
7/09/2021
The NBA Finals are set: this year the Phoenix Suns will compete against the Milwaukee Bucks in a best of seven game series for the NBA Championship. That’s a pretty straightforward sentence, but for the basketball sickos like me it forces us to do a double take. This year’s NBA finals will be the first year since 2006 to not feature one of Stephen Curry, LeBron James, or Kobe Bryant. Have the perennial playoff favorites fallen or have the young superstars solidified their place at the top?
Regardless of where the playoff giants might be, this year’s NBA finals will be one to remember for sure. In a year filled with uncertainty due to COVID-19, basketball fans might be able to finally take a deep breath and realize we’ve made it all the way to the finals. The new storyline this year is who will get their first ring: the Phoenix Suns’ Chris Paul or the Milwaukee Bucks’ two time MVP Giannis Antetokounmpo? However, the series doesn’t stop at these guys. Milwaukee has firepower in both Khris Middleton and Jrue Holiday, while Phoenix has a budding superstars in Devin Booker and Deandre Ayton. And you can count on both teams to pull deep contributions from bench players like Bobby Portis or Cameron Payne.
With all this interest in the NBA Championship, the playoffs are also a special time for players to really set themselves apart from their regular season narratives–for better or for worse (Playoff/Pandemic P). This year’s NBA post-season thus far has only buttressed the idea, as we’ve seen players like Reggie Jackson ball out and earn himself the title of Mr. June, and in contrast players like Julius Randle go from the Most Improved Player to the Most Inefficient Player in the Knicks early exit. The playoff energy, atmosphere, and pressure are transformative forces and act as a filter for the most clutch players to come out on top. Accordingly, I set out to find out which players across the past 10 NBA Playoffs have really answered the call put on them from their team and rose to the occasion. My question essentially boiled down to the following: Which player in the past decade had the greatest improvement in scoring contributions adjusted for minutes played from the regular season to the post season?
Section 1: Creating the Evaluation Metric
In order to evaluate a player’s change in performance from the regular season to the playoffs, I decided to isolate scoring as the sole metric for evaluation. While being a bucket-getter is more important in today’s NBA compared to what it might have been a decade ago, I still believe it’s the easiest and purest way to evaluate how clutch a player can become during the playoffs. Thus, in evaluating performance I looked at the difference in a player’s regular season and playoff minute adjusted scoring impact which I referred to as “the scoring impact spread” or simply just the “spread.”
The following is the equation I used for calculating the spread: \[\Delta = \left[\frac{\pi}{\frac{\log(\mu)}{48}}\right] - \left[\frac{\Pi}{\frac{\log(M)}{48}}\right]\] These are the variables along with their associated values: \[\begin{align*} \Delta & = Spread \\ \pi & = PointsPerGame_{RS} \\ \Pi & = PointsPerGame_{P} \\ \mu & = MinutesPerGame_{RS} \\ M & = MinutesPerGame_{P} \end{align*}\]
Figure 1.1 Comparison of Regular Season and Playoff Minutes Per Game
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
Figure 1.2 Comparison of Regular Season and Playoff Points Per Game
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
Both of the graphs above demonstrate a sigmoid like interaction between the regular season and playoff values, where values are asymptotic towards the extremes of regular season minutes played as well as regular season points per game. This is reflective of the fact that there are only so many minutes a player can play in a game until they’ve played every minute. However, for points per game there is no hard ceiling. Instead, a player’s points per game are simply limited by human capabilities. And in this sense, we see a bit more dispersion as we get to the extremes as well as a bit less of a taper off towards an asymptote. The implications for the analysis are that there is variance in the change in points per game from the regular season to the playoffs, whereas the minutes per game remains a bit more consistent across the league. We have a supposition that during the NBA playoffs players do increase/decrease their scoring while playing similar minutes, which ties back to the original question of how does scoring change in a playoff setting.
Figure 1.3 Minutes Per Game Versus Points Per Game
This graph shows the relationship between minutes per game and points per game in both the regular season and the NBA playoffs. Interestingly enough, the playoff values mirror the same relationship, except they’re shifted further over on the x-axis. While a preliminary observation in the data, it might suggest that as a whole player scoring efficiency decreases during the playoffs when scoring is evaluated based upon minutes played. The y-axis values don’t seem to be that different between the regular season and the playoffs, but there are a handful of playoff data points that exhibit more minutes per game than the majority of the regular season values. However, because this graph doesn’t pair the individual differences in regular season vs. playoff minutes and points per game, we cannot distinguish between one players regular season numbers and another players playoff numbers.
Figure 1.4 Random Sample of 10 Players’ Minutes and Points Per Game Graphed
This is a plot of a random sample of 10 entries from the data set I am using. There will be several players who have multiple entries in the data set, but each entry will correspond to a different NBA post-season they appeared in within the 2010 to 2020 timeframe. A 10-player sample is too small to draw conclusions as to how it relates to the whole data set, but it does serve as a neat window to observe individual entries and see how the data compares on a much more granular level.
Figure 1.5 Regular and Playoff Minute Adjusted Scoring Values
Figure 1.6 Regular Season vs. Playoff Minute Adjusted Scoring Values
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'`geom_smooth()` using formula 'y ~ x'
The final figure included here in this section shows the relationship between the regular season and playoff minute adjusted scoring values. The difference between these two points equals the “spread” value depicted in the equation at the beginning of this section. This chart reveals that these data points have a semi-linear relationship. There are two smoothing lines superimposed onto the relationship plot, both of which capture the data using different methods. The yellow line captures the data using the generalized additive model, whereas the purple line captures the data using the standard linear model. As observed, the purple and yellow predictor lines almost perfectly overlap across the majority of the data. While the r-squared term would better inform us of the strength of the two variables’ relationship, it isn’t necessary for our retrospective and comparative analysis.
Section 2: Understanding the Data and Important Considerations
My analysis in evaluating player spreads is based on NBA regular season and playoff data from the 2009-2010 season through the 2019-2020 season. I obtained the data all from Basketball Reference and removed a few rows where players had been traded mid-season and had appeared twice on the regular season lists. The data contains the players that played minutes in a playoff game from each team in the corresponding playoffs, along with their respective regular season performances.
I’ve decided to remove all players from the sample who played less than 5 regular season and playoff minutes per game. A game-altering spark can be made in less than 5 minutes, but overall these examples are one game outliers and distort the average data. Instead, by including players that played over 5 minutes per game in both their regular and post-season games, it ensures better consistency in their performances and therefore the numbers they’re putting up.
Table 2.1 Example of the Resulting Calculations
Teams Player Age Year Allstar Champion R_PPG P_PPG R_MP P_MP SPREAD
1 Toronto Raptors DeMar DeRozan 24 2014 No No 22.7 23.9 38.2 40.3 11.252439
2 Toronto Raptors DeMar DeRozan 25 2015 Yes No 20.1 20.3 35.0 39.8 -6.861167
3 Toronto Raptors DeMar DeRozan 26 2016 Yes No 23.5 20.9 35.9 37.3 -37.814763
4 Toronto Raptors DeMar DeRozan 27 2017 Yes No 27.3 22.4 35.4 37.3 -70.298024
5 Toronto Rapters DeMar DeRozan 28 2018 Yes No 23.0 22.7 33.9 35.4 -7.840917
6 San Antonio Spurs DeMar DeRozan 29 2019 No No 21.2 22.0 34.9 35.9 8.464104Figure 2.1 All the Spread Values from 2010-2020
Figure 2.2 Histogram of Spread Values
Figure 2.3 Density Function for Spread Values
# A tibble: 1 x 2
`Mean Spread` `Standard Deviation`
<dbl> <dbl>
1 -13.1 40.4The histogram and the density function both reveal that the spreads are normally distributed. On the density function, the mean and three standard deviations are superimposed. These boundaries reveal that a majority of the data lies within three standard deviations of the mean.
Figure 2.4 Spread Values Arranged Smallest to Largest
Here’s a graph of the spreads arranged from smallest to largest values. Since I calculated the spread by taking the log of a players minutes and dividing it by 48 (the most any player can play in a game without overtime) in both the regular and post-seasons, the graph is asymptotic towards the extreme changes in points per minute. However, the majority of the data represents a consistent trend where the middle observations show linear growth in a players scoring impact spread. The benefit of this shape in the spread’s distribution is that the best and worst performances will stand out in comparison to the rest of the data. However, the main drawback would be if player spreads are inflated by some component of an individual performance that made it comparatively easier to achieve an outstanding result.
Section 3: How do Spreads Compare for All-Stars versus Non All-Stars?
Naturally, one would expect the better players to show an improvement in their scoring come the playoffs out of all players in the league. Players who showed an ability to excel during the regular season would generally lend themselves well to the highly competitive and intense environment presented in the playoffs, and therefore should ideally be able to improve when it counts. Thus, I considered it an important part of the analysis to evaluate the split in how All-Stars performed compared to their Non All-Star counterparts.
Figure 3.1 Spread Boxplot for Non All-Stars and All-Stars
This box plot and jitter plot both show that the average spread is higher when isolating NBA All-Stars compared to Non All-Stars. When separating the data, I only considered a player an All-Star in the year they were selected for the corresponding All-Star Game. For example, while Paul George has been an All-Star in previous years when he also made the playoffs, he wouldn’t be considered an All-Star in the 2020 data even though the Clippers made the playoffs because he wasn’t selected as one.
Figure 3.2 All-Star Spreads With Each Year Represented by a Different Color
One observation to note from the graph above is the growing difference in the spread across the years. Entries from the playoffs at the beginning of the decade are more closely bound together, whereas they tend to fan out as time passes. This might be indicative of the growing importance of scoring in the NBA as players tend to prioritize getting points ahead of other contributions and therefore greater variance in their spread.
This chart also allows us to better evaluate individual player change in their minute adjusted scoring contributions across different years. The interesting thing to note here is that while these selections feature only All-Stars for a given year, the chart still captures some of the worst drop-offs in spreads in the entire data set. This next chart better visualizes the collective relationship between Non All-Star and All-Star spreads.
Figure 3.3 Spreads Accounting for All-Star vs. Non All-Star Status
As you can see, towards the bottom right there are some All-Star colored points showing that some of the worst drop-offs in minute adjusted scoring contributions have come in recent NBA post-seasons. The x-axis of player observations is chronologically ordered, with the first entries coming from the 2010 playoffs and moving all the way through the 2020 NBA bubble playoffs. Let’s take a look at these cases and show how All-Star versus Non All-Star status compared in their respective drop-offs.
Table 3.1 and 3.2 The Worst 6 Spreads from both All-Stars and Non All-Stars
# A tibble: 6 x 11
Teams Player Age Year Allstar Champion R_PPG P_PPG R_MP P_MP SPREAD
<chr> <chr> <dbl> <dbl> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Toronto Raptors Pascal Siakam 25 2020 Yes No 22.9 17 35.2 38 -84.3
2 Toronto Raptors Kyle Lowry 30 2017 Yes No 22.4 15.8 37.4 37.5 -87.6
3 Philidelphia 76ers Joel Embiid 24 2019 Yes No 27.5 20.2 33.7 30.4 -91.3
4 Golden State Warriors Klay Thompson 26 2017 Yes Yes 22.3 15 34 35.1 -101.
5 Houston Rockets Russell Westbrook 31 2020 Yes No 27.2 17.9 35.9 32.8 -118.
6 Portland Trail Blazers Damian Lillard 27 2018 Yes No 26.9 18.5 36.6 40.5 -119. # A tibble: 6 x 11
Teams Player Age Year Allstar Champion R_PPG P_PPG R_MP P_MP SPREAD
<chr> <chr> <dbl> <dbl> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Philidelphia 76ers Furkan Korkmaz 22 2020 No No 9.8 0.8 21.7 10 -136.
2 New York Knicks Amar'e Stoudemire 28 2011 No No 25.3 14.5 36.8 33.5 -139.
3 Dallas Mavericks Rodrigue Beaubois 23 2012 No No 8.9 0 21.7 6 -139.
4 Portland Trail Blazers Brandon Roy 25 2010 No No 21.5 9.7 37.2 27.7 -145.
5 Golden State Warriors David Lee 29 2013 No No 18.5 5 36.8 10.8 -145.
6 Boston Celtics Kelly Olynyk 24 2016 No No 10 0.5 20.2 8 -148.Interestingly, the6 worst collapses in performances from NBA All-Stars all come from the 2017 NBA Playoffs or later. None of the bottom 6 entries for All-Stars are all that surprising since they’re consistent with what the numbers show, but only 5 out of the 6 seem consistent with how the team actually performed. The Raptors 2017 and 2020 playoff performances were both disappointing and reflected underachievement compared to their regular season success. Similarly the 2019 series for Philly was unfortunately ended in the semis with a game 7 loss to the infamous Kawhi buzzer-beater. The Rockets bubble series was awful and really showed a team that didn’t work well together, as evidenced by Westbrook’s appearance on this list. And finally, while Dame Time is notoriously one of the clutchest performers (and especially in the playoffs) the sweep to the Pelicans back in 2018 hurts his reputation. However, despite all these playoff collapses from great players, they’re still not as bad in comparison to the bottom 6 performances from Non All-Stars, with all 6 entries coming in worse off than the worst All-Star performance.
The one really surprising appearance on here is 2017 Klay Thompson. Klay’s appearance comes from a title year and not the unfortunate 3-1 collapse from the year before. While playing increasing minutes in the playoffs (basically the same but just an additional minute), he averaged 7 fewer points per game. This might reflect the role player status he took on when Durant came to the team, and only exacerbated this in the playoffs where star players tend to try to take over. In order to better understand this performance, let’s take a look at all the Warriors contributions that year.
Table 3.3 Spreads for the 2017 Championship Warriors
Teams Player Age Year Allstar Champion R_PPG P_PPG R_MP P_MP Delta_PPG Delta_MP SPREAD
1 Golden State Warriors Kevin Durant 28 2017 Yes Yes 25.1 28.5 33.4 35.5 3.4 2.1 39.854301
2 Golden State Warriors Draymond Green 26 2017 Yes Yes 10.2 13.1 32.5 34.9 2.9 2.4 36.363229
3 Golden State Warriors Stephen Curry 28 2017 Yes Yes 25.3 28.1 33.4 35.4 2.8 2.0 32.038126
4 Golden State Warriors Damian Jones 21 2017 No Yes 1.9 1.8 8.5 5.3 -0.1 -3.2 9.192162
5 Golden State Warriors Patrick McCaw 21 2017 No Yes 4.0 4.1 15.1 12.1 0.1 -3.0 8.208346
6 Golden State Warriors Shaun Livingston 31 2017 No Yes 5.1 5.2 17.7 15.7 0.1 -2.0 5.452617
7 Golden State Warriors Ian Clark 25 2017 No Yes 6.8 6.8 14.8 13.7 0.0 -1.1 3.574174
8 Golden State Warriors JaVale McGee 29 2017 No Yes 6.1 5.9 9.6 9.3 -0.2 -0.3 -2.461833
9 Golden State Warriors David West 36 2017 No Yes 4.6 4.5 12.6 13.0 -0.1 0.4 -2.933202
10 Golden State Warriors Andre Iguodala 33 2017 No Yes 7.6 7.2 26.3 26.2 -0.4 -0.1 -5.749032
11 Golden State Warriors Zaza Pachulia 32 2017 No Yes 6.1 5.1 18.1 14.1 -1.0 -4.0 -8.597151
12 Golden State Warriors Matt Barnes 36 2017 No Yes 5.7 0.8 20.5 5.1 -4.9 -15.4 -67.014019
13 Golden State Warriors Klay Thompson 26 2017 Yes Yes 22.3 15.0 34.0 35.1 -7.3 1.1 -101.192980Out of all the players on this Warriors team, Klay had the biggest drop off in scoring impact during their championship run. However, both his and Matt Barnes’ poor showing in this evaluation do reflect a shortcoming of my metric. Players getting a lot of minutes but not providing much offense still can provide valuable contributions to a team’s success that aren’t captured from their box-score stats. Klay is a phenomenal teammate and provides unparalleled floor spacing and shooting when needed, and Matt Barnes is a veteran who gives leadership and experience.
Table 3.4 10 Best Spreads from 2010 to 2020
# A tibble: 10 x 11
Teams Player Age Year Allstar Champion R_PPG P_PPG R_MP P_MP SPREAD
<chr> <chr> <dbl> <dbl> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Los Angeles Lakers Andrew Goudelock 24 2013 No No 0 12 6 26.7 175.
2 Utah Jazz Donovan Mitchell 23 2020 Yes No 24 36.3 34.3 37.7 154.
3 Chicago Bulls Vladimir Radmanović 32 2013 No No 1.3 9 5.8 10 152.
4 Indiana Pacers Lance Stephenson 26 2017 No No 7.2 16 22 26.8 122.
5 Portland Trail Blazers CJ McCollum 23 2015 No No 6.8 17 15.7 33.2 114.
6 Orlando Magic Glen Davis 26 2012 No No 9.3 19 23.4 38 109.
7 Portland Trail Blazers Al-Farouq Aminu 27 2018 No No 9.3 17.3 30 32.8 107.
8 Minnesota Timberwolves Derrick Rose 29 2018 No No 5.8 14.2 12.4 23.8 104.
9 Orlando Magic Nikola Vučević 29 2020 No No 19.6 28 32.2 37 101.
10 Brooklyn Nets Caris LeVert 24 2019 No No 13.7 21 26.6 28.8 99.5Surprisingly only one All-Star makes the top 10 highest spreads from the past decade, that being Donovan Mitchell and his insane performance in the Jazz’s first round loss to the Nuggets in the bubble last year. Mitchell went from 24 to 36 points per game (a 12 point increase) while only playing an extra three and a half minutes per game.
Aside from Mitchell, this top 10 is supportive of the idea that role players or second-options are the ones who make a big impact in a teams scoring during the playoffs. Players like CJ McCollum or Vučević are All-Star level players and have been selected to games in different years, but their ability to turn on their scoring during the playoffs reflects another gear in these years that other All-Stars didn’t have. It isn’t to say they’re a better player than those All-Star selections, but more so to show that they made an impact when it counted. Nonetheless, none of the teams on this list of top 10 players made deep runs into the playoffs or won a championship so perhaps individual scoring performance in this case isn’t as important as a holistic ability to contribute.
Table 3.5 10 Best Spreads from 2010 to 2020 for All-Stars Only
# A tibble: 10 x 11
Teams Player Age Year Allstar Champion R_PPG P_PPG R_MP P_MP SPREAD
<chr> <chr> <dbl> <dbl> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Utah Jazz Donovan Mitchell 23 2020 Yes No 24 36.3 34.3 37.7 154.
2 Atlanta Hawks Paul Millsap 31 2017 Yes No 18.1 24.3 34 36.5 77.9
3 Golden State Warriors Kevin Durant 30 2019 Yes No 26 32.3 34.6 36.8 77.9
4 Washington Wizzards John Wall 27 2018 Yes No 19.4 26 34.4 39 77.5
5 New Orleans Pelicans Anthony Davis 21 2015 Yes No 24.4 31.5 36.1 43 75.4
6 Philidelphia 76ers Joel Embiid 25 2020 Yes No 23 30 29.5 36.3 74.7
7 Cleveland Cavaliers LeBron James 32 2017 Yes No 26.4 32.8 37.8 41.3 74.3
8 Los Angeles Clippers Chris Paul 27 2013 Yes No 16.9 22.8 33.4 37.3 71.2
9 Cleveland Cavaliers LeBron James 33 2018 Yes No 27.5 34 36.9 41.9 71.1
10 Miami Heat Dwyane Wade 28 2010 Yes No 26.6 33.2 36.3 42 70.9Mitchell tops the list as expected from the previous table, but impressively he’s not the youngest player to appear in the top-10. At only 21 years old Anthony Davis appears as the All-Star with the 5th best regular season to playoff improvement across the past 10 years. Out of all the players on this list the two that are the most underrated in their playoff performances might be Paul Milsap and John Wall during the 2017 and 2018 NBA Playoffs. Milsap contributing another 6 points per game while only playing an extra two and half minutes is an impressive contribution, as is Wall’s 6.5 point boost for an extra 4.5 minutes of playing time.
Perhaps this comes as a surprise to some or as expected to others, but LeBron James is the only player to appear in the top 10 twice. The surprise in this case is that he’s not higher, with his highest appearance coming in at 7 out of the top 10. Nevertheless, it shouldn’t come as a surprise that his two impactful increases in minute adjusted scoring come from the two years where Cleveland made the finals only to get beat by the 4 headed monster Warriors team with Curry, Klay, Durant, and Draymond.
Table 3.6 Top 10 Players with the Highest Average Spreads with a Minimum of at Least 5 Post-Season Appearances
# A tibble: 10 x 3
Player `Number of Playoff Appearances` `Average Spread`
<chr> <int> <dbl>
1 CJ McCollum 5 37.7
2 Chris Paul 10 37.5
3 Draymond Green 7 34.2
4 Rajon Rondo 7 33.5
5 Derrick Rose 6 28.8
6 Dirk Nowitzki 6 23.7
7 Nicolas Batum 5 22.2
8 Derek Fisher 5 20.9
9 Andre Iguodala 10 18.9
10 Kawhi Leonard 8 18.7The names on this list that seem appropriate and highlight the work they’ve done in contributing to playoff success are players like Chris Paul, Draymond, Rondo, D-Rose, Dirk, Iguodala, and Kawhi. I honestly would’ve expected Kawhi to appear higher on this list since he has two Finals MVP awards but his contributions are also pronounced on the defensive end which this metric does not capture. The rest of the players on this list are all players with experience in the playoffs and reputations as leaders, which creates a reinforcing loop. These players past performances support their reputations as leaders with experience, and as they are brought in to lead young playoff teams they’re given more opportunities to reinforce their status as a consistent playoff “improver.”
Section 4 Analyzing LeBron
Table 3.6 above in theory should reveal the most consistent playoff “improvers” across the past decade and it does seem to agree with what results might historically suggest. The biggest surprise from my perspective is the absence of LeBron on this list, but that isn’t to say his playoff performances weren’t important or good. This metric strictly looks at the change between the regular season and playoffs and not just at what the playoff performance was. Therefore, it could certainly be possible that LeBron was dominant from start to finish in the years where he won a title or took teams to the finals (i.e. almost every year).
Table 4.1 LeBron’s Spreads from 2010 through 2020
Teams Player Age Year Allstar Champion R_PPG P_PPG R_MP P_MP SPREAD
1 Cleveland Cavaliers LeBron James 25 2010 Yes No 29.7 29.1 39.0 41.8 -14.942868
2 Miami Heat LeBron James 26 2011 Yes No 26.7 23.7 38.8 43.9 -49.515094
3 Miami Heat LeBron James 27 2012 Yes Yes 27.1 30.3 37.5 42.7 28.499584
4 Miami Heat LeBron James 28 2013 Yes Yes 26.8 25.9 37.9 41.7 -20.644655
5 Miami Heat LeBron James 29 2014 Yes No 27.1 27.4 37.7 38.2 2.656772
6 Cleveland Cavaliers LeBron James 30 2015 Yes No 25.3 30.1 36.1 42.2 47.437682
7 Cleveland Cavaliers LeBron James 31 2016 Yes Yes 25.3 26.3 35.6 39.1 4.397306
8 Cleveland Cavaliers LeBron James 32 2017 Yes No 26.4 32.8 37.8 41.3 74.258714
9 Cleveland Cavaliers LeBron James 33 2018 Yes No 27.5 34.0 36.9 41.9 71.082147
10 Los Angeles Lakers LeBron James 35 2020 Yes Yes 25.3 27.6 34.6 36.3 26.160509Taking a closer look at LeBron, we can see that over time his spreads become more consistently positive. In fact, the earliest years represented in this data set show a negative spread for his last year in Cleveland and his first year in Miami. During his first title run he did improve his minute adjusted scoring but his second and third title run are negative and just above zero, respectively. While LeBron’s spread might not place him as highly as other players on this list, his impact is so difficult to quantify given that he elevates the play of everyone around him.
Table 4.2 Team Average Spread from each of LeBron’s Playoff Apprearances without LeBron’s Spread Included
# A tibble: 10 x 3
# Groups: Year [10]
Year Teams `Average Spread without LeBron`
<dbl> <chr> <dbl>
1 2010 Cleveland Cavaliers -26.0
2 2011 Miami Heat -18.3
3 2012 Miami Heat -14.3
4 2013 Miami Heat -13.8
5 2014 Miami Heat -22.2
6 2015 Cleveland Cavaliers -2.57
7 2016 Cleveland Cavaliers -23.1
8 2017 Cleveland Cavaliers -25.5
9 2018 Cleveland Cavaliers -34.4
10 2020 Los Angeles Lakers -10.8 This table shows that without LeBron’s contribution, the average spread of his supporting cast has been negative for each of his playoff appearances, including those where he also won a title.
Table 4.3 LeBrons Teams’ Spreads With and Without Him Included
# A tibble: 10 x 5
Year Teams `Spread without LeBron` `Spread with LeBron` `LeBron Impact`
<dbl> <chr> <dbl> <dbl> <dbl>
1 2010 Cleveland Cavaliers -26.0 -24.9 1.10
2 2011 Miami Heat -18.3 -20.7 -2.40
3 2012 Miami Heat -14.3 -10.4 3.89
4 2013 Miami Heat -13.8 -14.4 -0.625
5 2014 Miami Heat -22.2 -20.1 2.07
6 2015 Cleveland Cavaliers -2.57 2.43 5.00
7 2016 Cleveland Cavaliers -23.1 -20.6 2.50
8 2017 Cleveland Cavaliers -25.5 -16.4 9.07
9 2018 Cleveland Cavaliers -34.4 -26.3 8.12
10 2020 Los Angeles Lakers -10.8 -8.19 2.64 While this table doesn’t reveal anything we couldn’t have have deduced from the two tables before this one, it does help quantify the specific impact LeBron had on each of his team’s minute adjusted scoring spread. In theory, LeBron being a “play-elevator” for those around him would entail a positive scoring impact spread come the post-season as his experience and leadership should help players adjust to the playoff environment and setting. Nonetheless, the negative spreads could still very well indicate a positive impact from LeBron, except the impact wouldn’t be purely captured by a change in scoring. While LeBron could cause improvement in other box-score stats, there’s a easy argument to be made that his presence and leadership elevate his teammates’ defensive contributions. There’s the saying “defense wins championships” and it’s certainly possible that LeBron’s impact better lends itself to this basketball proverb.
Section 5: Evaluating Spreads from NBA Championship Winning Teams and the Final’s MVP
Since the ultimate goal of the NBA playoffs is to win a ring, performances that fall short of these expectations might be written off as not as clutch as those that manage to secure the title. Quantitatively, players can have massive improvements in their minute adjusted scoring come the playoffs, but if they consistently fail to achieve the end goal of winning a ring, are there performances less valuable compared to those that won the title?
Figure 5.1 Boxplot for Spreads from Championship Winning Players
NBA champions on average have a higher spread compared to the other players in the playoffs. However, the difference isn’t as pronounced as what might be expected. Comparing the averages for ring winning players and those who didn’t reveals a difference in the minute adjusted scoring spread of just ~1.55. In both cases, the average is negative which suggests that teams don’t dominate the post-season purely from their scoring output.
Another consideration to be made in the case of comparing teams that won championships and those that didn’t is their extended playoffs. To win a title, a team has to play a minimum of 16 games with the potential to play up to 28 games. Simply through a greater game sample size a player’s scoring improvement may normalize out compared to players on teams that saw first round exits. It’s easier for a player to turn it on for just one playoff series compared to the need to sustain a scoring improvement all the way through the finals. With this in mind, it might even suggest that positive spreads for players that won championships are even more impressive.
Figure 5.2 Spreads from the Finals MVPs Across the Years
This graph confirms the idea that NBA Final’s MVPs have a positive spread in their minute adjusted scoring, but as mentioned earlier the ability to achieve a positive spread across as many games as it takes to win the title is even more impressive. Here I’ve indicated the perceived difficulty of a player achieving their scoring spread through the color and size of their point. Larger and deeper red points indicate particularly difficult title runs as evidence through more playoff games being played. From this analysis, I’d arrive at the conclusion that Kawhi’s 2019 title run with the Raptors was the most impressive of the Final’s MVP list when it comes to individual player spread. It’s the third greatest out of all the Final’s MVPs but he had to play the most amount of games to get his ring which means his scoring improvement was prolonged longer than any of the others.
Section 6: Adjusting for Playoff Games Played
The thought above provokes the question: do spreads normalize over time as players play more playoff games. Intuitively, the answer should be yes. It’s much easier for a player to play out of their mind basketball for four games in a first-round sweep compared to someone making a deep title run through multiple seven game series. Below are some plots and tables that show spread variance with the amount of playoff games played.
Table 6.1 Spread Statistical Values for Playoff Games Played
Playoff Games Played Number of Observations Max Spread Min Spread Average Spread Standard Deviation
1 1 50 152.11747 -135.55930 -28.3009609 51.68048
2 2 55 92.12489 -138.82244 -14.1900057 48.65809
3 3 75 175.36043 -145.19338 -21.3553956 56.36742
4 4 227 121.74116 -148.15594 -16.9713030 46.98461
5 5 224 114.44001 -133.35439 -14.2470844 46.38801
6 6 247 99.52339 -145.43097 -8.3728753 40.21663
7 7 172 154.17433 -117.45530 -12.0901793 39.69690
8 8 24 82.91496 -118.45876 -30.0917974 45.15942
9 9 60 56.87179 -88.92459 -14.9149192 31.89814
10 10 106 91.57548 -87.08629 -11.6315154 33.61658
11 11 129 94.11911 -98.92887 -16.0391877 35.87849
12 12 77 77.85096 -87.50066 -7.4798152 37.49539
13 13 55 47.90914 -96.40799 -19.5626555 33.20560
14 14 53 77.84024 -68.04588 -10.9061949 30.59093
15 15 35 63.77243 -111.58868 -7.1143168 39.29762
16 16 50 52.67681 -67.60788 -12.9623012 25.16627
17 17 54 36.36323 -101.19298 -10.5640131 27.88756
18 18 36 74.25871 -70.73819 -14.3085240 31.65939
19 19 43 90.22756 -110.87034 -4.7611989 39.33100
20 20 42 47.43768 -69.15589 -10.9564996 25.10558
21 21 55 62.53870 -52.05789 -0.5843147 24.92597
22 22 14 71.47740 -73.10189 -4.9680785 39.71785
23 23 32 32.65983 -81.65023 -9.3229011 30.20712
24 24 18 37.25898 -69.30146 -6.1557047 30.20385Figure 6.1 Spread Values for Playoff Games Played
Figure 6.2 Spread Statistic Behaviour Across Playoff Games Played
Figure 6.3 Collective PDF Mapping Spreads for Number of Playoff Games Played
Figure 6.4 Individual PDFs Mapping Spreads for Number of Playoff Games Played
Figure 6.2 above does the best job at showing a trend for player spread values to converge closer towards zero as they play more playoff games. An interesting observation is that the average approaches zero as well, but comes up from under the x-axis which suggests player performance improves as they play more games. The sample size is greater for players playing fewer games, but the average performance for players playing fewer games is more negative compared to those playing over 20 games. The maximum spread decreases as games played increases, whereas the minimum increases as games played increases. While the sample size is smaller for the greater the number of games played, the variance in performance does decrease as evidenced by a dropping standard deviation. All told, these charts and tables suggest it is important to adjust spreads for the amount of playoff games played in order to better appreciate the difficulty in sustaining improvements and drop-offs.
Table 6.2 Maximum and Minimum Number of Playoff Games Played
# A tibble: 1 x 2
`Most Playoff Games Played` `Fewest Playoff Games Played`
<dbl> <dbl>
1 24 1Adjusted Spread for Playoff Games Played
\[Adjusted \Delta = \left[\left[\frac{\pi}{\frac{\log(\mu)}{48}}\right] - \left[\frac{\Pi}{\frac{\log(M)}{48}}\right]\right]*\left(\frac{\phi}{24}\right)\] Where we’ve added the following variable: \[\begin{align*} \phi & = Playoff Games Played \\ \end{align*}\]
This new adjusted spread accounts for the amount of playoff games played through a percentage. By diving the amount of playoff games a player played in a given year by the most any player in the data set has played, the goal is to then represent the accuracy of their performance as a percentage of what the most difficult situation might entail. Since we’ve concluded that it is more difficult to sustain a positive spread through a deeper playoff run, higher spreads across only a few games played are then penalized under this metric compared to spreads for players playing more playoff games. Below is a new plot of the adjusted spreads across playoff games and a table summarizing the top 10 adjusted spreads.
Figure 6.5 Adjusted Spreads for Playoff Games Played
Figure 6.6 Adjusted Spreads for Logarithmic Scaling of Playoff Games Played
In figure 6.6 the logarithmic scaling occurs by taking the log of the number of playoff games played and dividing it by 24. This calculation would serve to alter the spread in a similar fashion to the way the log of the players minutes per game is taken and divided by 48. However, there’s a bigger variance in spreads in the non logarithm scaled metric. While less variation would seem better, it’s the opposite of what is sought after in this case. Here, the goal is to reward higher spreads through more playoff games played given the difficulty, and penalize consistently negative spreads. Ultimately, it would seem like greater variance is the better alternative of the two options. The logarithmic scaling graph shows good intra-games played variation in that there seems to be a good dispersion of spread values at each interval of playoff games played. On the other hand, the dispersion gradually increases as playoff games played increases in figure 6.5 without taking the log and this pattern is what we’re looking for.
Table 6.3 Top 10 Adjusted Spreads Non-Logarithmic Scaling
# A tibble: 1,933 x 8
Teams Player Age Year `Playoff Games Played` Spread GPAS `Spread Adj Diff`
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Denver Nuggets Jamal Murray 22 2020 19 90.2 71.4 18.8
2 Golden State Warriors Draymond Green 28 2019 22 71.5 65.5 5.96
3 Cleveland Cavaliers LeBron James 33 2018 22 71.1 65.2 5.92
4 Cleveland Cavaliers LeBron James 32 2017 18 74.3 55.7 18.6
5 Cleveland Cavaliers Kyrie Irving 23 2016 21 62.5 54.7 7.82
6 Boston Celtics Rajon Rondo 25 2012 19 63.0 49.9 13.1
7 Orlando Magic Jameer Nelson 27 2010 14 77.8 45.4 32.4
8 Utah Jazz Donovan Mitchell 23 2020 7 154. 45.0 109.
9 Golden State Warriors Andre Iguodala 35 2019 21 51.3 44.9 6.41
10 Indiana Pacers Roy Hibbert 26 2013 19 56.7 44.9 11.8
# … with 1,923 more rowsIn order to format the table neatly without column titles that caused disjointed overlapping, I’ve abbreviated the “Games Played Adjusted Spread” metric as “GPAS” and the difference between the spread with and without the playoff games played adjustment is captured through the “Spread Adj Diff” column.
Table 6.4 Players Who Were most Affected by the Spread Adjustment
# A tibble: 1,933 x 8
Teams Player Age Year `Playoff Games Played` Spread GPAS `Spread Adj Diff`
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Los Angeles Lakers Andrew Goudelock 24 2013 3 175. 21.9 153.
2 Chicago Bulls Vladimir Radmanović 32 2013 1 152. 6.34 146.
3 Utah Jazz Donovan Mitchell 23 2020 7 154. 45.0 109.
4 Indiana Pacers Lance Stephenson 26 2017 4 122. 20.3 101.
5 Portland Trail Blazers CJ McCollum 23 2015 5 114. 23.8 90.6
6 Portland Trail Blazers Al-Farouq Aminu 27 2018 4 107. 17.8 88.9
7 Orlando Magic Glen Davis 26 2012 5 109. 22.7 86.4
8 New Orleans Pelicans Jordan Crawford 29 2018 2 92.1 7.68 84.4
9 Minnesota Timberwolves Derrick Rose 29 2018 5 104. 21.8 82.7
10 Orlando Magic Nikola Vučević 29 2020 5 101. 21.1 80.1
# … with 1,923 more rowsTable 6.5 Top Average Ranking for Spreads and Appearances with a Minimum of at least 2 Playoff Appearances
# A tibble: 438 x 5
Player `Playoff Appearances` `Playoff Games Played` `Average Adjusted Spread` `Average Rank`
<chr> <int> <dbl> <dbl> <dbl>
1 Nikola Jokić 2 33 33.4 26
2 Jamal Murray 2 33 45.6 44
3 Justin Anderson 2 8 13.2 186.
4 Carl Landry 2 18 10.5 234.
5 Anthony Davis 3 34 10.8 237
6 Rajon Rondo 7 81 16.4 249.
7 Draymond Green 7 123 21.8 260
8 Andre Roberson 2 23 9.36 282
9 Bradley Beal 4 40 13.7 304.
10 Kawhi Leonard 8 124 11.9 311.
# … with 428 more rowsTable 6.6 Variation Analysis of Adjusted Spreads with No Minimum for Playoff Appearances
Player Playoff Appearances Playoff Games Played Mean Sd CV Var Max Min
1 Nikola Jokić 2 33 33.450 8.634 0.258 74.539 39.555 27.345
2 Jamal Murray 2 33 45.609 36.516 0.801 1333.430 71.430 19.789
3 Andrew Goudelock 1 3 21.920 NA NA NA 21.920 21.920
4 Goran Dragic 1 17 21.599 NA NA NA 21.599 21.599
5 Tyler Herro 1 21 19.935 NA NA NA 19.935 19.935
6 Luguentz Dort 1 6 18.358 NA NA NA 18.358 18.358
7 Timothy Luwawu-Cabarrot 1 4 15.124 NA NA NA 15.124 15.124
8 Taurean Prince 1 6 14.718 NA NA NA 14.718 14.718
9 Justin Anderson 2 8 13.195 4.713 0.357 22.214 16.528 9.863
10 Dario Saric 1 10 12.277 NA NA NA 12.277 12.277
11 Francisco García 1 6 12.102 NA NA NA 12.102 12.102
12 Anthony Randolph 1 5 11.636 NA NA NA 11.636 11.636
13 Khyri Thomas 1 3 10.673 NA NA NA 10.673 10.673
14 Joey Graham 1 4 10.625 NA NA NA 10.625 10.625
15 Carl Landry 2 18 10.540 1.107 0.105 1.226 11.323 9.757
16 Michael Porter Jr. 1 19 10.515 NA NA NA 10.515 10.515
17 Anthony Davis 3 34 10.754 3.823 0.355 14.618 13.331 6.361
18 Rajon Rondo 7 81 16.357 16.449 1.006 270.565 49.895 1.942
19 Isaiah Canaan 1 3 10.168 NA NA NA 10.168 10.168
20 Jonas Valancunas 1 10 9.708 NA NA NA 9.708 9.708
21 Draymond Green 7 123 21.794 22.239 1.020 494.592 65.521 -8.664
22 Greivis Vásquez 1 13 9.506 NA NA NA 9.506 9.506
23 Luke Kennard 1 4 9.413 NA NA NA 9.413 9.413
24 Andre Roberson 2 23 9.365 4.771 0.509 22.766 12.739 5.991
25 Gary Clark 1 5 8.661 NA NA NA 8.661 8.661Table 6.7 Variation Analysis of Adjusted Spreads with a Minimum of 2 Playoff Appearances
Player Playoff Appearances Playoff Games Played Mean Sd CV Var Max Min
1 Nikola Jokić 2 33 33.450 8.634 0.258 74.539 39.555 27.345
2 Jamal Murray 2 33 45.609 36.516 0.801 1333.430 71.430 19.789
3 Justin Anderson 2 8 13.195 4.713 0.357 22.214 16.528 9.863
4 Carl Landry 2 18 10.540 1.107 0.105 1.226 11.323 9.757
5 Anthony Davis 3 34 10.754 3.823 0.355 14.618 13.331 6.361
6 Rajon Rondo 7 81 16.357 16.449 1.006 270.565 49.895 1.942
7 Draymond Green 7 123 21.794 22.239 1.020 494.592 65.521 -8.664
8 Andre Roberson 2 23 9.365 4.771 0.509 22.766 12.739 5.991
9 Bradley Beal 4 40 13.690 16.482 1.204 271.664 38.156 2.184
10 Kawhi Leonard 8 124 11.927 11.793 0.989 139.073 37.259 -2.863
11 Gerald Wallace 3 17 11.861 11.921 1.005 142.118 21.387 -1.508
12 Maurice Harkless 3 29 11.657 13.852 1.188 191.878 27.386 1.277
13 Caris LeVert 2 9 11.128 13.589 1.221 184.655 20.736 1.519
14 Chris Paul 10 92 11.032 11.196 1.015 125.358 24.569 -15.120
15 Goran Dragić 3 35 8.345 8.586 1.029 73.717 18.234 2.791
16 P.J. Tucker 4 50 12.200 13.838 1.134 191.477 23.798 -4.832
17 Justise Winslow 2 18 5.981 0.200 0.033 0.040 6.122 5.839
18 Beno Udrih 2 17 9.038 11.777 1.303 138.693 17.365 0.710
19 Michael Kidd-Gilchrist 2 10 5.632 2.774 0.493 7.696 7.594 3.671
20 Jayson Tatum 3 45 16.272 23.282 1.431 542.049 41.781 -3.832
21 Kentavious Caldwell-Pope 2 25 6.886 8.442 1.226 71.271 12.855 0.916
22 Zach Collins 2 20 4.828 2.805 0.581 7.869 6.812 2.845
23 Derrick White 2 10 9.931 16.058 1.617 257.848 21.286 -1.423
24 Derek Fisher 5 83 12.791 18.999 1.485 360.965 31.299 -16.461
25 CJ McCollum 5 41 10.023 13.671 1.364 186.903 23.980 -6.821This analysis in the tables above helps identify reliable playoff performers by arranging the data based off of the adjusted spreads and filtering the results so that players have to have played in multiple playoffs in order to be considered. Table 5.6 has no filter for playoff appearances and as evident, several players who have only played in 1 NBA post-season make the list of the top 25 performances. These entries won’t have standard deviations or variance to their spreads since there’s only 1 entry associated with them. By adding the filter, we’re removing these one-time entries. The table is sorted based off the player’s average ranking based off of when the data is sorted by their average adjusted spread. The alternative to taking their average ranking would be to sum their total ranking, but this unfairly penalizes players who’ve played in more playoffs since they’re going to have more entries in the data from 2010 through 2020.
The important consideration to keep in mind when evaluating this table compared to other analysis that’s already been explored here is that this table is prioritizing consistency in performances. The specific example that I feel deserves attention is the difference between how Donovan Mitchell’s 2020 series against the Nuggets would appear in this table compared to the one highlighted earlier. There’s no doubt that that performance was an all time great showing, but the difference is it was for one series in one year’s playoffs. This table is based off individual players and their ability to consistently perform when their team gets to the playoffs. The one downside to this analysis is that it might unfairly prioritize role players on teams that go deeper into the playoffs simply because these player’s spreads are also in theory tested by their ability to hold up their numbers across more playoff games. Nonetheless, if a role player demonstrates a marginal improvement in their scoring efficiency across more games, then it could be argued that this should be considered more “clutch” for their team during the playoffs compared to a player who becomes a superstar in the post-season only to lose in the first round.
While table 6.7 helps us better appreciate the consistency in putting up strong, positive spreads, there is still a bit more data science to be done in order to help quantify the difficulty behind a player’s averages across this 10 year playoff sample. Table 6.7 still allows players like Jokic and Murray to float to the top of the rankings from their incredible performance in the bubble, while potentially underrating the the 9 trips to the NBA finals LeBron made across the sample. The need to filter the data for playoff appearances gives creedence to the idea that if this analysis is to look at who the clutchest player across the decade may have been, we need a way to support multiple playoff appearances and consequently devalue one-time showings.
Section 7: Creating a Consistency Score
In order to better capture consistency and quantify the duration a player’s positive spread may have lasted for, I created a supplemental metric to the spread called the consistency score. The metric is displayed below along with the associated variables. In calculating this score, the sum is calculated of the number of playoff games a player played across the 2010-2020 sample, where each year is n=1 and the total sample period has 11 years.
\[\gamma = \log\left(\sum_{n=1}^{11} \phi\right)*\nu\]
Where we’ve included the following variables in the equation and subsequent analysis: \[\begin{align*} \gamma & = Consistency Score \\ \nu & = Total Number of Playoff Appearances \\ \phi & = Playoff Games Played \\ \mu & = Average Games Played Adjusted Spread \\ \Sigma\phi & = Total Number of Playoff Games Played \\ \frac{\gamma}{\sigma} & = Consistency Score over GPAS Standard Deviation \\ \mu*\frac{\gamma}{\sigma} & = Average GPAS Adjusted for Consistency \\ \end{align*}\]
Table 7.1 Players, Consistency Scores, and Average Adjusted Spreads
Player nu SigmaPhi mu gamma
1 LeBron James 10 200 14.669 52.98317
2 Kyle Korver 11 123 -9.387 52.93403
3 Andre Iguodala 10 149 12.038 50.03946
4 Serge Ibaka 10 144 -12.542 49.69813
5 George Hill 10 123 6.589 48.12184
6 James Harden 10 123 -9.941 48.12184
7 Al Horford 10 108 -2.521 46.82131
8 Russell Westbrook 10 106 5.493 46.63439
9 Chris Paul 10 92 11.032 45.21789
10 J.J. Redick 10 91 -13.492 45.10860
11 Danny Green 9 141 -7.851 44.53884
12 Kevin Durant 9 139 4.118 44.41027
13 Dwyane Wade 9 137 -6.947 44.27983
14 J.R. Smith 9 116 -6.820 42.78231
15 Manu Ginobili 9 111 -0.142 42.38577
16 Tony Parker 9 104 2.801 41.79952
17 Paul George 9 89 -0.412 40.39773
18 Joe Johnson 9 87 -1.594 40.19317
19 Kawhi Leonard 8 124 11.927 38.56225
20 Jeff Teague 9 71 2.449 38.36412
21 Marc Gasol 8 94 5.234 36.34636
22 Paul Pierce 8 93 -2.272 36.26080
23 Paul Millsap 8 86 -1.227 35.63478
24 Matt Barnes 8 84 -14.810 35.44653
25 Jeff Green 8 83 -10.236 35.35072
26 Jamal Crawford 8 74 -6.693 34.43252
27 Draymond Green 7 123 21.794 33.68529
28 Klay Thompson 7 123 -20.622 33.68529
29 Ian Mahinmi 8 67 -7.935 33.63754
30 LaMarcus Aldridge 8 66 1.225 33.51724Now we can better understand how deep certain players have gone into the playoffs as well as how many different years they’ve had to deliver improved performances come the post-season. I decided to take the log of the total number of playoff games a player has played across the sample in order to better scale it’s importance against the number of years a player has gone to the post-season. In theory, improving the minute adjusted scoring performance from the regular season to the post season across multiple different years should prove more difficult compared to doing this across fewer years but with deeper playoff runs. Two reason standout in particular: the first being the obvious one which is that players are simply older and therefore may not be as agile or fit to extend their season through the playoffs. The second reason is that a player may improve across different years and therefore their regular season minute adjusted scoring impact should go up. This means they’re held to a higher standard for improvement come the post season, and therefore if they keep their spread positive across multiple years that’s more impressive given that it’s benchmarked against more regular season data compared to an abundance of games in one post-season. In summary, the consistency score doesn’t actually measure a change in playoff versus regular season performance, but instead captures how consistently a player made the playoffs and made deep playoff runs across the 11 year sample.
Table 7.2 Consistency Score Interaction with Spread Performance
Player nu Sigmaphi mu sigma gamma gamma.sigma mu.gamma.sigma
1 Justise Winslow 2 18 5.981 0.200 5.780744 28.9037176 172.873135
2 Carl Landry 2 18 10.540 1.107 5.780744 5.2219905 55.039780
3 Chris Paul 10 92 11.032 11.196 45.217886 4.0387536 44.555530
4 Kawhi Leonard 8 124 11.927 11.793 38.562253 3.2699273 39.000423
5 Andre Iguodala 10 149 12.038 17.468 50.039463 2.8646361 34.484489
6 Draymond Green 7 123 21.794 22.239 33.685290 1.5146945 33.011251
7 Rajon Rondo 7 81 16.357 16.449 30.761144 1.8700920 30.589096
8 Anthony Davis 3 34 10.754 3.823 10.579082 2.7672199 29.758683
9 Nikola Jokić 2 33 33.450 8.634 6.993015 0.8099392 27.092467
10 LeBron James 10 200 14.669 33.934 52.983174 1.5613595 22.903583
11 George Hill 10 123 6.589 14.160 48.121844 3.3984353 22.392290
12 Marc Gasol 8 94 5.234 10.236 36.346358 3.5508361 18.585076
13 Mike Conley 7 61 5.784 9.329 28.776117 3.0845875 17.841254
14 Ian Clark 3 41 2.925 1.900 11.140716 5.8635348 17.150839
15 Shaun Livingston 6 114 7.306 13.150 28.417191 2.1610031 15.788289
16 Glenn Robinson III 2 6 0.671 0.161 3.583519 22.2578816 14.935039
17 Derek Fisher 5 83 12.791 18.999 22.094203 1.1629140 14.874833
18 James Ennis 3 22 2.892 1.936 9.273127 4.7898385 13.852213
19 P.J. Tucker 4 50 12.200 13.838 15.648092 1.1308059 13.795832
20 CJ McCollum 5 41 10.023 13.671 18.567860 1.3581933 13.613171
21 Russell Westbrook 10 106 5.493 20.317 46.634391 2.2953384 12.608294
22 Andre Roberson 2 23 9.365 4.771 6.270988 1.3143971 12.309329
23 Jimmy Butler 7 73 5.785 14.171 30.033216 2.1193435 12.260402
24 Bradley Beal 4 40 13.690 16.482 14.755518 0.8952504 12.255979
25 Dirk Nowitzki 6 48 9.590 18.595 23.227206 1.2491103 11.978968
26 Justin Anderson 2 8 13.195 4.713 4.158883 0.8824280 11.643637
27 Derrick Rose 6 48 6.742 14.012 23.227206 1.6576653 11.175979
28 Goran Dragić 3 35 8.345 8.586 10.666044 1.2422600 10.366660
29 Zach Collins 2 20 4.828 2.805 5.991465 2.1359945 10.312581
30 Ricky Rubio 2 11 4.210 2.056 4.795791 2.3325830 9.820174In this case, there are two ways the consistency score interacts with the player’s spread to factor in the difficulty in sustaining their improvement. The first is accounting for variance in their performance, which is done by taking the consistency score \(\gamma\) and dividing it by the standard deviation \(\sigma\) of their spreads. This calculation accounts for variability across the number of years a player has appeared in the post-season. That is, players who’ve gone to many playoffs and have consistently put up similar spreads will have higher scores than those who go frequently, but are inconsistent in performing. Similarly, players who go infrequently will have lower consistency scores and therefore won’t appear as highly when sorted by their adjusted consistency score \(\frac{\)\(}{\)\(}\).
The next calculation done here multiplies a player’s average spread \(\mu\) by their adjusted consistency score \(\frac{\)\(}{\)\(}\). The average adjusted spread in this calculation represents the average of all the player’s adjusted single playoff spreads, and therefore the difficulty in achieving their spread is only reflective of a single playoff run at a time. However, if a player achieves a positive spread after two deep playoff runs in a row, that would seem more impressive than a higher positive spread only done in one playoffs. Thus, the interaction with their variance adjusted consistency score allows us to evaluate which players most frequently put up the highest spreads across the past decade.
The results from this table a bit surprising, given that the top two entries are Justice Winslow and Carl Landry, two players who’ve played two post-seasons but fewer than 20 games. The rest of the table seems better reflective of the notable performances in the post-seasons, but in order to remove outlying performances like that we’ll add a filter for a minimum of more than 20 playoff games played on top of 2 post-season appearances.
Table 7.3 Consistency Score Interaction with a Minimum of more than 20 Games Played
Player nu Sigmaphi mu sigma gamma gamma.sigma mu.gamma.sigma
1 Chris Paul 10 92 11.032 11.196 45.217886 4.0387536 44.555530
2 Kawhi Leonard 8 124 11.927 11.793 38.562253 3.2699273 39.000423
3 Andre Iguodala 10 149 12.038 17.468 50.039463 2.8646361 34.484489
4 Draymond Green 7 123 21.794 22.239 33.685290 1.5146945 33.011251
5 Rajon Rondo 7 81 16.357 16.449 30.761144 1.8700920 30.589096
6 Anthony Davis 3 34 10.754 3.823 10.579082 2.7672199 29.758683
7 Nikola Jokić 2 33 33.450 8.634 6.993015 0.8099392 27.092467
8 LeBron James 10 200 14.669 33.934 52.983174 1.5613595 22.903583
9 George Hill 10 123 6.589 14.160 48.121844 3.3984353 22.392290
10 Marc Gasol 8 94 5.234 10.236 36.346358 3.5508361 18.585076
11 Mike Conley 7 61 5.784 9.329 28.776117 3.0845875 17.841254
12 Ian Clark 3 41 2.925 1.900 11.140716 5.8635348 17.150839
13 Shaun Livingston 6 114 7.306 13.150 28.417191 2.1610031 15.788289
14 Derek Fisher 5 83 12.791 18.999 22.094203 1.1629140 14.874833
15 James Ennis 3 22 2.892 1.936 9.273127 4.7898385 13.852213
16 P.J. Tucker 4 50 12.200 13.838 15.648092 1.1308059 13.795832
17 CJ McCollum 5 41 10.023 13.671 18.567860 1.3581933 13.613171
18 Russell Westbrook 10 106 5.493 20.317 46.634391 2.2953384 12.608294
19 Andre Roberson 2 23 9.365 4.771 6.270988 1.3143971 12.309329
20 Jimmy Butler 7 73 5.785 14.171 30.033216 2.1193435 12.260402
21 Bradley Beal 4 40 13.690 16.482 14.755518 0.8952504 12.255979
22 Dirk Nowitzki 6 48 9.590 18.595 23.227206 1.2491103 11.978968
23 Derrick Rose 6 48 6.742 14.012 23.227206 1.6576653 11.175979
24 Goran Dragić 3 35 8.345 8.586 10.666044 1.2422600 10.366660
25 Tony Parker 9 104 2.801 12.097 41.799518 3.4553623 9.678470
26 Jeff Teague 9 71 2.449 9.959 38.364119 3.8522059 9.434052
27 Jamal Murray 2 33 45.609 36.516 6.993015 0.1915055 8.734375
28 Maurice Harkless 3 29 11.657 13.852 10.101887 0.7292728 8.501134
29 Kevin Durant 9 139 4.118 22.180 44.410265 2.0022662 8.245332
30 Patrick Beverley 5 37 4.582 10.076 18.054590 1.7918410 8.210215The resulting table is probably the final holistic (i.e. no filtering for All-Stars, MVPs, LeBron teammates, etc.) that we would need to do to evaluate players who most consistently improve when it comes to the NBA playoffs. From this, the top 5 results are Chris Paul, Kawhi Leonard, Andre Iguodala, Draymond Green, and Rajon Rondo. Interestingly enough, 3 out of the top 5 players might be considered role players and 4 out of the top 5 aren’t even considered pure scorers, with Kawhi being the exception. However, the top 30 is made up of a mix of pure scorers and role players. Players like Westbrook, Derrick Rose, Dirk Nowitzki, Kevin Durant, and even Jamal Murray take on scorer roles for their team in their post-season appearances. However, important defensive presences like Patrick Beverly and PJ Tucker also appear in the top 30, which suggests that as these players are given more post season minutes with added defensive responsibilities, they’re not offensive liabilities like some other players might be.
Table 7.4 Bottom 30 Results for Adjusted Consistency Score Interaction
Player nu Sigmaphi mu sigma gamma gamma.sigma mu.gamma.sigma
1 Randy Foye 2 27 -25.195 1.668 6.591674 3.951843 -99.56668
2 Brandon Bass 5 43 -12.204 2.500 18.806001 7.522400 -91.80337
3 Quinn Cook 2 34 -31.710 3.113 7.052721 2.265571 -71.84124
4 J.J. Redick 10 91 -13.492 10.559 45.108595 4.272052 -57.63852
5 Spencer Hawes 5 34 -5.883 2.060 17.631803 8.559127 -50.35335
6 Kosta Koufos 4 27 -12.205 3.232 13.183347 4.079006 -49.78427
7 Amar'e Stoudemire 6 42 -13.853 6.954 22.426018 3.224909 -44.67467
8 Ryan Anderson 6 46 -25.522 13.164 22.971848 1.745051 -44.53719
9 Matt Barnes 8 84 -14.810 13.382 35.446534 2.648822 -39.22905
10 Mason Plumlee 5 60 -30.724 16.272 20.471723 1.258095 -38.65371
11 James Harden 10 123 -9.941 12.739 48.121844 3.777521 -37.55234
12 Enes Kanter 5 54 -21.074 11.554 19.944920 1.726235 -36.37868
13 J.R. Smith 9 116 -6.820 8.626 42.782312 4.959693 -33.82511
14 Richard Jefferson 6 62 -8.875 6.777 24.762806 3.653948 -32.42879
15 Kyle Korver 11 123 -9.387 15.673 52.934028 3.377402 -31.70368
16 Matt Bonner 6 78 -15.395 12.834 26.140253 2.036797 -31.35649
17 David Lee 5 43 -23.425 14.330 18.806001 1.312352 -30.74184
18 Daequan Cook 3 39 -17.804 6.396 10.990685 1.718369 -30.59383
19 Pau Gasol 7 80 -18.242 19.600 30.674186 1.565010 -28.54890
20 Lou Williams 7 59 -14.580 14.589 28.542762 1.956458 -28.52515
21 Aron Baynes 6 54 -8.584 7.464 23.933904 3.206579 -27.52527
22 Jae Crowder 7 72 -6.274 6.837 29.936663 4.378626 -27.47150
23 Serge Ibaka 10 144 -12.542 23.125 49.698133 2.149108 -26.95412
24 Zaza Pachulia 6 50 -4.011 3.540 23.472138 6.630547 -26.59513
25 Leandro Barbosa 4 71 -16.729 11.864 17.050720 1.437181 -24.04261
26 Tiago Splitter 5 65 -19.777 17.704 20.871936 1.178939 -23.31588
27 Mike Miller 5 74 -11.881 10.985 21.520325 1.959065 -23.27565
28 Tyson Chandler 5 47 -16.706 13.928 19.250738 1.382161 -23.09038
29 Cory Joseph 7 82 -5.334 7.204 30.847035 4.281932 -22.83982
30 Klay Thompson 7 123 -20.622 30.424 33.685290 1.107195 -22.83257Table 7.4 above shows the worst 30 players in descending order with the worst at the top. This isn’t to say these players are bad, but it does capture some of the undesirable qualities these players present when it comes to the post-season. To start, all of their average adjusted spreads are negative, which means that these players generally demonstrate scoring drop-offs when it comes to the post-season. Secondly, the interaction between their \(\sigma\) and their \(\gamma\) is important to understand because of the fact that it’ll be multiplied by a negative \(\mu\) and not a positive value. In this case, higher standard deviations are better because that lowers the output from \(\frac{\gamma}{\sigma}\). With a lowered output, the product of the negative \(\mu\) and \(\frac{\gamma}{\sigma}\) is greater since it’s essentially less negative than the others. While greater variance is generally a bad thing, in this case it means players who on averaged performed negatively do have potential to perform much better than what their average shows. On the other hand, low variance and a negative average in this calculation suggests that a player consistently drops off come the playoffs and doesn’t present much scoring potential or upside based off their track record.
To better understand the logic I just discussed above, I’ll break down the example of value #30 Klay Thompson compared to value #13 J.R. Smith. In this case, J.R. has performed worse across the sample when compared to Klay. The two players have \(\mu\) values of -6.8 and -20.6 for J.R. and Klay respectively. Purely based off of averages, Klay has performed worse. However, when accounting for their consistency scores and standard deviations, the \(\frac{\gamma}{\sigma}\) term values are 4.96 and 1.107 respectively. This suggests that J.R. consistently puts spreads closer to his \(\mu\) value when compared to Klay. They both have pretty high \(\gamma\) values of 42.8 and 33.7 for J.R. and Klay respectively, which means that both players have been to the playoffs a good amount of times and have played a ton of playoff games as well. Therefore, if one player is putting up numbers closer to their negative \(\mu\) value more often than the other due to the other player have a higher \(\sigma\), then the player with greater variance might have performed markedly better in other post-seasons and thus, should be ranked higher.
Figure 7.1 The Top and Bottom 30 Consistency Score Adjusted Spreads
In this chart, the yearly performance (GPAS) is plotted on the y-axis but the adjusted consistency score is factored into the size and color and the transparency of the points. The binary scale for the color of the points is important in distinguishing when players who have a negative adjusted consistency score for the sample, but still manage to play better in a specific years playoffs than they did in that regular season, and vice versa. Larger, more prominent points are indicative of a player who’s performance across the sample size was most consistent based of the adjusted consistency score metric.
Concluding Thoughts
This analysis is merely scratching the surface of player impact and improvement come the playoffs. My metric only looks at their scoring output and therefore is fairly rudimentary in capturing how a player benefits their team come the post season. This metric utilizes a players minutes and points per game to create a value which can be used to compare their performance to other players. Given that this metric focuses on scoring efficiency, a positive spread could be indicative of other improvements such as player shot selection, improvements in field goal percentage, or even simply more efficient scoring in a reduce role.
Two areas for further analysis that I am interesting in exploring would be looking at changes in other box score and advanced stats beyond just points and minutes per game, as well as building a machine learning model to predict and explain the relationship between various features and the spread. For the former, I’m particularly interested in exploring how player field goal percentage changes from the regular season to the playoffs since this might reveal another side to the negative spread stories. Some players might take on a reduced role during the playoffs and be asked to distribute the ball more or play extra minutes to add intensity on the defensive side while starters can catch a break. In these settings a player might take fewer shots and put up fewer points per game. But, if their efficiency per attempt increases compared to their efficiency per minute then this would be another area to consider in terms of their playoff improvement. Similarly, free throw percentage becomes incredibly important in the playoffs when games come down to the wire and are decided by a few points. If players score fewer points on the whole but excel in the clutch when it comes to making their free throws, then there’s another side to consider and capture when painitng a wholistic picture of playoff improvement.
With regards to future analysis on spread prediction, we’ve already added and explored some of the features I’d add in a model like whether or not a player was an All-Star, an NBA Champion, on a team with LeBron, or even a Final’s MVP. Features I would certainly like to add and explore further would be the number of playoff games won, the number of playoff series won, and the order of the games won (i.e. game 7 should count for more in a “clutch” analysis). These features help build out a better profile of who is a clutch player as well as give us a better sense of how accurate the spread metric is at capturing the truth in the post-season clutch narrative.
At the end of all this analysis, it’s hard to determine who has been the “clutchest” performer come the playoffs when looking at the past 10 years of playoff performances. Nonetheless, there are clearly players who consistently improve come the playoffs, even if their improvement isn’t as pronounced as some isolated cases. From my analysis, the final takeaway would suggest either Chris Paul or Kawhi Leonard should get the title of the most consistent “improver” come the playoffs; this is essentially another way to say they get hot at the clutchest time of the year.
Even with as thorough analysis as I was able to conduct, the numbers don’t tell the whole story. Basketball fans of the like know that Chris Paul has had his struggle with injuries and has disappeared in some clutch playoff moments, which would in theory alter his outcome. Similarly, the purest regular season scorers might not be able to show their impact as much as some of the more all-around contributors since they’re already operating closer to the theoretical ceiling. A shortcoming of my metric is that it doesn’t take into account how much more difficult a 5 point per game increase is when you’re already scoring 25 points per game compared to a player averaging around 10 during the regular season. This might be why players like Iguodala, Green, and Rondo all crack the top 5 as well.
But all the analysis in the world won’t change my favorite player: Chef Steph Curry