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Let’s Get Weird: Unique Box Scores and Pareto Frontiers

Which player has the most unique box scores?

New Orleans Pelicans v Philadelphia 76ers Photo by Mitchell Leff/Getty Images

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.

pareto-2018

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

Figure 1: Pareto games since 1990 (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

Figure 2: Pareto games since 1990 (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

Figure 3: Pareto games since 1990 (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.

Figure 4: Product of average scaled distance from Pareto frontiers

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.