NBA Points, Points per Game, Points per Centage?

[Latrinsorm]

Here is a weird thing about the NBA. There is no clear consensus on how to determine the best scorer. We currently (and for the past many but not all years) use points per game to christen a scoring champion for any given year, but we also indulge Kobe's climb on the points per career chart. Quick review of the top 5 on each:

Jordan, Wilt, LeBron, Baylor, West
Kareem, Karl, Jordan, Kobe, Wilt

And what about pace? Jordan is .05 points per game ahead of Wilt, but Wilt's games had about 3000 more possessions each (conservative estimate). What to make of all these conflicting rankings? If we've learned anything from xkcd, it's to introduce yet another ranking.

Behold: points percentage!

A = Player's total number of points
B = total number of points scored in league
C = Player's number of games played divided into total number of games played in league during career
(notice how we automatically account for teams per league, games per season, league-wide pace trends? do you see how my mind works? it's like an ideologically neutral laser. Ideally we would use minutes instead of games to account for overtimes, but that data is not as readily available and I'm not too worried about it.)
A/B * C = points percentage

Let's see how that number looks for the eight names listed above, and we'll throw in Durant.


Jordan 0.292
LeBron 0.281
Durant 0.268
Wilt 0.265
Kobe 0.263
Karl 0.248
Baylor 0.240
West 0.240
Kareem 0.226


As anyone with half a brain would expect, Jordan runs way out ahead, Wilt falls way back, Kobe gets a little bump (from 11th in points per game), Baylor and West are still basically identical, Kareem is pretty low because he played until he was post-middle-age-crisis but also is higher than his 16th points per game rating would suggest, LeBron is still astonishing given that he has had a jump shot for 1 of his 10 years, has had a post game for 2, etc.

[DoctorUnne]

That's really interesting, although I think it would be better if you could convert it into a kind of adjusted PPG metric that would look more like standard PPG, so basically just PPG adjusted for pace of play. Would also be interested in seeing the top individual seasons just to see how dominant Wilt's 40 ppg season was. West, and probably others like Oscar not on your list would get a boost with the three pointer. Not a huge boost since theoretically it would have increased league scoring as well.

[Latrinsorm]

While I have done simple pace adjustments in the past (especially as pertains to career points), I feel like the percentage mechanism is better because it accounts for year-to-year changes in play: the three pointer (more on this in a second), the rate fouls are called, the number of free throws per foul, rule changes such as hand checking, zone, Reggie Miller kick, Mark Jackson 5, etc.

The theory is that West wouldn't get much of a boost from the 3 pointer because everyone else in those years would get the same boost, therefore the percentage of points he scored in that year would be about the same. Obviously there's no way of saying how many shots that he did take would have been 3s or how many shots he would have turned into 3s, but we can do the problem backwards with a guy like LeBron this year. I pick LeBron because he is (like West) a high volume scorer with an above average outside shot.

LeBron actual: 2036 points with 103 3s and 76 games. 2013 NBA actual: 241,230 points with 17,610 3s and 1229 games.
result: .136
(Important note! I just realized now that I left out a factor of 2 in my original analysis, because the home team and the away team score, so everyone's value above should be halved.)

LeBron when all 3s become 2s: 2036-103 = 1933 points, 241230-17610 = 223620 points, result = .141
This is a pretty surprising outcome, his points percentage actually goes up, even if not by very much. Again, there's no way of saying how many of those shots would have been taken somewhere else, but at least we've got a bead on the second half of the problem.

We can do the same thing with a high volume scorer with a below average outside shot: 2013 Kobe. Perhaps surprisingly, his % also goes up, from .139 to .141. I wonder if his having a below average 3P% is less important than the raw volume of his 3 point attempts, which is of course very high. These questions are academically interesting but the small overall change in the values make me happy that the metric corrects for it to a large degree: Kobe's points go up 6.6% but his points percentage only goes down 1.2%.

.

I like the idea of adjusting it into a PPG looking thing, though. I think what I'll do is graph out everyone's value for a season, then every season leader's value, see whether linear scaling or something fancier makes more sense. It'll certainly look prettier, anyway.

[Latrinsorm]

Adjustment to above note: that factor of two actually should not have been included because in most (though not all (http://www.basketball-reference.com/boxscores/197811080PHI.html)) cases a player can only score for one team.

469 players played in the NBA in the 2013 season from Quincy Acy to Tyler Zeller. Applying the above equation gives values from Carmelo Anthony's .292 to 7 players' 0s, places of honor going to Darko Milicic and two Lakers (of course): Andrew Goudelock and Darius Johnson-Odom. If we want to scale these values in some way, we should have a look at the distribution. Here is the whole NBA:

http://img.photobucket.com/albums/v456/johnnyoldschool/NBAPointsPerCentage_zpsc89f6dfd.jpg

It looks like there are some notches in the data, but that could be a graphical artifact or a coincidence or both. The average value is .081; or, the average NBA player scored 8% of the average team's points. Obviously we don't have a normal distribution, though, and the median is way down at .069. We can still take a standard deviation and get .056, so let's see how bins of .06 look:

27 above .18
82 between .18 and .12
152 between .12 and .06
208 below .06

3*divider would be a good place to put 30, but 27 people in the 30 "point" club in a season seems a bit much. Let's try bins of .08 instead:

5 above .24
44 between .24 and .16
151 between .16 and .08
269 below .08

5 is a much more appealing number for elite scorers per year, so let's take all the seasons for Wilt, Michael, Kareem, Kobe, and LeBron, scale by /.008, and see what happens...

1961-62 52.99 Wilt
1962-63 48.60 Wilt
2005-06 45.62 Kobe
1986-87 42.18 Michael
1963-64 41.50 Wilt
1959-60 40.76 Wilt
1960-61 40.64 Wilt
2005-06 40.42 LeBron
1987-88 40.41 Michael
2006-07 39.97 Kobe
1971-72 39.52 Kareem
2002-03 39.45 Kobe
1964-65 39.23 Wilt
1989-90 39.22 Michael
1992-93 38.67 Michael
1996-97 38.24 Michael
1995-96 38.16 Michael
1997-98 37.58 Michael
2000-01 37.58 Kobe
2007-08 37.54 LeBron

If we compare to unadjusted points per game...
1. Wilt has the top spot by 36% over Michael's 1987 season rather than 16% over Kobe's 2006.
2. Wilt has the top 4 spots rather than the top 2 (of the named players).
3. LeBron doesn't show up until 18 instead of 8, although his 20 only gets shuffled down to 23.
4. Kareem goes the other way, from #9 and #15 to #11 and #24.
5. I didn't see this coming at all, but it so happens that Wilt's 50 is still the only 50, so that's cool.

We could get similar results with basic pace adjustment, except pace can only be estimated prior to the recording of turnovers (1978), which rules out Wilt's career entirely and the part of Kareem's where he was scoring at a high rate. We give up some accuracy by using league-wide figures instead of pace (which is team-specific), but I like the outcome so far. Next I'll apply it to ppg leaders by season.

[DoctorUnne]

Makes Wilt's numbers seem even more crazy

[Latrinsorm]

I find this pretty interesting:

http://img.photobucket.com/albums/v456/johnnyoldschool/NBAPointsPerCentageLeaders_zpsacdff916.jpg

I think it was already pretty well-established that Wilt's peak was WILT'S PEAK, but this really drives it home. MJ was more an implacable plateau that also marked Bryon Russell with an eternal curse, but from Wilt there was nowhere to hide for kids or wives. I was really hoping this analysis would provide another way to criticize Carmelo, but it turns out Alex English is the Nugget. Also, Shaq's leading the league in scoring is a lot less impressive by this analysis: those years were apparently pretty devoid of competition or otherwise do not stack up historically.

While we should keep in mind that there could be guys who cracked 40 but didn't lead the league (e.g. The Brown James), here is a list of guys who did both:

Kobe
T-Mac
AI (twice)
Jordan (twice)
McAdoo
Wilt (FIVE TIME, FIVE TIME, FIVE TIME)
Mikan (twice)

Which brings up an interesting point: which is more impressive, LeBron scoring 31.4 points per game in 2006 (3rd in league) or 30.0 points in 2008 (led league)? I'm pretty sure his Hall of Fame plaque isn't going to reference being 3rd highest in the league in 2006... but should it?