A year ago, I looked at the efficiency of 40 point games from Kobe Bryant in his recent seasons (from 2008-09 to the present) and compared to the rest of the league. He had been on a binge of 40 point games, causing the media to predictably overreact and namely him an MVP candidate and one of the best players of all-time due to his scoring at an advanced age with serious mileage. However, he had also hijacked the offense and made it his own, for better or worse. Some critics mentioned how with Bynum and Gasol on the team there was no need for Kobe to jack up shots at a historical level, which is a valid consideration with Kobe's career low shooting percentages at the time and how he's using a higher percentage of his team's possessions than all but the four highest seasons all-time.
But what is the nature of these high-scoring games? Are most of these from players selfishly throwing up shots to pad their point totals? Or are 40 point games where the player hurts his team from shooting inefficiently rare? The answer about the nature of 40 point games in the modern NBA is complicated with surprising results. These bursts of scoring, buoyed by singular talent, have more to tell than what would seem.
A simple and effective way to evaluate shooting efficiency is true-shooting percentage. For those who are unsure about what makes it true, it's basically a field-goal percentage adjusted for three pointers and one that counts most free throws as a shot attempt. Just imagine two throws equating to one shot attempt. This is true in many cases where a player is fouled while taking a shot but misses the attempt, which doesn't count as a field goal in the box score if he misses. However, there are free throws that are not tied to a possession the same way. Technical free throws are not counted in the calculation, and the same is true for and-1's fouls (where a player makes a shot but goes to the line for a free throw) and other situations. In the vast majority of cases, the number of non-shot attempt free throws is estimated from the league average for true-shooting percentage. As you can see in the formula below, instead of .5 (because two free throws equals one shot attempt) .44 is used.
TS% = PTS / ( 2*(FGA + .44*FTA.) )
Using basketball-reference's website, every 40 point and over game from the 1985-86 season to the present with playoff games included was imported into a spreadsheet. If you think playoff games shouldn't count, the below graphs show how those games have the same distribution as the ones in the regular season. If you worry that true-shooting percentage has changed too much in the past compared to the present game, don't fret -- the average TS% of the 40 point games from the 1986-1999 seasons was 67.77 compared to 67.73 for 1999 to 2012. The efficiency has been going down slightly, but the pace has been slow enough that any adjustment for year would not be worth the time to undertake it.
Results
With nearly 28 seasons including playoffs and 1861 different 40 point games, there's enough data to play around with and locate trends. The first important result is the average TS% of the 40 point games -- 68.6. For reference, the Heat are leading the league with a TS% of 58.8, and Tyson Chandler broke the record for single season TS% set by Artis Gilmore with 70.8. The average TS% for 40 point games would be eighth all-time on the single season chart. So yes, that means the average 40 point game would be historically great for a season even for a role player. In fact, only 4.8% of the games are below 55 TS%, which is typically a little over the season total average, and just 0.97% are below 50 TS%, which is truly inefficient.
As you can see in the graph below, there's an obvious pattern to these games: a triangle is created. Somehow, the more points you score, the more likely your shooting efficiency will be close to the mean of every 40 point game. On one level this is not surprising. When you score more points you're taking more shots, and with more shots there's less random variation. However, that doesn't completely explain how sharp the pattern is, and there's also the matter of why the average is such an efficient game.
The ultimate point of the graph is to study the pattern of the 40 point games. There does appear to be a range of possible values, and there are a mechanisms that create this triangle. One limit to high scoring game is the number of shots possible. True-shooting percentage is calculated by by assuming free throws are attempts too, and the highest number of "true-shots" recorded was 54.8. The more shots you take, the more attention you receive, and the more you freeze out your teammates. Conversely, thanks to regression to the mean, the more shots you take, the less likely you're able to keep a high shooting efficiency. But you also won't make the 40 point list if your shooting efficiency is low. Those factors are important in understanding the "frontier" or boundary lines, which are used to shape the triangle (Frontier lines in terms of volume and efficiency were first discussed by EvanZ.)
To study this further, it's wise to do more plotting to visualize the data better. The graph below shows the relationship between shot attempts and efficiency for all 40 point games. The red line separates all 40 point games from lower scoring ones. Obviously, as your shot attempts increase, your efficiency decreases. It's a deceptively beautiful graph because the further away from the 40 point boundary line you are, the more points you scored: that's why the dots are all in perfect curved lines. Also, remember this is only showing the 40 point games, so this would only be a slice of all possible games; we're looking at the extremes here.
Plotting points or shot attempts against TS% is problematic in that TS% already has those terms encoded in itself (consider the definition of TS%: points/true-shot attempts.) Looking at true-shot attempts versus points, there's a boundary line for highly efficient scoring games. The line represents the minimum number of shot attempts to score a certain amount of points. (There's still that mysterious dot to the left of the boundary line at 46 points, but I'll discuss that later.) This isn't a perfect system because there aren't enough super high-scoring games to judge the boundary line at those limits, but a decent estimate for helping judge which ones are truly efficient and special high-scoring games and which ones are normal.
Bringing this back to the original graph, I extrapolated the boundary line from the graph above to the one below, as well as adding a line for low efficiency. The high efficiency line is non-linear here, but remember this was transformed from true-shot attempts. (Previously, I created the high-efficiency line by looking at the change in standard deviation as points increased, so I have found a non-linear pattern using another technique.) The lines can be used to locate truly impressive scoring frenzies. Examining the lines, there's also the obvious question of where they intersect, as this in a sense is an estimate of the highest theoretical point total possible. I've left the intersection off the graph to build up some suspense here: they intersect almost exactly at 90 points. This would, to reiterate, be the estimated limit for the highest possible points based on 40 point game data from 1986 to 2013. Kobe Bryant has one last life goal to cross off.
You can also compare players and their 40 point games. Jordan, obviously, is the master here: the highest average points but only a decent efficiency. One observation is that extremely high scorers like Kobe and Jordan have a lot of low efficiency 40 point games because they take so many shots that they could simply have a slightly above average game and make the cut, while most players need an exceptional shooting night. A few players like Malone, Ewing, and Bird are extremely efficient when they do score 40. The most efficient 40 point scorers appear to be Cedric Ceballos, Ginobili, and Reggie Miller. Many feel that sometimes guys score to the detriment of their teammates and pass less often, but there are plenty of gaudy assist numbers in the table. LeBron, for example, averages over 7 assists, while a few point guards somehow manage to average over 10 assists. (My favorite observation is that Tim Duncan averages more assists than Monta Ellis in 40 point games, even though Monta's career average is significantly higher.) But a further examination of 40 point games, efficiency, turnovers, and assists will be covered in a later study.
(Here's a random note: the only playoffs without a 40 point game was 1999, the year of the dominating Spurs twin towers defense and the Knicks making it to the finals without Ewing.)
Discussion
In sterile data, outliers have no personality; they're just grubby data points that screw up your model. However, in basketball these are interesting stories. The greatest outlier here in terms of efficiency is on the far right of the graph shown above. Not only is the TS% incendiary at 103.8, but the point total is decent as well -- 46 points. This is 8.3 TS% better than the boundary line. Who is it? The answer is a little tricky to guess right away, but once you see it he's not surprising.
The answer of course is Gilbert Arenas. A 103.8 TS% meant he averaged over two points per shot when including free throws as shots. It's also 2.9 points per field goal attempt. 13/16 from the field, 7/10 with his three's, and 13/14 from the line. Let me enforce how amazing that is -- whenever he takes a shot, including drawing a foul, he's on average scoring 2.1 points, so if he pulled up for a midrange jumper and made it that would actually bring his efficiency down. The other three guys with 100 or over TS% scored 40, 40, and 41 points respectively -- Jeff Hornacek who was 8/8 on his three's, Paul Pierce last season with 13/16 from the field and perfect from the line with six three's, and Terry Porter with 12/14 from the field and 13/14 from the line in the playoffs. Arenas destroyed New York that night.
The punchline? He only played 30 minutes.
The other outlier (outside of the boundary lines) for the dubious honor of least efficient 40 point game -- and it's not even close -- since 1986 goes to none other than Kobe Bryant. His TS% was downright abysmal at 40.9 with 41 points; it was 4.9 TS% below the boundary line. He was 17/47 from the field -- yes, he took 47 shots including eight from three point range, which he all missed. Luckily, he was perfect from the line at 7/7; he could have easily been worse. To top it off he had 5 turnovers in the loss to Boston. I need to reiterate something: 47 shots is an insane number, especially when you aren't hitting anything. For comparison, when he scored 81 against Toronto he had only 46 field goals -- yes, he took more field goals scoring 41 points than 81. The rest of his team took 48 field goals. The highest number of field goals in this period was 49 from Michael Jordan in his 64 point game against Orlando. So was it a recent Kobe game where he's hobbled but still shooting, his ego outweighing his conscience? No, it was in 2002, and yes, Shaq did not play. Plus it was in overtime. Does that excuse his chucking? Of course not ... or, well, it does partly when you see who else was playing. Here's the box score.
Another game of note is one from Donyell Marshall. He's the one tied for the record for three pointers in one game. Despite hitting 12 three pointers he failed to eclipse 40 points and somehow only scored 38. If you don't believe me check here. A three-point specialist can't be defined any better than that. At the other end of the spectrum is Malone's scoring outburst versus the Bucks where he scored 61 points in only 33 minutes. He was one of the filled-in dots on the boundary line since he was 21/26 from the field and an incredible 19/23 from the line. He also had 18 rebounds and his team nearly won by 50. In terms of points per minute, he was still behind two Kobe games -- 81 point and the game where he outscored Dallas through three quarters -- but he was third among all 40 point games, just ahead of a Sleepy Floyd game where he scored 40 points in 24 minutes.
I almost glossed over Jordan, but you can't ignore his dominance. He has more 40 point games in the playoffs (38) than nine other players since 1986. He has only two less total than LeBron James, Karl Malone, Larry Bird, Hakeem Olajuwon, and Dirk Nowitzki combined. Although Wilt had 271 (in the regular season,) Jordan amassed his in a more modern game with better defense while also retiring three different times.
Conclusion
Studying the efficiency of 40 point games you can see a beautiful pattern underlying all the data. These aren't all shot-chuckers demanding the ball so they can pad their totals. If you hit 40 points, it's likely because you're shooting well. That sounds obvious, but there's more to that -- the more points you score the narrower your window of shooting efficiency is. It's a delicate balance between forcing shots to drop your percentage and getting enough attempts to score more points, and outliers are indeed rare. Jordan does own the most games with 40 points, but Malone is the master at efficiency for players with 40 or more such games with Durant hot on his tail, and Iverson the dubious distinction of the least efficient even when you look at players with only 5 such games (Zach Randolph has three games of 40 points with a 56.1 TS%.)
Even Iverson has higher TS% in those games than most players do for a season. If you score 40 points, it's because your performance has elevated enough above the surface due to your shot attempts and good efficiency, which are both inextricably linked to bound each other at higher point totals. And different players have different peaks, some experiencing 40 point games as barely a blip in the season like Jordan while others can only visit one after a lucky barrage of three's. Nonetheless, from 1986 to the present day the pattern has remained the same, consistently conforming these special games by mechanisms unseen.
TS% = PTS / ( 2*(FGA + .44*FTA.) )
Using basketball-reference's website, every 40 point and over game from the 1985-86 season to the present with playoff games included was imported into a spreadsheet. If you think playoff games shouldn't count, the below graphs show how those games have the same distribution as the ones in the regular season. If you worry that true-shooting percentage has changed too much in the past compared to the present game, don't fret -- the average TS% of the 40 point games from the 1986-1999 seasons was 67.77 compared to 67.73 for 1999 to 2012. The efficiency has been going down slightly, but the pace has been slow enough that any adjustment for year would not be worth the time to undertake it.
Results
With nearly 28 seasons including playoffs and 1861 different 40 point games, there's enough data to play around with and locate trends. The first important result is the average TS% of the 40 point games -- 68.6. For reference, the Heat are leading the league with a TS% of 58.8, and Tyson Chandler broke the record for single season TS% set by Artis Gilmore with 70.8. The average TS% for 40 point games would be eighth all-time on the single season chart. So yes, that means the average 40 point game would be historically great for a season even for a role player. In fact, only 4.8% of the games are below 55 TS%, which is typically a little over the season total average, and just 0.97% are below 50 TS%, which is truly inefficient.
As you can see in the graph below, there's an obvious pattern to these games: a triangle is created. Somehow, the more points you score, the more likely your shooting efficiency will be close to the mean of every 40 point game. On one level this is not surprising. When you score more points you're taking more shots, and with more shots there's less random variation. However, that doesn't completely explain how sharp the pattern is, and there's also the matter of why the average is such an efficient game.
The ultimate point of the graph is to study the pattern of the 40 point games. There does appear to be a range of possible values, and there are a mechanisms that create this triangle. One limit to high scoring game is the number of shots possible. True-shooting percentage is calculated by by assuming free throws are attempts too, and the highest number of "true-shots" recorded was 54.8. The more shots you take, the more attention you receive, and the more you freeze out your teammates. Conversely, thanks to regression to the mean, the more shots you take, the less likely you're able to keep a high shooting efficiency. But you also won't make the 40 point list if your shooting efficiency is low. Those factors are important in understanding the "frontier" or boundary lines, which are used to shape the triangle (Frontier lines in terms of volume and efficiency were first discussed by EvanZ.)
To study this further, it's wise to do more plotting to visualize the data better. The graph below shows the relationship between shot attempts and efficiency for all 40 point games. The red line separates all 40 point games from lower scoring ones. Obviously, as your shot attempts increase, your efficiency decreases. It's a deceptively beautiful graph because the further away from the 40 point boundary line you are, the more points you scored: that's why the dots are all in perfect curved lines. Also, remember this is only showing the 40 point games, so this would only be a slice of all possible games; we're looking at the extremes here.
Plotting points or shot attempts against TS% is problematic in that TS% already has those terms encoded in itself (consider the definition of TS%: points/true-shot attempts.) Looking at true-shot attempts versus points, there's a boundary line for highly efficient scoring games. The line represents the minimum number of shot attempts to score a certain amount of points. (There's still that mysterious dot to the left of the boundary line at 46 points, but I'll discuss that later.) This isn't a perfect system because there aren't enough super high-scoring games to judge the boundary line at those limits, but a decent estimate for helping judge which ones are truly efficient and special high-scoring games and which ones are normal.
Bringing this back to the original graph, I extrapolated the boundary line from the graph above to the one below, as well as adding a line for low efficiency. The high efficiency line is non-linear here, but remember this was transformed from true-shot attempts. (Previously, I created the high-efficiency line by looking at the change in standard deviation as points increased, so I have found a non-linear pattern using another technique.) The lines can be used to locate truly impressive scoring frenzies. Examining the lines, there's also the obvious question of where they intersect, as this in a sense is an estimate of the highest theoretical point total possible. I've left the intersection off the graph to build up some suspense here: they intersect almost exactly at 90 points. This would, to reiterate, be the estimated limit for the highest possible points based on 40 point game data from 1986 to 2013. Kobe Bryant has one last life goal to cross off.
You can also compare players and their 40 point games. Jordan, obviously, is the master here: the highest average points but only a decent efficiency. One observation is that extremely high scorers like Kobe and Jordan have a lot of low efficiency 40 point games because they take so many shots that they could simply have a slightly above average game and make the cut, while most players need an exceptional shooting night. A few players like Malone, Ewing, and Bird are extremely efficient when they do score 40. The most efficient 40 point scorers appear to be Cedric Ceballos, Ginobili, and Reggie Miller. Many feel that sometimes guys score to the detriment of their teammates and pass less often, but there are plenty of gaudy assist numbers in the table. LeBron, for example, averages over 7 assists, while a few point guards somehow manage to average over 10 assists. (My favorite observation is that Tim Duncan averages more assists than Monta Ellis in 40 point games, even though Monta's career average is significantly higher.) But a further examination of 40 point games, efficiency, turnovers, and assists will be covered in a later study.
(Here's a random note: the only playoffs without a 40 point game was 1999, the year of the dominating Spurs twin towers defense and the Knicks making it to the finals without Ewing.)
Player
|
40 point games
|
PPG
|
TS%
|
TOV
|
APG
|
Date of first 40 point game
|
Date of last 40 point game
|
Michael Jordan
|
204
|
45.5
|
64.1
|
2.8
|
5.1
|
4/17/1986
|
2/21/2003
|
Kobe Bryant
|
133
|
44.8
|
63.0
|
3.2
|
4.3
|
3/12/2000
|
4/10/2013
|
Allen Iverson
|
89
|
44.7
|
61.3
|
3.7
|
6.2
|
4/7/1997
|
12/5/2007
|
Shaquille O'Neal
|
61
|
42.8
|
65.4
|
2.7
|
2.7
|
2/16/1993
|
2/27/2009
|
LeBron James
|
60
|
44.4
|
67.2
|
3.7
|
7.2
|
3/27/2004
|
6/7/2012
|
Dominique Wilkins
|
57
|
44.6
|
64.1
|
3.0
|
3.1
|
11/1/1985
|
12/17/1994
|
Tracy McGrady
|
49
|
44.0
|
63.5
|
2.9
|
5.0
|
12/2/2000
|
5/2/2008
|
Karl Malone
|
48
|
43.1
|
70.4
|
3.6
|
3.0
|
2/4/1988
|
3/12/2003
|
Hakeem Olajuwon
|
42
|
42.8
|
64.9
|
3.5
|
3.7
|
11/5/1985
|
3/29/1997
|
Dwyane Wade
|
39
|
43.1
|
66.0
|
3.9
|
5.9
|
4/14/2005
|
5/24/2012
|
Larry Bird
|
35
|
43.5
|
68.3
|
3.3
|
6.7
|
11/27/1985
|
3/15/1992
|
Vince Carter
|
34
|
43.8
|
67.3
|
2.8
|
4.4
|
1/14/2000
|
2/8/2010
|
Carmelo Anthony
|
33
|
43.2
|
67.8
|
2.4
|
3.1
|
3/30/2004
|
4/5/2013
|
Patrick Ewing
|
32
|
42.9
|
70.5
|
3.4
|
2.4
|
12/13/1986
|
1/19/1996
|
Kevin Durant
|
31
|
42.6
|
70.2
|
3.1
|
3.1
|
4/16/2008
|
4/27/2013
|
Gilbert Arenas
|
30
|
44.0
|
69.4
|
3.9
|
5.6
|
3/23/2003
|
12/18/2009
|
Charles Barkley
|
26
|
43.3
|
73.3
|
3.6
|
3.3
|
12/13/1986
|
11/29/1997
|
Dirk Nowitzki
|
25
|
43.2
|
69.9
|
2.4
|
2.5
|
5/14/2001
|
4/16/2012
|
Paul Pierce
|
24
|
42.5
|
68.3
|
3.4
|
3.7
|
11/24/2000
|
12/19/2012
|
David Robinson
|
23
|
44.3
|
68.7
|
3.4
|
3.4
|
3/2/1990
|
4/28/1996
|
Clyde Drexler
|
23
|
42.3
|
71.4
|
2.6
|
6.7
|
3/14/1986
|
11/5/1997
|
Amare Stoudemire
|
22
|
42.5
|
71.4
|
2.6
|
2.2
|
1/2/2005
|
3/4/2011
|
Alex English
|
19
|
43.7
|
66.8
|
3.1
|
4.5
|
10/25/1985
|
3/10/1989
|
Ray Allen
|
16
|
43.3
|
75.0
|
2.8
|
4.3
|
4/18/1998
|
4/30/2009
|
Glen Rice
|
16
|
43.3
|
74.0
|
2.1
|
2.6
|
4/11/1992
|
5/5/1999
|
Stephon Marbury
|
16
|
42.1
|
69.7
|
2.8
|
8.4
|
2/17/1999
|
3/30/2007
|
Dale Ellis
|
15
|
43.6
|
70.2
|
2.4
|
2.6
|
1/21/1987
|
4/19/1990
|
Joe Dumars
|
14
|
42.0
|
74.0
|
2.9
|
4.1
|
4/18/1989
|
11/8/1995
|
Bernard King
|
13
|
45.6
|
62.2
|
3.9
|
4.5
|
4/4/1989
|
3/6/1991
|
Tom Chambers
|
13
|
44.2
|
67.1
|
2.7
|
2.6
|
3/10/1987
|
3/24/1990
|
Michael Redd
|
12
|
43.8
|
70.1
|
1.9
|
3.0
|
1/21/2004
|
1/16/2009
|
Latrell Sprewell
|
12
|
43.1
|
69.5
|
3.3
|
4.9
|
2/10/1994
|
3/14/2002
|
Reggie Miller
|
12
|
42.3
|
77.3
|
1.7
|
2.8
|
1/10/1990
|
4/24/2001
|
Jerry Stackhouse
|
10
|
43.5
|
64.9
|
4.3
|
3.7
|
3/8/2000
|
1/23/2002
|
Chris Bosh
|
10
|
41.2
|
68.5
|
2.0
|
3.0
|
2/7/2007
|
11/3/2012
|
Monta Ellis
|
9
|
43.8
|
69.8
|
3.9
|
4.0
|
4/1/2009
|
2/7/2012
|
Tim Duncan
|
9
|
43.4
|
66.4
|
3.6
|
4.2
|
12/9/1999
|
4/19/2008
|
Mitch Richmond
|
9
|
42.2
|
71.8
|
3.2
|
5.0
|
3/4/1989
|
2/13/1997
|
Chris Mullin
|
9
|
42.2
|
68.6
|
2.9
|
3.9
|
11/12/1988
|
12/28/1992
|
Kevin Martin
|
8
|
44.9
|
75.4
|
3.0
|
3.3
|
12/21/2006
|
1/5/2011
|
Jamal Crawford
|
8
|
44.8
|
71.4
|
2.6
|
4.4
|
12/27/2003
|
12/20/2008
|
Antawn Jamison
|
8
|
44.5
|
69.6
|
1.5
|
1.9
|
12/3/2000
|
11/24/2007
|
Jeff Malone
|
8
|
43.0
|
71.8
|
2.3
|
3.6
|
1/19/1986
|
11/28/1992
|
Jason Richardson
|
8
|
41.5
|
69.0
|
2.0
|
3.8
|
4/16/2002
|
4/22/2010
|
Michael Adams
|
7
|
43.7
|
66.3
|
4.4
|
10.0
|
12/26/1990
|
11/2/1991
|
Adrian Dantley
|
7
|
43.1
|
72.6
|
3.3
|
4.1
|
11/15/1985
|
11/21/1987
|
Kevin Johnson
|
7
|
42.9
|
67.3
|
3.0
|
10.1
|
12/3/1988
|
5/20/1995
|
Magic Johnson
|
7
|
42.6
|
64.1
|
4.1
|
8.4
|
12/23/1986
|
5/8/1991
|
Chuck Person
|
7
|
42.4
|
70.9
|
3.0
|
3.9
|
2/11/1987
|
2/19/1992
|
Isiah Thomas
|
7
|
41.7
|
64.1
|
3.7
|
8.4
|
1/2/1988
|
4/9/1993
|
Mark Aguirre
|
7
|
41.3
|
64.7
|
3.1
|
3.4
|
11/2/1985
|
1/11/1989
|
Manu Ginobili
|
6
|
43.5
|
77.3
|
2.3
|
6.0
|
1/21/2005
|
4/2/2010
|
Ben Gordon
|
6
|
43.2
|
74.9
|
3.2
|
4.2
|
12/27/2006
|
3/21/2012
|
Dwight Howard
|
6
|
42.7
|
70.3
|
4.3
|
1.7
|
2/17/2009
|
1/12/2012
|
Richard Hamilton
|
6
|
42.7
|
68.7
|
2.7
|
4.0
|
3/14/2001
|
12/27/2006
|
Gary Payton
|
6
|
41.8
|
67.1
|
1.2
|
8.0
|
2/15/2000
|
12/4/2002
|
Nick Van Exel
|
6
|
41.7
|
68.1
|
2.3
|
7.7
|
2/20/1995
|
5/10/2003
|
Joe Johnson
|
6
|
40.5
|
69.1
|
3.0
|
8.0
|
1/28/2006
|
12/19/2009
|
Jamal Mashburn
|
5
|
45.4
|
62.7
|
4.4
|
4.4
|
11/12/1994
|
3/26/2003
|
Tony Parker
|
5
|
44.6
|
68.0
|
2.4
|
8.8
|
4/25/2008
|
2/4/2012
|
Brandon Roy
|
5
|
43.6
|
71.5
|
1.8
|
3.6
|
12/18/2008
|
3/11/2010
|
Glenn Robinson
|
5
|
43.0
|
72.3
|
3.2
|
3.0
|
12/7/1996
|
2/25/2001
|
Chris Webber
|
5
|
42.8
|
62.6
|
2.8
|
5.2
|
12/27/1995
|
3/9/2001
|
Scottie Pippen
|
5
|
42.2
|
75.7
|
3.0
|
4.0
|
2/23/1991
|
2/18/1997
|
Grant Hill
|
5
|
42.2
|
64.1
|
3.6
|
7.0
|
2/8/1999
|
1/8/2000
|
Russell Westbrook
|
5
|
42.2
|
63.5
|
3.0
|
6.6
|
11/26/2010
|
6/19/2012
|
Cedric Ceballos
|
5
|
42.0
|
77.7
|
3.8
|
1.2
|
3/9/1993
|
4/15/1995
|
Chris Paul
|
5
|
42.0
|
68.8
|
2.2
|
8.6
|
12/7/2007
|
4/10/2009
|
Tim Hardaway
|
5
|
41.8
|
68.0
|
3.8
|
11.6
|
1/18/1991
|
3/7/1997
|
Mike Bibby
|
5
|
41.6
|
67.0
|
2.0
|
4.8
|
2/4/2005
|
1/29/2006
|
David West
|
5
|
40.8
|
67.2
|
2.2
|
2.2
|
11/16/2007
|
2/26/2010
|
Gerald Wallace
|
5
|
40.6
|
67.3
|
2.0
|
2.4
|
3/28/2006
|
3/27/2011
|
In sterile data, outliers have no personality; they're just grubby data points that screw up your model. However, in basketball these are interesting stories. The greatest outlier here in terms of efficiency is on the far right of the graph shown above. Not only is the TS% incendiary at 103.8, but the point total is decent as well -- 46 points. This is 8.3 TS% better than the boundary line. Who is it? The answer is a little tricky to guess right away, but once you see it he's not surprising.
The answer of course is Gilbert Arenas. A 103.8 TS% meant he averaged over two points per shot when including free throws as shots. It's also 2.9 points per field goal attempt. 13/16 from the field, 7/10 with his three's, and 13/14 from the line. Let me enforce how amazing that is -- whenever he takes a shot, including drawing a foul, he's on average scoring 2.1 points, so if he pulled up for a midrange jumper and made it that would actually bring his efficiency down. The other three guys with 100 or over TS% scored 40, 40, and 41 points respectively -- Jeff Hornacek who was 8/8 on his three's, Paul Pierce last season with 13/16 from the field and perfect from the line with six three's, and Terry Porter with 12/14 from the field and 13/14 from the line in the playoffs. Arenas destroyed New York that night.
The punchline? He only played 30 minutes.
The other outlier (outside of the boundary lines) for the dubious honor of least efficient 40 point game -- and it's not even close -- since 1986 goes to none other than Kobe Bryant. His TS% was downright abysmal at 40.9 with 41 points; it was 4.9 TS% below the boundary line. He was 17/47 from the field -- yes, he took 47 shots including eight from three point range, which he all missed. Luckily, he was perfect from the line at 7/7; he could have easily been worse. To top it off he had 5 turnovers in the loss to Boston. I need to reiterate something: 47 shots is an insane number, especially when you aren't hitting anything. For comparison, when he scored 81 against Toronto he had only 46 field goals -- yes, he took more field goals scoring 41 points than 81. The rest of his team took 48 field goals. The highest number of field goals in this period was 49 from Michael Jordan in his 64 point game against Orlando. So was it a recent Kobe game where he's hobbled but still shooting, his ego outweighing his conscience? No, it was in 2002, and yes, Shaq did not play. Plus it was in overtime. Does that excuse his chucking? Of course not ... or, well, it does partly when you see who else was playing. Here's the box score.
Another game of note is one from Donyell Marshall. He's the one tied for the record for three pointers in one game. Despite hitting 12 three pointers he failed to eclipse 40 points and somehow only scored 38. If you don't believe me check here. A three-point specialist can't be defined any better than that. At the other end of the spectrum is Malone's scoring outburst versus the Bucks where he scored 61 points in only 33 minutes. He was one of the filled-in dots on the boundary line since he was 21/26 from the field and an incredible 19/23 from the line. He also had 18 rebounds and his team nearly won by 50. In terms of points per minute, he was still behind two Kobe games -- 81 point and the game where he outscored Dallas through three quarters -- but he was third among all 40 point games, just ahead of a Sleepy Floyd game where he scored 40 points in 24 minutes.
I almost glossed over Jordan, but you can't ignore his dominance. He has more 40 point games in the playoffs (38) than nine other players since 1986. He has only two less total than LeBron James, Karl Malone, Larry Bird, Hakeem Olajuwon, and Dirk Nowitzki combined. Although Wilt had 271 (in the regular season,) Jordan amassed his in a more modern game with better defense while also retiring three different times.
Conclusion
Studying the efficiency of 40 point games you can see a beautiful pattern underlying all the data. These aren't all shot-chuckers demanding the ball so they can pad their totals. If you hit 40 points, it's likely because you're shooting well. That sounds obvious, but there's more to that -- the more points you score the narrower your window of shooting efficiency is. It's a delicate balance between forcing shots to drop your percentage and getting enough attempts to score more points, and outliers are indeed rare. Jordan does own the most games with 40 points, but Malone is the master at efficiency for players with 40 or more such games with Durant hot on his tail, and Iverson the dubious distinction of the least efficient even when you look at players with only 5 such games (Zach Randolph has three games of 40 points with a 56.1 TS%.)
Even Iverson has higher TS% in those games than most players do for a season. If you score 40 points, it's because your performance has elevated enough above the surface due to your shot attempts and good efficiency, which are both inextricably linked to bound each other at higher point totals. And different players have different peaks, some experiencing 40 point games as barely a blip in the season like Jordan while others can only visit one after a lucky barrage of three's. Nonetheless, from 1986 to the present day the pattern has remained the same, consistently conforming these special games by mechanisms unseen.
