In my last post, I introduced the idea of a “convex hull” for the usage vs. efficiency relationship. If we agree that the upper-right edge of that relationship represents “greatness” (in terms of scoring), then it is a simple matter to quantify the relative greatness of all other player-seasons by measuring the distance from each point to that edge (see the plot below).
The equation for the fitted line (black) was determined to be:
$$ TS\% = 90\%-0.89*USG\%$$
Using this equation we can find the distance from each point to that line (a few examples are highlighted by the red “drop down” lines). We can use the distance right away to rank the players, but the values don’t have much meaning. To put the measurement in some context, I am reporting the distance as 1.0 minus the ratio of the distance to that of a hypothetical average player (54% TS, 20% USG). Therefore, a player that is very close to the line will have a measurement of close to 1. A player close to average will be around 0. Here is a list of the players since the 3-pt rule took effect that have had TS%>55% and USG%>25% (as you can see, all players who were used to create the “greatness” line were given the same rank):
Go to Google Spreadsheet
From the current season, we have:
| RANK | NAME | SEASON | DIST | AGE | TEAM | USG% | TS% |
| 19 | Kevin Durant | 2011-12 | 0.899 | 23 | OKC | 31.0 | 60.80% |
| 20 | LeBron James | 2011-12 | 0.897 | 27 | MIA | 31.3 | 60.50% |
| 81 | Dwyane Wade | 2011-12 | 0.726 | 30 | MIA | 31.8 | 56.90% |
| 105 | Russell Westbrook | 2011-12 | 0.683 | 23 | OKC | 32.7 | 55.30% |
| 175 | Kevin Love | 2011-12 | 0.594 | 23 | MIN | 28.5 | 57.40% |
| 207 | Dirk Nowitzki | 2011-12 | 0.546 | 33 | DAL | 29.4 | 55.70% |
| 228 | Kyrie Irving | 2011-12 | 0.526 | 19 | CLE | 28.1 | 56.50% |
| 249 | Dwight Howard | 2011-12 | 0.498 | 26 | ORL | 26.4 | 57.50% |
| 270 | Paul Pierce | 2011-12 | 0.475 | 34 | BOS | 27.6 | 56.00% |
| 301 | LaMarcus Aldridge | 2011-12 | 0.436 | 26 | POR | 26.9 | 55.90% |
| 317 | Blake Griffin | 2011-12 | 0.407 | 22 | LAC | 27.2 | 55.10% |
| 360 | David Lee | 2011-12 | 0.306 | 28 | GSW | 25.1 | 55.10% |
Are all points on the frontier equally as valuable? I dunno. Only a few points to work with but Jordan’s 3 right in the middle are the only frontier seasons that coincided with a championship. It that the extreme offensive player sweet point or just his in his situation?
Where are all the leader player championship seasons and what does this relationship look like for just those seasons compared to all of them? What does that frontier look like overall and by era and by position and by big twos vs big 3s (or solo superstars or “team efforts from 4 or more guys)?
How does the data look if you combine it into big 2s and big 3s? What is the relationship and frontier for that?
What if you shifted the greatness scale from the overall frontier to the championship frontier or even just the average championship data point for top star or for big 2s and 3s?
One could shift from a distance measure to perhaps reporting a championship frequency % for stars with similar usage / efficiency locations, though clearly this is not a prediction because all things are not equal.
But perhaps a regression could be run on the 4 factors * 2 and this additional criteria to see what it says about its significance.
One could also look specifically at teams with 4 factor data comparable to championship average who fell short or well short of that playoff outcome and look at the usage-efficiency of their star and see if it is close to championship average or significantly different.
The top dozen on your distance measure are mostly wings. There isn’t a full-time PG in the top 100. I think that has some meaning, especially about the importance of scoring PGs.
Oops I guess I missed one season of Gilbert Arenas, though he did only lead Washington to a 42-40 record and a first round exit.
Only 11% of the top 100 on this won titles. That seems pretty low. Maybe being at the frontier is not that good or important. 7% of the second hundred won titles. A modest difference.
40% of the top 100 were bigs. And they won 4 of those 11 titles. No over-representation there.
good passing shooting guards had 7. The expectation would be just 2 so they are overrepresented. Take out Jordan though and it would only be a slight over-representation, so I am not sure one should give new priority to SGs who pass well.
Average age of top 100- 27. Average age of guys in top 100 who won titles that season- 31.4. I would not be expecting a young superstar to lead me to a title.
For the top 100, the simple unweighted usage was 30.7 and the TS% was 59.6%.
For the eleven title winners in the top 100, the simple unweighted usage was 31.4 and the TS% was 58.7%. A small difference but in favor of slightly higher usage guys even at a slight TS% expense.
Mildly interesting was that the championship average usage and age were identical at 31.4.
Among title winners Jordan was closest to the frontier, Bryant the farthest. Not that some Kobe fans want to hear or acknowledge that.
Shaq and Jordan have 7 of the 11 titles among the top 100 performances by this measure. No one else with more than one finish in this group.
derrick rose not in the top 360, even in his “mvp” season? hmm…
where are the scoring PGs are tha bomb crowd?
Does Westbrook at 105 and second fiddle do what no PG in or near the top 100 has done before and win a title that season?
I think Bird had the lowest ranking on the list of any titlewinner, in 1983-84 at 332. No other Celtic made this list that season to help him in this way.
Players scoring over .9 only won a title about 5.5% of the time so Durant and James should not be celebrating yet.
Players between roughly .75 and .8 won over 20% of the time. I guess that is the sweeter spot historically. Not at the frontier, just reasonably close to it. No one is in that range this season. Wade is the closest.
This is awesome, I am a little confused about what the line represents though. I think the negative relationship between usage rate and efficiency (In this case, TS%) is a clever theory that makes a lot of sense. When I think about this in terms of Kobe, it seems like that if he just stopped taking lower percentage shots, he would be much more efficient in helping his team win. While this would also give Bynum and Gasol more shots and, in theory, decrease there efficiency, I think the reduction of possessions used by Kobe would for sure be more optimal if he wants to get his 6th ring
Evan, first of all, a good idea. But I find a couple of things wrong.
1. USG% includes TOV, TS% does not. Either combine TOV% and TS% or use true shooting attempts instead of USG%.
2. Bigs are different than wings. I guess you will find a different equation, if you once use bigs and once use wings. I guess the slope will be different.
3. Dantley may have had a lower USG%, but in reality he had the ball in his hand for much longer time. His TS% actually was a result from extended amount of handling the ball and looking for his own scoring opportunity. If you look at the team overall offense, you will notice that Dantley did not do much to improve that despite having such a high volume and such a high efficiency. Dantley put his teammates in bad spots when the shot clock ran out and Dantley didn’t see a good opportunity for himself.
4. Stoudemire was getting assisted by Nash in his high efficient seasons, when he played without Nash on the court he was worse. That can also be seen by the numbers he has now on the Knicks. So, in contrast to Dantley Stoudemire had actually the ball way less in hand and didn’t have to create offense for himself.
Mystic, as to #1, if both the x- and y- variables depend on TOV, there will automatically be correlation. Why would you want that here?
As for the other comments, I’m not sure I would consider them as things I did “wrong”. You might suggest these as further lines of inquiry, but I think it’s unfair to say what I have done so far is “wrong”.
Evan, maybe “wrong” is the wrong word here, but I find it misleading.
1. What you are comparing now are two slightly different things. Usage includes more than just shooting, while you want to determine how much the scoring efficiency depends on the used opportunities. If someone is turning the ball over more often due to more passes and not due to more tries to create a shooting opportunity you will end up with a misleading picture. You can erase that effect by comparing the true shooting attempts with the true shooting percentage. That would be my first suggestion. The other suggestion (combining TS% and TOV%) would a worse solution.
I really think that you should think about doing it for bigs and smalls. Bigs have the tendency to have higher efficiency, but it is also harder to get them the ball into a good position. It is not like Barkley for example took the ball on the perimeter and created his scoring opportunities by himself.
You should also look into the league average for the respective seasons. It might make a difference as well. I would suggest an adjustment for league average true shooting. You can controll for rule changes like the different interpretation of the no-handchecking rule in 2004 by that. In that case a differentiation between bigs and wings makes also sense, because in 2004 we saw a clearly increase in scoring efficiency by the wing players. For example, in 1987 the wing player efficiency was at 52.5 TS%, overall it was 53.7 TS%, while in 2006 the wing player efficiency was at 53 TS% and overall at 53.5 TS%. Well, the wanted effect by the rule change showed up.
Mystic, don’t be offended by what I’m about to say. I appreciate your suggestions, but your choice of “misleading” I still find insulting. I know you’re German, so I can write it off as a language issue most likely. When you say something is misleading, it implies some sort of sinister motivation on my part.
All you really had to say was you find the analysis incomplete (as all models tend to be), and that you have some suggestions for future revisions. Your suggestions are good ones, although I’m not sure I like the idea of adjusting for position. Perhaps, if assisted FGA were available for all years, that would be useful, but we have no way of knowing those stats for all but the last few seasons. Adjusting for league averages is a good idea.
Sorry Evan, I did not want to imply any kind of hidden agenda on your part. I just think that the method of choice will give misleading results (in a sense of inaccurate). You picked certain players in order to determine “greatness” while we do not know that those players are indeed “great” in terms of actual improving the offense for the whole team.
As for the position adjustment: Look at the highest efficient scorers in your figure with lower usage like Barkley, Dantley, Stoudemire or Malone. Those were mainly post scorers. It would be good to see whether you get a different slope for wing scorers and post scorers (well, Malone is tricky, given the fact that he also changed up his game over the time to go with more midrange shooting).
Mystic, you see that those post scorers (Barkley, Stoudemire, Malone) and the wing scorers like MJ and Kobe all seem to lie along the same line. So, at least, from these data, what slope are you expecting to be different?
In other words, if I fit a line to Barkley, Malone, and Stoudemire, the slope won’t be very different from a line fitted to the other players. If it were, the R^2 wouldn’t be close to 1 when I fit all of the players included on the graph.
As far as the results leading to the team outcome, we all know there is more to that than just scoring. But those are undoubtedly some of the greatest scorers to have played the game, are they not? I know you don’t like Dantley, but do you not think he was a great scorer?
Well, if you connect two points, they will lie on the same line too. 😉
I once did look at the usage vs. efficiency stuff and I noticed that bigs tend to go faster down with increased usage than wings. If you cut out the top low usage scorers like Barkley or Dantley and replace them with the best low usage wing scorers, you will likely notice a similar thing. I found something like -1 as slope for bigs and -0.5 for wings while usage is x in a normaler linear function and y is TS%.
I don’t like Dantley’s offensive game, because he stopped ball movement and didn’t improve the team offense as much as his scoring efficiency suggest. Whether he can be actually used in order to determine “great” scorers, is questionable imho. I think scoring which happens within the flow of the game without stopping ball movement is more valuable in order to get a better team offense. If other players had picked their shooting opportunities as much as Dantley did (Dantley avoided tough shots), they would have likely also seen an increase in their efficiency. As a team you want to use the possession as efficient as possible, using up the shot clock while letting your teammates bail you out, will likely not help offensively afterall. But we are probably running just into a problem which can’t be solved by individual boxscore numbers.
Fascinated by your approach I did a cross-check of your spreadsheet and found that even though I love the logic behind the analysis some of the better performance seasons in the history of the NBA actually didn’t make your list. Players who made season 1st team All NBA like Magic or Charles were off when Dale Ellis or Kelly Tripucka were on in their stead (and yes, I know they were very good scorers). If a player makes 1st team All NBA that surely is a bid for greatness.
Here is a screenshot of some of the seasons that failed to make their mark in your measurement
:http://img593.imageshack.us/img593/6826/bestseasonsper.png
Not wanting to nitpick a stat because every stat analysis has its weaknesses, but results should pass the comparison test too.
@mediasres Remember PER includes other things, especially rebounding and assists. Most of the players on that list of yours were great rebounders and shot blockers. The metric being discussed in this post is only about *scoring*. It’s not about rebounding, assists, blocked shots, etc.
Look up the TS% and USG% for those players and see where those points would fall on the plot.
@thecity2 Multiple high PER season omissions of Allen Iverson, Charles Barkley, Olajuwan, O’Neal, McGrady, some of the greatest scorers in the history of the league, while players like Corey Maggette (who??), Tysdale, Drew do make it. The point isn’t where they fall on the plot, it’s whether the plotting actually is measuring what it is supposed to be measuring. I know no analysis is perfect, but I think we are missing something here by giving so much credence to USG. Just my opinion tho.
@mediasres Barkley had one of the all time best scoring seasons when he shot 67% on 27% USG. In 85-86 (the season that I “omitted”), he shot 62% TS on 22% USG. That’s a huge difference. James Harden did better than that this year.
@thecity2 ..as I’ve mentioned elsewhere, I do think that passing and rebounding are big parts of scoring. Wilt was an impossible scorer to stop, but part of that was that he also was very hard to keep off the boards. If Jordan couldn’t pass worth a lick, he would have been much easier to defend. The overall impact on the game is part of scoring, I believe.
@mediasres But Jordan appears on my list multiple times. Wilt would probably appear to, but I’m only counting since 1980. If rebounding and assists help you score, that’s great. Then a player who can do those things should have no trouble appearing on this list.
But this is the problem. You keep referring to your own ranking system in discussions about whether the ranking system is even capturing what it is supposed to be capturing, you are justifying itself by itself. Saying that James Harden outperformed Barkley’s 85-86 season is exactly the problem. There is no way that last season James Harden was a greater scorer than Barkley was in 85-86. It just takes the eye-ball test. Barkley was a beast. He distorted defenses. Harden was a very nice complimentary offensive player on a good team. It means, to me, your rankings are askew. The point isn’t whether such and such a player makes your list or not, it is: Does your list capture true scoring greatness? and Are great scorer seasons failing to make your list. I think because of the over-weighting of USG there are some difficulties here.
In the larger philosophical question of great scorer capture this is the reason why I think PER is better than USG. USG we know is a pure volume stat and can reward a lot of ineffective play. PER is both an efficiency and a volume stat, it cuts the volume dimension by adding in other performance features. The reason why I do think that rebounding and assists – for instance – are a part of capturing what truly great scoring is is that a scorer is someone who can create his shot. Being able to rebound or dish is a significant aspect of being able to create a shot.
Try this thought experiment. Picture Dominique Wilkins (I hope you saw him play because it helps). What a dynamic scorer he was. Now imagine that he was capable of 9 boards a game or 6 assists. Suddenly he becomes more than a dunker and jump shooter. He becomes a next level scorer. He is all that more unstoppable. Or take Lebron now. Imagine his game only contained 3 assists a game, or 4 rebounds. He just is a different player, and nowhere near as impactful or threatening as a scorer. If he kept the same USG he would just be a gunner, and not a truly great scorer.
Look at nearly all the great scorers in history, all the Hall of Famers. Nearly all of them were also VERY good at rebounding or passing the ball for their position. It is no accident. It allows you to control the game. The image we have of the “pure” scorer is I think partly a false one or at least rare. Great scorers impose their will on a game and PER captures that better than USG does I think.
I know you like USG vs TS% because they are so categorically different, but maybe great scoring is best measured by scaling two different efficiency metrics.
@mediasres Keep using PER. I’ll use this. Not everybody has to agree on everything.
@thecity2 then keep telling me that Corey Maggette (5 seasons) Jim Paxon (82-83, Wayman Tysdale (89-90), Rik Smits (2 seasons) were greater scorers than Kareem Abdul-Jabbar 1979-80 Charles Barkley 1986-86 1989-90, Hakeem Olajuwon 1990-91 Shaquille O’Neal 1995-96 1996-97, Michael Jordan* 1997-98, David Robinson 1998-99, Allen Iverson 2000-01 Tracy McGrady 2000-01
The eyeball test. Sometimes you just have to look.
I do agree that we don’t have to agree on everything.
@mediasres In this post, I limited the data points to those with > 25% USG.
The full analysis with all players includes those with USG < 25%. Some of those are players you mentioned. Out of 10,000 player seasons total, here is where those other seasons you mentioned are ranked:
Kareem ’80 (#104)
Barkley ’90 (#37)
Barkley ’87 (#60)
Hakeem ’91 (#1234) 55% TS 25% USG = not all that great
Shaq ’96 (#75) ’97 (#232) 31.1% USG 55.6% TS (not great by his standards)
Jordan ’98 (#231) 33.7% USG 53.3% TS (not great by his standards)
Robinson ’99 (#1098) 23.8% USG 56.4% TS (would be a somewhat above average mark today)
Iverson ’01 (#184) 35.9% USG 51.8% TS (high-volume chucker, but arguably it was necessary on that team)
McGrady ’01 (#600) 31.2% USG 52.1% TS (Monta Ellis territory)
Your cherry picked examples for most case show the weakest seasons of each particular player. Overall, I think you’ve helped me make my point even better. Thanks.
@thecity2 lol – you just measured their seasons by the very stat that is under question USG. I”m saying USG is a bad measurement of great scoring here are some examples. You are saying: Those examples all have low USG. Well, what else do you expect? Of course they have low USG, that is the entire point.
I would contend though that Charles Barkley’s or Michael Jordan’s lower USG seasons are STILL better “scoring greatness” season than Corey Maggette or Kelly Tripucka’s best USG seasons. These are Hall of Famers.
@thecity2 another way of saying this is – using a contemporary example – while Kobe Byrant’s USG has been steadily going up the last 5 years, his PER has been going down. According to you by these two factors he has been improving as a scorer, while I suggest he as been declining.
@mediasres No, he hasn’t been improving according to me. You can read my other post which uses this metric to study aging:
http://www.d3coder.com/thecity/2012/04/08/using-the-usage-efficiency-distance-metric-to-create-aging-curves-for-the-nba/
@mediasres Also, you’re not understanding the relationship that I’ve found between TS% and USG%. It’s the perpendicular distance of the data point (TS%, USG%) relative to the “frontier” on the edge of the data set. It’s not just “high USG = better”. That’s only true if it’s accompanied with some relatively high level of TS%.
@thecity2 check the above for instance: In Barkley 87 he earned 2nd Team All NBA – that is one of the 10 best players in the league by position vote. He was 6th in MVP shares. In ’90 he won 1st Team All NBA, one of the 5 best players in the league and was 2nd in MVP shares. But you think because of USG Corey Maggette had 5 better “great scorer” seasons than he did in these two seasons? It just makes no sense to me.
@mediasres You can always cherry pick stats like these.
If I used PPG, you’d cherry pick that. If I used PER, you’d cherry pick that. There are 10,000 data points. I’m glad you found 1 you don’t like. That means I got it right 99.99%.
@mediasres If you know of a stat that will give “perfect” results, let me know.
It’s not PER, though. Or PPG.
@thecity2 check the above for instance: In Barkley 87 earned 2nd Team All NBA – that is one of the 10 best players in the league by position vote. He was 6th in MVP shares, made it to the All Star game. He averaged 20.5 pts per game with a TS% of .660 and a USG% 23.1, In 04 Maggette scored 20.7 pts a game with a TS% of .586 and USG% of 25.2 and did not make the All Star game (in fact never has). You think because of a few points of USG Corey Maggette (04) had better “great scorer” season than Barkley (87) ? It just makes no sense to me.
@thecity2 I’m just suggesting – and would love to see – the correlation between TS% and PER. I wonder what the frontier line would look like. I don’t think you did anything wrong here at all. It just begins the thought process: How could it possibly be better? If we saw the frontier line for PER v TS% we could then criticize that data group too. But one has to say that giving a player like Maggette who hasn’t even made an All Star game 5 of the greatest scorer seasons in the 3 pt era raises eyebrows. We all know he isn’t that good.
@mediasres There would be a very high correlation between TS% and PER, that’s the problem. By definition, PER is correlated to shooting efficiency. USG is not.
Maggette is a very good scorer. He can’t do anything else. But he can score. I have no problem with that.
@mediasres I already explained in the other post that Barkley’s ’87 season is rated #60 out of all 10,000 data points. It’s just not on the spreadsheet included in this post. Maggette’s highest rated season is #106 (2010) when he shot 61.5% TS on 26.7% USG.
Now go cherry pick the next one you have a problem with.
@mediasres Maggette in ’04 had the #452 best season. That’s nowhere near as good as Barkley’s ’87 season according to my metric.
@mediasres Kelly Tripucka’s best season rates #325 on the full list.
@thecity2 hmm. “No, he hasn’t been improving according to me.”…you didn’t read what I wrote. I said “by these two factors (USG vs PER)” you are counting improvement. In other words, because you are weighting USG you are failing to capture just how MUCH he has declined. If you used TS% and PER you would see a much more notable decline as both have plummeted for Kobe.
I actually came here through your aging post, which was a great one. In fact you commented on my Kobe’s 5 Year Efficiency Decline post to begin with.
@thecity2 “It’s not just “high USG = better”. That’s only true if it’s accompanied with some relatively high level of TS%.” actually this is not the case (pending what “relatively” means). The USG gives outliers like the Maggette oddity. Barkley’s ’87 TS% was nearly a full 8 percentage points higher than Maggette’s ’04 season, but because Maggette’s USG was a few points higher he showed up closer to the frontier. line. In other word USG is too heavily weighted. A few points in USG outweighs several in TS% which makes no sense .
@thecity2 “There would be a very high correlation between TS% and PER, that’s the problem. By definition, PER is correlated to shooting efficiency. USG is not.”
That is actually what I wonder. Would there be a noticeable and effective frontier line of players with high TS% and lower PER, or high PER and lower TS%? Only by running the data would we know.
Maggette is a good scorer, but nowhere near a great scorer. He is the traditional high volume shooter on bad teams scorer.
@mediasres I repeatedly told you that Barkley’s ’87 season rated #37, while Maggette’s best season (2010) rated #106. Are you just choosing to ignore this?
@thecity2 I guess I can help it if all your data isn’t in the spread sheet. I can only look at the data you gave me. 🙁
@thecity2 this is the thing, and maybe you can clear the whole thing up for me. Your spread sheet, which I took to included ALL the data you felt was relevant because you ranked the players in it, doesn’t have Barkley at #60, it has Dirk at #60, and Barkley was missing, as are a lot of other players.
Below is the spread sheet I have from you, and included are the missing players with great PER seasons (in gray). If all or most of these gray marked players are actually ranked high by your DIST stat, then we have no big disagreement
with PER added: https://docs.google.com/spreadsheet/ccc?key=0AhuaUsq2ln9JdHBZOUtyeHlmME1nNkFWNjdSazQ2M3c
I’m not sure why you disqualified players based on TS% and USG% minimums, but all could go on was your ranking. If you are telling me that your spread sheet was partial and your rankings were somewhat provisional then this was largely a misunderstanding.
Honestly above when you were telling me what number Barkley and others were I had no idea you were talking about your own rankings (I was reading quickly) because they did not match what you presented. I thought you were talking about USG or another stat.
@mediasres “If you are telling me that your spread sheet was partial and your rankings were somewhat provisional”
That is what I’ve been trying to tell you. In this post I only showed players with > 25% USG, but I went back later and included all players. That’s why on the other spreadsheet you’ll see Artis Gilmore with a 70% TS 19% USG season on the list.
@mediasres “Try this thought experiment. Picture Dominique Wilkins (I hope you saw him play because it helps). What a dynamic scorer he was. Now imagine that he was capable of 9 boards a game or 6 assists. Suddenly he becomes more than a dunker and jump shooter. He becomes a next level scorer. He is all that more unstoppable. Or take Lebron now. Imagine his game only contained 3 assists a game, or 4 rebounds. He just is a different player, and nowhere near as impactful or threatening as a scorer. If he kept the same USG he would just be a gunner, and not a truly great scorer.”
I don’t understand the point of your counterfactuals. Can we just talk about what actually happens?
@thecity2 There is what is happening (events in the world), then there is aesthetic judgement of those events (“this class of events were ‘great'”), and then there is statistical measurement of events attempting to capture the aesthetic judgment. But lets not pretend that statistical measures ARE the aesthetic judgment. Counterfactuals help in pointing out the nature of the aesthetic judgment itself, why we say someone is a “great scorer”.
Otherwise why not just use average points per game, a nice firm easy to understand number, and say that the greatest scorers are the players that score the most points in a game?
@mediasres You are free to use PPG. I think people will have more issues with that list than mine, though, including yourself perhaps.
In any case here is a Google Doc spread sheet of your Distance data with PER added in. In gray are player seasons that did not make the Distance list. PER was only added to seasons that made the NBA reference All Time season PER list
https://docs.google.com/spreadsheet/ccc?key=0AhuaUsq2ln9JdHBZOUtyeHlmME1nNkFWNjdSazQ2M3c
At the very least your distance metric makes for great discussion. The above spread sheet may very well have errors as PER was added by hand.