This article was entirely inspired by Liberty Baller commentators sp8ce and QuakerQrazies following our discussion on Ben Simmons’ interesting box scores in the comments of my recent box score oddities piece.
Pareto Game
In order to understand the majority of the content here, we need to first understand what is meant by Pareto Frontier in this specific context. Since it came up in discussion relation to a fivethirtyeight article on James Harden and his Pareto games, we’ll use their definition.
“A player has a Pareto game if no other player has ever posted better numbers in all three stats in a single game. Certainly other players have scored more points than Harden in a single game (60), and some have done so with more assists or more rebounds. But no player has beaten him in all three categories at the same time.”
With that knowledge, we need to keep something in mind. Uniqueness does not necessarily equal quality. While unique games are often of extraordinary quality, the intention here is not to measure who is better or which games are better.
Methods
We will be focusing exclusively on points, assists, and rebounds, the big three of counting statistics from the 1990-2018 seasons. In order to visualize a full Pareto game we need a three axis, or 3D plot. Below is an interactive plot that you can move around to check out all the three way Pareto games since 1990.
However, what I want to do is not possible for my abilities in three dimensions, so we will reduce to two dimensions at time, looking at Pareto games with pairs of statistics as x/y locations, points/rebounds, points/assists, and assists/rebounds. Any ties that occur will be labeled in the following figures as the oldest game performance with that specific pair.
Now that an individual Pareto game is defined we next move to the Pareto Frontier, which is the line connecting each individual Pareto game. That line is a step function which moves exclusively in right angles and represents the border of all unique games compared to all others.
For each pair of statistics, Pareto games will be identified and a corresponding frontier will be created. Then, for every other game log (>680,000), the distance from that performance’s statistic pair to the corresponding frontier will be calculated and averaged by player. If this does not make conceptual sense, I promise the graphs will.
Results
Points/Rebounds
Table 1: Top 10 Pareto frontier distance (points/rebounds)
Player | Games | Avg. Distance |
---|---|---|
Player | Games | Avg. Distance |
Dennis Rodman | 544 | 18.8 |
Andre Drummond | 501 | 20.0 |
Karl-Anthony Towns | 289 | 20.2 |
Dwight Howard | 1041 | 20.3 |
Charles Barkley | 603 | 20.4 |
Joel Embiid | 135 | 20.6 |
Shaquille O'Neal | 1202 | 20.6 |
Anthony Davis | 446 | 20.8 |
DeMarcus Cousins | 535 | 21.0 |
Karl Malone | 1067 | 21.2 |
Don’t worry about the units on the distance column, just that a smaller number indicates a player’s average game is closer to the Pareto frontier than a player with a larger distance. You’ll see some of the great rebounders of the modern era on that list, but also ones that can score enough to move their average points/rebounds pairing close to the frontier. By this metric, Dennis Rodman would be the “most unique” player in terms of points/rebounds. Again, a lower distance indicates an increased level of uniqueness.
Points/Assists
Table 2: Top 10 Pareto frontier distance (points/assists)
Player | Games | Avg. Distance |
---|---|---|
Player | Games | Avg. Distance |
LeBron James | 1174 | 14.5 |
Magic Johnson | 109 | 14.9 |
Russell Westbrook | 773 | 15.1 |
Chris Paul | 903 | 15.6 |
Allen Iverson | 873 | 15.7 |
John Wall | 567 | 15.8 |
Stephen Curry | 636 | 16.2 |
Kevin Johnson | 467 | 16.3 |
Michael Jordan | 642 | 16.5 |
Damian Lillard | 498 | 16.6 |
An additional note is that comparing the raw distance between separate statistic pairs is not advised as the actual units are different. We’ll take care of that comparison issue after the following section.
Assists/Rebounds
Table 3: Pareto frontier distance (assists/rebounds)
Player | Games | Avg. Distance |
---|---|---|
Player | Games | Avg. Distance |
Dennis Rodman | 542 | 10.8 |
Charles Barkley | 603 | 12.5 |
Magic Johnson | 110 | 12.7 |
Ben Simmons | 123 | 12.9 |
Andre Drummond | 501 | 13.2 |
Larry Bird | 105 | 13.2 |
Karl-Anthony Towns | 289 | 13.4 |
Dwight Howard | 1042 | 13.5 |
DeMarcus Cousins | 534 | 13.6 |
Brad Daugherty | 269 | 13.6 |
One 76er in the top ten in each a category which is kind of fun.
Combined P/R, P/A, A/R
In order to combined the metrics into one, I scaled each distance from one to ten so that the different magnitude of the units (you can have more points than rebounds or assists) would not affect the overall. The lowest distance was scaled to one, and the largest to ten. I then multiplied each of the scaled values together to get a combined score. If a player finished dead last in uniqueness, they would have a score of 1000 (10 * 10 * 10), whereas a player who was most unique in each category would have a score of 1 (1 * 1 * 1). In the following graph (Figure 4), the top ten unique players are colored green, and Ben Simmons is in orange.
I am inordinately pleased for that Joel and Ben are so close. Further, let’s look at the table of data for the top ten (and Ben) that is ranked by their respective values. For reference, there were 1507 players eligible for this table by virtue of playing 82 or more games between 1990-2018.
Table 4: Top Ten by Product of Scaled Pareto Distances (and Ben)
Player | Games | P/R Rank | P/A Rank | A/R Rank | Overall Rank |
---|---|---|---|---|---|
Player | Games | P/R Rank | P/A Rank | A/R Rank | Overall Rank |
Dennis Rodman | 544 | 1 | 899 | 1 | 1 |
LeBron James | 1174 | 26 | 1 | 24 | 2 |
Charles Barkley | 603 | 5 | 37 | 2 | 3 |
Magic Johnson | 110 | 99 | 2 | 3 | 4 |
Russell Westbrook | 774 | 56 | 3 | 19 | 5 |
Karl-Anthony Towns | 289 | 3 | 77 | 7 | 6 |
Karl Malone | 1067 | 10 | 24 | 17 | 7 |
Joel Embiid | 135 | 6 | 45 | 11 | 8 |
Larry Bird | 105 | 28 | 16 | 6 | 9 |
DeMarcus Cousins | 535 | 9 | 59 | 9 | 10 |
Ben Simmons | 123 | 50 | 22 | 4 | 13 |
By my metric here (and literally every other aspect of his life) Dennis Rodman is the most unique player since 1990 in terms of box scores. His slightly more famous teammate Michael Jordan was 25th. And now, in the below table we look at some players I found interesting that did not make the top ten plus Ben cutoff.
Table 5: Selection of Players with Pareto Scaled Distance Ranks
Player | Games | P/R Rank | P/A Rank | A/R Rank | Overall Rank |
---|---|---|---|---|---|
Player | Games | P/R Rank | P/A Rank | A/R Rank | Overall Rank |
Aaron McKie | 793 | 768 | 596 | 598 | 668 |
Alaa Abdelnaby | 256 | 818 | 1144 | 1024 | 1041 |
Alexey Shved | 182 | 1133 | 610 | 1019 | 909 |
Allen Iverson | 914 | 132 | 5 | 170 | 30 |
Alonzo Mourning | 838 | 39 | 221 | 88 | 78 |
Andre Iguodala | 1078 | 267 | 178 | 157 | 182 |
Andrei Kirilenko | 797 | 248 | 287 | 222 | 244 |
Blake Griffin | 569 | 20 | 25 | 21 | 19 |
Brad Daugherty | 270 | 15 | 45 | 10 | 14 |
Chauncey Billups | 1043 | 504 | 72 | 315 | 197 |
Chris Paul | 918 | 209 | 4 | 28 | 23 |
Chris Webber | 830 | 18 | 35 | 13 | 17 |
Dario Saric | 201 | 150 | 275 | 163 | 179 |
David Lee | 829 | 51 | 265 | 50 | 75 |
Dirk Nowitzki | 1484 | 40 | 75 | 80 | 49 |
Dominique Wilkins | 435 | 55 | 56 | 128 | 60 |
Draymond Green | 496 | 156 | 284 | 59 | 124 |
Drazen Petrovic | 213 | 457 | 109 | 753 | 298 |
Drew Gooden | 790 | 127 | 490 | 172 | 219 |
Elton Brand | 1058 | 46 | 197 | 63 | 65 |
Eric Snow | 846 | 999 | 396 | 426 | 557 |
Giannis Antetokounmpo | 432 | 49 | 78 | 42 | 42 |
Hakeem Olajuwon | 770 | 14 | 76 | 22 | 22 |
Hassan Whiteside | 306 | 16 | 391 | 30 | 36 |
Ish Smith | 509 | 1042 | 478 | 655 | 702 |
James Harden | 727 | 91 | 11 | 89 | 32 |
Jason Kidd | 1391 | 158 | 40 | 24 | 40 |
Jermaine O'Neal | 1011 | 104 | 359 | 149 | 167 |
John Stockton | 1016 | 578 | 14 | 29 | 39 |
Keith Van Horn | 575 | 97 | 220 | 167 | 131 |
Kevin Durant | 814 | 26 | 15 | 64 | 25 |
Kevin Garnett | 1462 | 19 | 79 | 16 | 26 |
Kevin Johnson | 500 | 365 | 9 | 67 | 35 |
Kevin Love | 638 | 11 | 127 | 15 | 20 |
Lamar Odom | 961 | 63 | 174 | 35 | 61 |
LaMarcus Aldridge | 914 | 36 | 112 | 71 | 52 |
Nikola Jokic | 270 | 31 | 88 | 17 | 28 |
Nikola Mirotic | 301 | 183 | 414 | 269 | 283 |
Nikola Pekovic | 271 | 137 | 440 | 243 | 246 |
Nikola Vucevic | 498 | 22 | 193 | 27 | 37 |
Ricky Rubio | 470 | 423 | 89 | 74 | 115 |
Rony Seikaly | 525 | 29 | 264 | 47 | 59 |
Scottie Pippen | 944 | 100 | 44 | 54 | 51 |
Shaquille O'Neal | 1206 | 7 | 48 | 18 | 11 |
Shareef Abdur-Rahim | 830 | 60 | 111 | 83 | 68 |
Shawn Kemp | 970 | 42 | 232 | 68 | 73 |
Shawn Marion | 1163 | 45 | 226 | 62 | 71 |
Stephen Curry | 657 | 130 | 7 | 99 | 31 |
Steve Nash | 1217 | 522 | 26 | 79 | 85 |
Tim Duncan | 1392 | 13 | 86 | 12 | 18 |
Tim Hardaway | 788 | 363 | 13 | 90 | 48 |
Tim Hardaway Jr. | 377 | 683 | 323 | 983 | 586 |
Tracy McGrady | 938 | 111 | 53 | 117 | 76 |
Vince Carter | 1445 | 236 | 116 | 306 | 177 |
Vlade Divac | 1052 | 67 | 247 | 45 | 77 |
Yao Ming | 486 | 21 | 138 | 52 | 43 |
Zach Randolph | 1116 | 33 | 182 | 49 | 53 |
Wrap-Up
I thought this was a fun and informative trip through basketball history, as well as a break from Serious Basketball Writing. I mostly made this up as I went along in ways that I thought made sense numerically and gave interpretable results. Let me know in the comments if you think I blew anything, or if you want me to pull you a specific player that I did not include in the table of my Sixer-adjacent selections.