You Are Here > Basketball-Reference.com > BBR Blog > NBA and College Basketball Analysis

SITE NEWS: We are moving all of our site and company news into a single blog for Sports-Reference.com. We'll tag all Basketball-Reference content, so you can quickly and easily find the content you want.

Also, our existing Basketball-Reference blog rss feed will be redirected to the new site's feed.

Basketball-Reference.com // Sports Reference

For more from Neil, check out his new work at BasketballProspectus.com.

Optimizing the Rockets II

Posted by Neil Paine on April 20, 2010

As if everyone isn't already tired of this debate (one which will never be satisfactorily settled, I'm sure), here's a final note on who contributed the most to the 1995 Rockets' offense during the playoffs, Hakeem Olajuwon (mega-high usage, average efficiency) or Clyde Drexler (mid-to-high usage, mega-high efficiency)...

My last post attempted to create a simple model of team offensive efficiency using Dean Oliver's Offensive Rating, Possession %, and what Dean called "Skill Curves", or the relationship between changes in individual usage and efficiency rates. In general, both Oliver and Eli Witus found a quantifiable inverse relationship between increases in usage and predicted offensive efficiency -- in other words, there's diminishing returns to increasing your usage, and as you add more usage you become less and less efficient (which only makes sense to anyone who's ever played basketball).

This model -- based on a ton of real-world evidence, not mere hunches and beliefs -- predicted that the 1995 Rockets' starting lineup would actually be better off on offense by taking some possessions away from Hakeem and re-allocating them to Drexler, and it implied that Drexler was in fact the player who added the most on a per-team-possession basis to the Rockets. In essence, when the Rockets' starting 5 was on the court together, Drexler was their most important offensive player and should have even taken a bigger role in the offense if the Rockets wanted to maximize points per possession.

However, although the model holds for all players in general, there's always the chance it could be flawed for specific players with specific playing styles, and Olajuwon/Drexler could certainly be one of those cases. When I was putting together a WARP-style stat based on Skill Curves, APBRmetrician Dave Lewin once warned me that a player's impact on team offense is not entirely explained by his offensive rating and possession rate, and that a regression between an on/off points per possession metric and box score stats could surprise me in the sense that its outcomes would not always match the general Skill Curve model.

But luckily for us, in 2005 Lewin's mentor Dan Rosenbaum actually did run a regression using boxscore numbers to predict his Adjusted Offensive +/- metric. If you're unfamiliar with adjusted offensive +/-, it's the same as regular adjusted +/- but it only deals with the team's points scored per 100 possessions when a player is on the court vs. off, adjusting for the quality of his teammates, backups, and opponents. The results?

                                           The SAS System       14:08 Wednesday, August 10, 2005  63

Model: MODEL1
Dependent Variable: OFF1                                               

                                        Analysis of Variance

                                           Sum of         Mean
                  Source          DF      Squares       Square      F Value       Prob>F

                  Model           12 9291008.6501 774250.72084      118.118       0.0001
                  Error         1081 7085843.2932 6554.8966634
                  C Total       1093 16376851.943

                      Root MSE      80.96232     R-square       0.5673
                      Dep Mean      -0.42353     Adj R-sq       0.5625
                      C.V.      -19115.86189

                                        Parameter Estimates

                                 Parameter      Standard    T for H0:
                Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

                INTERCEP   1     -7.056284    0.61411305       -11.490        0.0001
                PTS        1      0.702730    0.06387650        11.001        0.0001
                TSA        1     -0.525243    0.06276998        -8.368        0.0001
                FTA        1      0.083834    0.06323568         1.326        0.1852
                TA         1      0.327152    0.04249266         7.699        0.0001
                AS         1      0.640857    0.04863086        13.178        0.0001
                OR         1      0.733202    0.10084425         7.271        0.0001
                DR         1     -0.138614    0.05560930        -2.493        0.0128
                TO         1     -1.042591    0.14327755        -7.277        0.0001
                ST         1      0.713849    0.14956205         4.773        0.0001
                BK         1     -0.111075    0.10316250        -1.077        0.2819
                PF         1     -0.093128    0.08545434        -1.090        0.2760
                MPG        1      0.043603    0.01161761         3.753        0.0002
Where:
PTS = points per 40 minutes
TSA = true shooting attempts per 40 minutes
FTA = free throw attempts per 40 minutes
TA  = three point attempts per 40 minutes
AS  = assists per 40 minutes
OR  = offensive rebounds per 40 minutes
DR  = defensive rebounds per 40 minutes
TO  = turnovers per 40 minutes
ST  = steals per 40 minutes
BK  = blocks per 40 minutes
PF  = personal fouls per 40 minutes
MPG = minutes per game

So now we can look at what Dave was talking about -- perhaps Hakeem and Clyde are a situation where the skill curve model works on paper but is contradicted in the real-life results...

(Note: Minute-weighted sum of team OPM was forced to equal tmOrtg - lgORtg.)

Player Yr Ag Tm g mpg pts40 tsa40 fta 3pa40 ast40 orb40 drb40 tov40 stl40 blk40 pf40 OPM
Hakeem Olajuwon 1995 32 HOU 22 42.2 30.2 27.0 6.8 0.2 4.1 1.8 7.6 2.9 1.1 2.6 4.0 1.79
Clyde Drexler 1995 32 HOU 22 38.6 20.5 17.5 6.4 4.5 5.1 2.1 5.0 2.1 1.5 0.7 3.1 3.80
Robert Horry 1995 24 HOU 22 38.2 13.2 11.2 3.6 5.1 3.5 1.8 5.3 1.2 1.5 1.2 3.2 1.58
Kenny Smith 1995 29 HOU 22 29.6 14.1 11.6 2.4 6.2 5.9 0.4 2.5 1.8 0.8 0.2 2.7 1.71
Mario Elie 1995 31 HOU 22 28.9 12.2 9.5 2.7 4.0 3.3 1.2 2.6 1.3 1.3 0.1 3.4 0.48
Sam Cassell 1995 25 HOU 22 22.0 19.4 16.5 6.8 4.8 7.1 0.6 2.7 2.6 1.7 0.2 5.3 2.90
Chucky Brown 1995 26 HOU 21 15.5 11.2 11.0 4.4 0.2 0.8 2.4 5.3 1.4 1.1 0.2 5.5 -4.27
Pete Chilcutt 1995 26 HOU 20 16.2 10.8 8.6 2.0 4.3 2.2 1.8 5.2 1.3 0.8 0.5 4.7 -1.67
Charles Jones 1995 37 HOU 19 12.5 2.3 3.0 2.0 0.2 0.0 2.0 5.2 0.8 0.7 1.6 9.0 -7.64
Zan Tabak 1995 24 HOU 8 3.9 7.5 7.3 2.5 0.0 1.2 1.2 0.0 2.5 1.2 3.7 6.2 -6.96
Vernon Maxwell 1995 29 HOU 1 16.0 7.3 18.0 2.4 4.8 2.4 0.0 7.3 2.4 0.0 0.0 2.4 -11.82
Carl Herrera 1995 28 HOU 1 6.0 12.9 6.4 0.0 0.0 6.4 0.0 0.0 0.0 0.0 0.0 0.0 2.32

...Or not. Using a completely different method, one which takes into account how each player plays, the interaction effects of those styles, and one which was also built using real-life evidence and a large sample of real NBA results, we once again see that Drexler had a bigger positive impact on Houston's offense than Olajuwon. I realize this fairly overwhelming amount of evidence will still not convince a large number of you, dear readers, but I just wanted to put it out there. No bias, just more cold hard numbers derived from real NBA data.

ShareThis

51 Responses to “Optimizing the Rockets II”

  1. Neil Paine Says:

    Also, why do we keep referring to Drexler's "advanced age" as a barrier to him taking on more possessions? Putting aside the possibility that perimeter players age earlier/more dramatically than big men, he was actually the same age (32) in 1995 that Olajuwon was!

  2. ryan. Says:

    Ahhh, way too soon for me to go straight on to reading this one. For anybody interested, I can provide download-links for the entire 95 Finals series.

    I'll get around to reading this later tonight, or tomorrow.

  3. Travis Says:

    I'd be interested in those links

  4. DSMok1 Says:

    Neil, did you notice that there is no TSA^2 term in that regression, but that it is highly significant in the overall SPM regression? I think the lack of that term is putting Olajuwon at a big disadvantage in this analysis compared to Drexler.

  5. Neil Paine Says:

    Yes, I noticed that. However, he actually got a much higher R-squared (0.56) than I was able to get on any SPM regression, so I'm not sure which equation actually fits better. Meaning I should probably re-run the SPM model with only the variables Dan laid out in the regression here, and see if it's actually an improvement over the one we've been using. Obviously I'd like to regress separately on pure offensive and defensive APM, but to my knowledge that data is not publicly available online. It's much easier to find overall adjusted +/- for some reason.

  6. sp6r=underrated Says:

    I think people talk about Drexler's age because age is considered (I've never really studied this matter so it could be a myth) more important for elite wings than elite bigs.

    One thing we can agree on though is the 95 rockets are the worst or one of a handful of the worst NBA champions in league history.

  7. Mike G Says:

    Here's what we see on the '95 Rockets' page:

    player - OWS - DWS - WS - WS/48
    Drexler - 2.2 - 0.8 - 3.0 - .167
    Hakeem - 1.5 - 1.3 - 2.8 - .143

    So on offense, Clyde got about 50% more offensive credit (in 91% of the minutes),
    while on defense, Dream got about 60% more.

    And combining offense + defense, Drexler was 17% better than Olajuwon. (.167/.143)
    I'd say Hakeem was 40-60% better than Drexler.
    And I doubt there was any question who was Finals MVP.
    Or (if there were such a thing) who was Conference Finals mvp.

  8. DSMok1 Says:

    It's obvious that you should get a higher R^2 for an offense-only SPM-APM regression. Why? Because the box score stats measure offensive contribution FAR better than defensive contribution. In other words, much of the error in the APM-SPM regression comes from the failure of box score stats to capture defensive contribution.

    What was your R^2? 0.3? Interesting. His R^2 for defense was 0.35.

    It is possible also (perhaps even likely) that his R^2 is overstated because of over-parametrization of the problem, since he was using only 1 year of data for the regression.

  9. Mike G Says:

    http://www.basketball-reference.com/play-index/tiny.cgi?id=xYxFw
    Players who are credited with at least 1.5 Win Shares in the 1995 playoffs.
    Ranked by WS/48, Olajuwon ranks 11th of the 16.
    Behind Drexler; also behind (Phx) KJ and Barkley; (SA) Robinson, Rodman, and Avery Johnson; (Orl) Shaq; (NY) Oakley; (Ind) Miller and Smits.
    Barely ahead of Horry, Sean Elliott, Horace Grant.

    I've heard people describe Houston's championships as "Olajuwon and 4 guys off the street", and this is really hyperbole. But statistically claiming he was just another playoff starter is about as far-fetched, in the other direction.

    He didn't block a lot of shots or get his usual steals. And about half his minutes were vs Shaq and DRob.

  10. DSMok1 Says:

    Actually, the R^2 makes sense: to sum them, I believe the formula would be:

    1/R^2tot = 1/R^2A + 1/R^2B, or 1/R^2tot = 1/0.35 + 1/0.58

    ===> R^2tot = 0.22

    And your combined R^2 is 0.3, indicating a better fit.

    Am I missing something? Isn't that the right equation for combining R^2's that are uncorrelated?

  11. J.D. Says:

    I've been thinking about the trade-off between usage and efficiency a lot, and I've thought of an "idiot check" for the factor of 1.25 between ORtg and usage rate (or whatever factor you want to use).

    We all know that long 2's are the worst shots in basketball. They're also available to most players pretty much whenever they want to take them. If you take a Drexler-type player and added a number of long 2's, at an average shooting percentage, would his usage-adjusted ORtg improve or decline? A test like this could help determine what is the most accurate factor.

  12. Anthony Coleman Says:

    I know that I was the main reason for both posts so I'll say it to you that I don't care about what the predictive stats say. What I do go by is the on the court past results in patterns for the playoffs and for Drexler. All of the players I mentioned in my post (except for Wade), had taken more shots per game and had a lower TS% to and as the number of shots and points approached 30, the numbers dipped into the 55-56% range. That's why I find it very unlikely that he would have kept up that high percentage if he had taken more contested shots.

    Also, why do we keep referring to Drexler's "advanced age" as a barrier to him taking on more possessions? Putting aside the possibility that perimeter players age earlier/more dramatically than big men, he was actually the same age (32) in 1995 that Olajuwon was!

    The reason why is that at that age he was clearly into his decline period. Go check up on the stats from the previous 2 seasons. The wear and tear was catching up to the guy, he missed significant time due to leg injuries and was slowing down. He could still play as an all-star when he could, but wasn't the same player from the dominant Blazers teams. When he was traded to the Rockets his role was defined clearly as being a second reinforcement to Olajuwon. Of course he still had more in the tank and made two more all-star teams, but his best days were clearly behind him.

    BTW his own regular season and playoff stats for his entire career is another reason why I am so skeptical that he'd keep that offensive load up. Even during the Blazers contender years when he was the focal point of the offensive and thus dominated the ball, his true shooting percentage maxed out at 56.4% in the 1987-88 regular season and 55.6% in the 1991 playoffs. The 58.9% is a clear outlier and it happened around the same time in which he was in a supporting offensive role. When he was the go-to guy for the Blazers and the focal point of the opposing defense, he never came close to that efficiency (and before anybody else mentions; before the trade Drexler's TS% was 55%, exactly in-line with his average in his prime). In fact the reason why Olajuwon was selected to be the focal point of the offense is because he had shown to be the better scorer in the previous years. There was no evidence going into the playoffs that Drexler deserved the bulk of the load or equal parity.

    Drexler was one of my favorite players growing up, one of the best dunkers ever, and a tremendous all-around performer. Yet just going by the data I presented I have significant doubts that he would have been as effective with more shot attempts.

  13. Anthony Coleman Says:

    Players who are credited with at least 1.5 Win Shares in the 1995 playoffs.
    Ranked by WS/48, Olajuwon ranks 11th of the 16.
    Behind Drexler; also behind (Phx) KJ and Barkley; (SA) Robinson, Rodman, and Avery Johnson; (Orl) Shaq; (NY) Oakley; (Ind) Miller and Smits.
    Barely ahead of Horry, Sean Elliott, Horace Grant.

    I've heard people describe Houston's championships as "Olajuwon and 4 guys off the street", and this is really hyperbole. But statistically claiming he was just another playoff starter is about as far-fetched, in the other direction.

    He didn't block a lot of shots or get his usual steals. And about half his minutes were vs Shaq and DRob.

    And now I can definitively say that in at least a playoff context WS/48 is useless. As the days go by, despite its defensive limitations, I am coming more and more convinced that PER is the best formula we have for evaluating players. People can imaginary neg me all they want, but I am sticking by it (and that includes using the defensive stats too even though it favors Olajuwon big time).

    BTW, Mike you'd agree with me too, I challenge people to this before "if Olajuwon was carrying this team then why didn't he win the title back in 87 or 88?"

  14. Mike G Says:

    ... the 95 rockets are the worst or one of a handful of the worst NBA champions in league history.

    In the last 20 years, they have about the 200th-best regular season record (of almost 600 team-seasons).
    But they're one of 20 teams to win a title.

    That's because they were so much better in the playoffs.

    It seems a bit odd to speculate -- "optimizing the '95 Rockets" -- on improving this team's postseason performance.

  15. Anon Says:

    I know that I was the main reason for both posts so I'll say it to you that I don't care about what the predictive stats say.

    That much is obvious. It's what happens when people already come to the table of discussion with their minds already made up about the matter at hand. Forget the evidence.

    As the days go by, despite its defensive limitations, I am coming more and more convinced that PER is the best formula we have for evaluating players.

    Because it's the only stat that satisfies your bias towards Hakeem in the '95 playoffs?

  16. AYC Says:

    Players who are credited with at least 1.5 Win Shares in the 1995 playoffs.
    Ranked by WS/48, Olajuwon ranks 11th of the 16.
    Behind Drexler; also behind (Phx) KJ and Barkley; (SA) Robinson, Rodman, and Avery Johnson; (Orl) Shaq; (NY) Oakley; (Ind) Miller and Smits.
    Barely ahead of Horry, Sean Elliott, Horace Grant.

    Thanks, Mike G; that says it all doesn't it?

    As for the 95 Rockets, they had injury problems and didn't have Drexler for 1st half of the reg season; they proved how good they were by beating teams with 62,60,59 and 57 wins; no team has ever beaten that many good teams en route to the title.

    I would take 95 Rockets to beat last year's lakers in a heartbeat

  17. Neil Paine Says:

    DSM, good points. I went back to re-run the SPM regression, and found that I had used slightly out-of-date APM data from BBvalue the first time, so I updated the data and also threw out the insignificant variables this time (which I wanted to do for a while), so you'll see a different set of coefficients and variables here:

    http://www.basketball-reference.com/blog/?page_id=4122

    After re-running the regression with and without it, here's no doubt that removing the TSA^2 term makes the model a worse fit. But I always wondered, why would Dan run those offensive/defensive regressions without it (or the Versatility Index, for that matter)? He posted the OSPM/DSPM formulae in 2005, and the original model was published in 2004, so why would he use a model that did a worse job of predicting APM a year later? My only guess is that he wasn't working for a team when he published the "difference makers" paper, and he was by the time he posted at APBR in 2005, so at that point he couldn't give away too many "state secrets".

  18. Anthony Coleman Says:

    Because it's the only stat that satisfies your bias towards Hakeem in the '95 playoffs?

    That and also Duncan for the first two title reigns, Shaq in the Laker dynasty, MJ in the Bulls Dynasty, Magic in the Showtime era, Larry Bird in 1984 and 86 playoffs, Lebron and Kobe in last year's playoffs, Wade in 06, Barkley in 1994 and 95, Moses in 1983. Do you want me to keep it going? I've studied the playoff careers for the past couple years and I've analyzed the patterns of playoff success and PER accurately gives the proper credit to Usage and Efficiency in relates to the impact in the offense. I didn't just wake up and decide that Drexler's 1995 scoring stats were inferior to Olajuwon's. I had been studying them for quite sometime and matching up the scoring stats for everybody for a long, long, long time (mostly because I've been considering doing a writing project about the ten greatest playoff players ever). I've long known that the efficiency shooting rates for players who have won the titles and their scoring averages, because I've studied them for so long. Plus because the Blazers had that three year playoff success I had long known Drexler's playoff success and looked at the outlier that was his 1995 playoffs. Yes Olajuwon is one of my favorite players ever, but I've long been consistent in my ratings for all of the players I've listed.

    That much is obvious. It's what happens when people already come to the table of discussion with their minds already made up about the matter at hand. Forget the evidence.

    Convenient that you chose to ignore my rebuttal to that said evidence. Besides until you answer my last post directed at you, I'll be looking past you and not at you.

  19. Neil Paine Says:

    Anthony, we found an inverse relationship between usage and efficiency (which the concept what your rebuttal on the other post seemed to center around). The model I presented yesterday factored this in, yet still found that unless Drexler and Olajuwon differed greatly from the usual usage/efficiency relationship, Olajuwon should have used fewer possessions and Drexler should have used more, until they reached the efficiency-maximizing point. Surely, as someone who subscribes to the inverse relationship, you can see that letting a 110 ORtg guy use 34% of possessions and a 120 ORtg guy use 24% isn't optimal -- no matter how steep you think the tradeoff curve is, the offense would benefit from assigning Olajuwon possessions to Drexler even if you think efficiency changes by +/-10 points for every +/-1% change in usage.

  20. DSMok1 Says:

    Good work, Neil!

    Could you create a "Library" on that page of BBRef of different regressions with different variables? I'd like to see this new regression, but also the old (i.e. so I don't have to keep a copy of it myself to document my older work--I've linked to that page but now you've changed what it shows...).

    Also, could you go ahead and run the regressions I requested over at APBR (the one without MPG, and the one to use as a prior that uses MPG, MPG^2, MPG^3, SRS of team, etc)? Sometime soon I'd like to get to work on a full-blown SPM prediction system.

  21. Neil Paine Says:

    Yeah, I have an archive of old regressions in a text file, so I'll make a page for those. I think I'm going to settle on this current one, though, until next season is finished. Barring the addition of 2007 per-100 possession regular-season data, I don't see any improvement that could be made.

    Also, I'll try to run those regressions you asked for tonight while this is fresh in my mind. I'd love to see what you're going to do with an SPM projection system (I tried that last summer, and it was an OK predictor of 2010 standings).

  22. DSMok1 Says:

    Perhaps Dan R. wanted to use a purely linear SPM for some reason? So it would be easier to scale? The TSA^2 term breaks down the regression for extreme outliers; I think the Versatility term does as well. For instance--imagine a TRUE center who just scored and got rebounds--and almost 0 assists--the regression would SEVERELY underrate him because most of the scoring and rebounding dependence is wrapped up in the versatility term.

    In fact, I struggled with just that fact when developing a system for single-game SPM scores. I ended up calculating the SPM for the season with the game and without the game and back-calculating the game SPM. Calculating it forward didn't work at all!

  23. Neil Paine Says:

    We don't have to go far to imagine such a player -- he's basically Leon Powe. Powe had 0 assists this season, and consequently his SPM was -8.88 because his V.I. was 0.

  24. Travis Says:

    I understand the point Neil and others are trying to make. I don't at all pretend to understand the complex statistical analyses that are going into making these arguments. Not that I don't have the capacity, but as a computer scientist, I don't have the time to delve that deeply while I'm at work.

    So why am I posting, you might ask? Well, to refer to a rule that would normally seem completely out of place on a forum like this, that old stand by - K.I.S.S. It seems that the mistake being made is a common one for mega-stat geeks such as ourselves - that being the tendency to get lost in overly-convoluted algorithms when some obvious things maybe should be given a little more focus. Namely this -

    For the '95 playoffs, Hakeem played two of the best centers in the history of the game, on the road more often than not, and came out on top - big time. We don't need "PER", "WS/48", or esp "ORtg" (which I have found again and again to be a virtually useless stat) or any other phantasmagoric statistical amalgamations to tell us this. Just hard numbers - he averaged 33 pts/game @ 53%, 10+ boards, nearly 3 blocks a game, and, to quote Shaq himself (not the humblest of players), "...Hakeem whupped my butt."

    By anyone's measurement, those are awesome numbers. How much more can you ask out of a premier big man? And you wanna take possessions AWAY from somebody putting up numbers like that?? Tell me what coach would agree that is a wise statistical maneuver?

    If ORtg is so important, I guess Reggie Miller is the best basketball player of all-time.

    Btw, Anthony, I'd like to see your top ten list. Sounds interesting

  25. Travis Says:

    Oh and I agree about PER; from studying this website a bit myself over the years, it does seem to have the strongest case for "most accurate assessment" as far as players' production on the court.

  26. Jason J Says:

    Clyde's age is mentioned more than Hakeem's because Hakeem was coming off an MVP, DPoY, and Finals MVP, and Clyde was coming off of back to back off years where he was nursing a bad knee and playing out of position with Porter and Strickland in the back court. He seemed older than he was coming into '95 (though he had a great year and probably should have been All-NBA first team - I think it went to Penny and Gary or Penny and Stockton), and Hakeem seemed to be in his absolute prime.

    Top Guards in 1995 by PER, WS, and WS/48

    http://www.basketball-reference.com/play-index/tiny.cgi?id=ocv48

    Plus Hakeem didn't start losing his hair until '98 and Drexler started losing his 14 years old or so.

  27. Anthony Coleman Says:

    Anthony, we found an inverse relationship between usage and efficiency (which the concept what your rebuttal on the other post seemed to center around). The model I presented yesterday factored this in, yet still found that unless Drexler and Olajuwon differed greatly from the usual usage/efficiency relationship, Olajuwon should have used fewer possessions and Drexler should have used more, until they reached the efficiency-maximizing point. Surely, as someone who subscribes to the inverse relationship, you can see that letting a 110 ORtg guy use 34% of possessions and a 120 ORtg guy use 24% isn't optimal -- no matter how steep you think the tradeoff curve is, the offense would benefit from assigning Olajuwon possessions to Drexler even if you think efficiency changes by +/-10 points for every +/-1% change in usage.

    Neil I understand what you're coming from and thank you for responding and I had considered that in my own initial analysis when I studied this the regression numbers between usage and efficiency, and I noticed the TS% for all of those players with the highest scoring averages. It came to my attention that not just Olajuwon, but all the high usage players who went deep in the playoffs, saw their playoff true shooting percentage drop.

    The relationship seemed to in relation in points averaged (and Wade's increase in efficiency in those last two rounds was also slightly offset by his turnover rate going Rick James high). With players with significant playoff games you've only seen the greatest player of all-time with a 60 TS% and 30+ points in the playoffs and the heir apparent with his amazing performance last year (and a handful of others, I believe Kareem in 1980 was one of them). My assumption was the norm being pounded by the usual decline from regular season efficiency to the playoffs. The original numbers of slight drop in efficiency per shot attempt was possibly much to do with regular season data, and would correct itself in an 82 game season.

    Plus, I still think its clear that Drexler's efficiency was a beneficiary of less offensive attention and responsibility. During the Blazers run from 1989-1992 (specifically in 92 when they gave the Bulls their most difficult Finals fight) when he was the main scorer his TS% in the playoffs and regular season hovered around the 55% percent mark. Plus there is evidence to suggest that a scorer who takes a volume of shots, even if they are just mediocre, can make it easier to get other players higher percentage shots.

    From just judging the past playoff successes of the other individual players and Drexler's own efficiency (his numbers by 1995 said that he was still an all-star, but not superstar level talent), and then having such a very high TS% that is clearly deviated from his norm and coincided with playing with a player who was taking the brunt of the offense and the more double teams and the more difficult contested shots and that the dude was in decline and hadn't shown the kind of effectiveness that Olajuwon had shown in the previous two and a half seasons (the reason why he was brought into support Olajuwon in the first place) I'm just not buying it. There is nothing in his statistical record that shows that he had the capability to be that efficient and the increases in shots from the past showed that he was actually less effective with more possessions. I take it as a very extreme example of "the volume scorer making it easier for other the other players."

    I also must say that I am shocked that I'm not the only one who noticed the outliers and trends in past performances. Also I must say too that while I think that Drexler benefitted from Olajuwon, I think that Olajuwon's volume was helped by Drexler keeping the rest of the team honest. All of those top players, except for Duncan, had a legitimate second scoring option that definitely made things easier and Drexler helped him out big time.

  28. AYC Says:

    My list, not that anyone asked:

    1) MJ
    2) Russell
    3) Magic
    4) Kareem
    5) Shaq
    6) Hakeem
    7) Bird
    8) TD
    9) West
    10) Kobe

  29. Gabe Says:
                                     Parameter      Standard    T for H0:
                    Variable  DF      Estimate         Error   Parameter=0    Prob > |T|
    
    
                    FTA        1      0.083834    0.06323568         1.326        0.1852
                    BK         1     -0.111075    0.10316250        -1.077        0.2819
                    PF         1     -0.093128    0.08545434        -1.090        0.2760
    

    I know that "P<0.05" is essentially an arbitrary cutoff, but the presence of the above 3 variables leads me to wonder about the results.

  30. Mike G Says:

    ... the offense would benefit from assigning Olajuwon possessions to Drexler ...

    Once again, how can you seriously propose that the 1995 postseason Rockets could have done better, when perhaps no team has EVER improved as much, from season to playoffs?

    In the '95 Finals, Hakeem scored 30.7% of what the entire opposition (Orl) scored.
    Next best: Shaq scored 24.6% of what his opponents (Hou) totaled.
    They played equal minutes.

    ... they proved how good they were by beating teams with 62,60,59 and 57 wins; no team has ever beaten that many good teams en route to the title.

    Can both of these statements be true?

  31. AYC Says:

    Oh and I agree about PER; from studying this website a bit myself over the years, it does seem to have the strongest case for "most accurate assessment" as far as players' production on the court.

    Not if defense matters to you. Unless you think Bill Russell isn't one of the top 50 (or 80!) players in history...

  32. Anon Says:

    Convenient that you chose to ignore my rebuttal to that said evidence.

    You mean the same evidence that has already been countered in two separate blog posts? It's right here in front of you. It doesn't matter though, because once again the sentiment of some posters on these threads is "*I* think Player X is the best, and any stat that doesn't have them where *I* think they should be is automatically wrong, and needs to be changed to reflect my bias". The concern is no longer about about building models that correctly reflect the principles of the game; it's about manipulating numbers so players of your selective choosing come out on top. I find it amazing that the basketball community clamors for "better numbers" that depict what takes place on the court (since per game numbers don't cut it), and yet when they are presented with any work that goes about improving our understanding of the sport (and keep in mind I'm saying this with the full awareness that these models can always be improved upon), these same people get mad with the results, and return to metrics that do NOTHING to start with. If numbers come out that show that John Doe is a better player than Michael Jordan and, within reason, the methodology evince the fundamentals of basketball, how can you possibly dispute the results? It's not necessarily the names that matter here. I really couldn't care less if Drexler or Olajuwon was the better performer in the '95 playoffs; just make sure the methodology and reasoning behind your investigation is sound. I don't mind at all cleaning up the statistical methods that are used to arrive to these conclusions or introducing variables that can enhance these models; I DO mind those who argue with the data because they happen to have a personal preference for Hakeem.

    But since that's what people like to do around here, I'm going to hereby propose that Robert Horry is the greatest player of the past 20 years, because you know, I *said * he's the best. If he played Paul Pierce one-on-one in his prime, I guarantee you Big Shot Rob would destroy him.

  33. Neil Paine Says:

    So Mike, you're saying that just because the Rockets acquired Drexler and improved themselves at the trading deadline, that's somehow proof that the Rockets couldn't possibly improve further via strategic/tactical changes? Why does the former preclude the latter? I mean, ask any coach, he'll tell you that you can always improve. No team has ever executed perfectly & played a perfect game, and no coach has ever had a perfect coaching performance. But because the Rockets acquired Drexler at the deadline, they're suddenly perfect and couldn't be improved further?

  34. David Lewin Says:

    Neil,

    I would love to see what you get if you add the TSA^2 term. I don't know if you have the data to do this, I think it's still out there from Dan's stuff.

  35. DSMok1 Says:

    I would be interested in seeing a full regression of SPM that does not have the nonlinear terms (TSA^2 and Vers). The fact that Leon Powe's numbers are so off is bad for this regression. In fact, how different is the R^2 with and without the "Versatility" term? Is there another route that could be used to get the same interaction effect without the breakdown? Perhaps 2 terms, one (sqrt(assists^2 + pts^2) and the other sqrt(pts^2 + rebounds ^2))? I'm not sure why versatility was chosen in the first place... there are definite issues with its use.

  36. Neil Paine Says:

    Well, not wanting to calculate AOPM myself at the moment (I'll probably have to do it eventually, but it's a real pain to set it up in Excel), I found this site that actually had AOPM data from 2006-09:

    http://www.3hoopsfans.com/2010/01/converting-per-to-statistical-offensive-adjusted-plus-minus/

    So I set up the regression with the (non-pace adjusted) variables Dan had, plus a TSA^2 term:

                 Estimate Std. Error t value Pr(>|t|)    
    (Intercept) -7.486970   1.829201  -4.093 6.27e-05 ***
    pts40        0.820426   0.130063   6.308 1.91e-09 ***
    tsa40       -0.814025   0.215986  -3.769 0.000218 ***
    tsa40sq      0.009597   0.005126   1.872 0.062729 .  
    fta40        0.121213   0.118371   1.024 0.307119    
    3pa40        0.344555   0.075487   4.564 8.93e-06 ***
    ast40        0.738477   0.092751   7.962 1.45e-13 ***
    orb40        0.811321   0.212289   3.822 0.000179 ***
    drb40        0.098351   0.104200   0.944 0.346425    
    tov40       -1.295009   0.317114  -4.084 6.50e-05 ***
    stl40       -0.017556   0.317979  -0.055 0.956027    
    blk40        -0.379592   0.217721  -1.743 0.082851 .  
    pf40        -0.143733   0.200393  -0.717 0.474087    
    mpg          0.056397   0.029852   1.889 0.060368 .  
    ---
    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
    
    Residual standard error: 1.495 on 192 degrees of freedom
    Multiple R-squared: 0.766,      Adjusted R-squared: 0.7502 
    F-statistic: 48.35 on 13 and 192 DF,  p-value: < 2.2e-16 

    Dropping the insignificant variables, we get:

    Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
    (Intercept) -8.253848   1.502898  -5.492 1.22e-07 ***
    pts40        0.895628   0.112222   7.981 1.17e-13 ***
    tsa40       -0.851185   0.197830  -4.303 2.66e-05 ***
    tsa40sq      0.009722   0.004876   1.994  0.04756 *  
    3pa40        0.323769   0.068934   4.697 4.95e-06 ***
    ast40        0.759086   0.078240   9.702  < 2e-16 ***
    orb40        0.779396   0.156450   4.982 1.37e-06 ***
    tov40       -1.319595   0.262863  -5.020 1.15e-06 ***
    mpg          0.068744   0.023236   2.959  0.00347 ** 
    ---
    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
    
    Residual standard error: 1.495 on 197 degrees of freedom
    Multiple R-squared: 0.7598,     Adjusted R-squared: 0.7501 
    F-statistic:  77.9 on 8 and 197 DF,  p-value: < 2.2e-16 
    

    By this measure, Hakeem was Houston's best offensive player, over Drexler:

    Player G MP OSPM
    Olajuwon 22 929 5.38
    Drexler 22 849 3.84
    Horry 22 841 0.93
    Smith 22 652 1.00
    Elie 22 635 -0.75
    Cassell 22 485 1.99
    Brown 21 326 -5.88
    Chilcutt 20 323 -2.58
    Jones 19 237 -8.51
    Tabak 8 31 -9.59
    Maxwell 1 16 -13.82
    Herrera 1 6 2.31
  37. Mike G Says:

    So Mike, you're saying that just because the Rockets acquired Drexler and improved themselves at the trading deadline, that's somehow proof that the Rockets couldn't possibly improve further via strategic/tactical changes?

    Nothing of the sort. In the season, they were 30-17 with Otis Thorpe. After Drexler came over, they went 17-18 the rest of the way.

    I have no idea how they then went 15-9 vs the best 4 teams anyone's ever beaten in a postseason.

    That is why I have to wonder how they could/should have been further 'optimized'. A .573 team (or a .486 team) that has won the title doesn't need second-guessing on their strategy.

  38. Jason J Says:

    Neil - Any plan to add SPM to the play index and player profile pages?

  39. Anthony Coleman Says:

    You mean the same evidence that has already been countered in two separate blog posts? It's right here in front of you. It doesn't matter though, because once again the sentiment of some posters on these threads is "*I* think Player X is the best, and any stat that doesn't have them where *I* think they should be is automatically wrong, and needs to be changed to reflect my bias". The concern is no longer about about building models that correctly reflect the principles of the game; it's about manipulating numbers so players of your selective choosing come out on top. I find it amazing that the basketball community clamors for "better numbers" that depict what takes place on the court (since per game numbers don't cut it), and yet when they are presented with any work that goes about improving our understanding of the sport (and keep in mind I'm saying this with the full awareness that these models can always be improved upon), these same people get mad with the results, and return to metrics that do NOTHING to start with. If numbers come out that show that John Doe is a better player than Michael Jordan and, within reason, the methodology evince the fundamentals of basketball, how can you possibly dispute the results? It's not necessarily the names that matter here. I really couldn't care less if Drexler or Olajuwon was the better performer in the '95 playoffs; just make sure the methodology and reasoning behind your investigation is sound. I don't mind at all cleaning up the statistical methods that are used to arrive to these conclusions or introducing variables that can enhance these models; I DO mind those who argue with the data because they happen to have a personal preference for Hakeem.

    But since that's what people like to do around here, I'm going to hereby propose that Robert Horry is the greatest player of the past 20 years, because you know, I *said * he's the best. If he played Paul Pierce one-on-one in his prime, I guarantee you Big Shot Rob would destroy him.

    Anon set your strawman on fire, OK. I gave plenty of reasons why I thought the Win Shares overrating Drexler's offensive production and the predictive stats of him maintaining his high shooting percentage throughout the playoffs didn't jive with reality because the occurrence of players scoring 29 PPG through the Finals and maintaining such a high TS% is low. Only Michael Jordan and Kareem were able to maintain over 57% from the first round. These are arguably the two greatest players in league history and clearly ahead of Drexler in terms of talent. The rest were around 56%.

    2)Drexler never averaged anywhere near 58.9 percent in the playoffs or regular season before that. This made me question when I first saw it because it is a clear outlier, then I realized that he was taking less of an offensive role and less of the attention of the defense and was able to stay so sky high with less shots. That is the obvious hypothesis to me at least.

    3) He never was anywhere near efficient in his Portland days when he was the main man on offense and the main attention of the defense. It was always around 55 or 56 percent for playoffs and regular season.

    4) The reason why Olajuwon was the focal point of the offense because over the previous three seasons he proved himself to be the greater high volume/ efficiency scorer than any point in Drexler's career. He shot more and hit the net with more frequency. He had shown to be more reliable and their was no evidence to suggest that was going to change.

    I've made my case and I've shown my cards and I think there is more than enough evidence that Drexler was probably not going to maintain that level and his offensive production was artificially enhanced by having Olajuwon take more of the possession (to think otherwise the more I look at the stats is laughable). If the offensive roles were reversed I doubt that Drexler would have succeeded in that role because he hadn't show anywhere close to that talent when he was younger. You can get all mad if you want me to and claim that I'm just trying to avoid WS because its giving me a result that I don't like, but I gave you enough reason why I think that Drexler's scoring performance was inflated. As far as I'm concerned I am done with this discussion.

  40. Anthony Coleman Says:

    Travis I'll show the list later on.

  41. Neil Paine Says:

    What you're doing, Anthony, is a poor man's version of what I did -- looking at usage with PPG as your proxy, and efficiency with TS% as your proxy. Trouble is, those are not the best measures of either usage or efficiency. Offensive rating measures efficiency better than TS% because it factors in turnovers, assists, and offensive rebounding; possession % measures usage far better than PPG because it takes into account all possessions (not just scores), it properly weights them, it's naturally pace-independent, and it adds up to 100% for each on-court unit.

    Olajuwon
    Year Age Tm G MP ORtg %Pos DRtg DPA
    1985 22 HOU 82 2914 112.4 23.3 102.6 3.04
    1986 23 HOU 68 2467 112.8 25.2 101.6 3.81
    1987 24 HOU 75 2760 110.9 26.3 98.7 4.56
    1988 25 HOU 79 2825 109.4 25.9 98.0 4.59
    1989 26 HOU 82 3024 108.5 27.2 94.9 5.90
    1990 27 HOU 82 3124 104.4 27.2 93.4 6.47
    1991 28 HOU 56 2062 108.9 24.5 93.4 6.72
    1992 29 HOU 70 2636 110.1 24.8 98.9 5.78
    1993 30 HOU 82 3242 113.8 28.1 96.1 5.55
    1994 31 HOU 80 3277 109.0 28.6 94.9 4.45
    1995 32 HOU 72 2853 109.5 30.3 100.3 3.45
    1996 33 HOU 72 2797 107.7 30.7 100.7 2.79
    1997 34 HOU 78 2852 105.1 29.3 99.0 2.40
    1998 35 HOU 47 1633 105.1 23.6 101.2 3.15
    1999 36 HOU 50 1784 105.4 25.0 95.8 3.32
    2000 37 HOU 44 1049 95.8 22.1 100.5 2.25
    2001 38 HOU 58 1545 106.4 21.7 98.0 2.84
    2002 39 TOR 61 1378 91.3 18.4 95.9 3.75
    Drexler
    Year Age Tm G MP ORtg %Pos DRtg DPA
    1984 21 POR 82 1408 101.9 21.7 104.9 0.67
    1985 22 POR 80 2555 110.0 24.2 105.1 0.60
    1986 23 POR 75 2576 107.4 25.8 105.7 0.45
    1987 24 POR 82 3114 114.4 24.0 107.0 0.46
    1988 25 POR 81 3060 117.7 27.7 105.9 -0.21
    1989 26 POR 78 3064 116.8 27.1 106.0 0.15
    1990 27 POR 73 2683 117.5 25.4 103.4 0.60
    1991 28 POR 82 2852 117.1 26.0 103.4 0.61
    1992 29 POR 76 2751 117.0 28.7 103.1 0.55
    1993 30 POR 49 1671 112.3 26.3 103.9 0.76
    1994 31 POR 68 2334 109.6 24.8 105.4 -0.22
    1995 32 POR 41 1428 119.1 26.6 104.9 0.09
    1995 32 HOU 35 1300 119.0 23.7 106.3 0.31
    1996 33 HOU 52 1997 113.2 24.1 105.4 0.95
    1997 34 HOU 62 2271 112.6 23.9 103.0 0.88
    1998 35 HOU 70 2473 109.5 25.9 107.6 -0.42
  42. Neil Paine Says:

    Neil - Any plan to add SPM to the play index and player profile pages?

    I'd like to at some point, but Justin and I have to work on cleaning up the formula and making it as rigorous as possible. Which is sort of what we've been doing in this thread, too.

  43. DSMok1 Says:

    Neil: You saw the six-year APM that Ilardi calculated, right? Of course, the problem with it is that he weighted the playoffs at 2x the regular season. That isn't too big a deal, though, since we're using per-possession stats anyway. I presume that the playoffs should be a slightly better measure of a player's true contribution, at any rate.

  44. DSMok1 Says:

    I might add--Ilardi's APM is actually split into offensive and defensive APM.

  45. Anon Says:

    You can get all mad if you want me to and claim that I'm just trying to avoid WS because its giving me a result that I don't like, but I gave you enough reason why I think that Drexler's scoring performance was inflated.

    Even if this were the case, you seemed all but ready to dismiss the entire metric altogether based on this one example. That's not a valid way to critique anything from an objective standpoint. And by the way, this isn't a straw man argument by any means. Simply an attempt to remind people what the goal of this whole blog and these stats are in the first place: to give as accurate a representation of the sport as possible. Names and results simply reflect the construction, philosophies, and methodologies of the metric in question. Those things are more important than finding a way to spit out the name "Hakeem" or "Clyde" when someone asks who the best offensive player for the Rockets in the '95 playoffs was, for example.

    Also, this whole thing reminds me of the "80/20" argument that Bill James used in his studies. Asking questions is fine, but people shouldn't be so quick to dismiss something because it gives a result you don't expect. That is part of the nature of learning.

  46. Jason J Says:

    Neil - the way you were modifying the SPM formula throughout this post is what made me ask in the first place. I think it would be a great addition because it measures such different things than WS or PER.

    Very interesting to see Clyde's and Dream's ORtgs laid out like that. I've very surprised Hakeem's were so low (relative to his skill level / success), and it's also probably telling that Drexler's regular season ORtg didn't change at all when he moved from Portland to Houston in '95. He was in the middle of his most efficient year when he got traded, and he kept it up.

  47. Neil Paine Says:

    DSM, here's the regression without the versatility term:

    Residuals:
          Min        1Q    Median        3Q       Max 
    -19.77436  -3.06230   0.09454   3.15127  18.08864 
    
    Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
    (Intercept) -7.63483    1.36781  -5.582 2.70e-08 ***
    pts40        0.80394    0.10274   7.825 8.07e-15 ***
    tsa40       -1.37758    0.19088  -7.217 7.45e-13 ***
    tsa40^2      0.01815    0.00517   3.510 0.000457 ***
    3pa40        0.42556    0.07036   6.048 1.74e-09 ***
    fta40        0.42231    0.10522   4.013 6.20e-05 ***
    ast40        0.69283    0.08403   8.245 2.90e-16 ***
    orb40        0.50781    0.16804   3.022 0.002543 ** 
    drb40        0.39389    0.09694   4.063 5.02e-05 ***
    tov40       -1.57465    0.23722  -6.638 4.06e-11 ***
    stl40        2.70845    0.27003  10.030  < 2e-16 ***
    blk40        0.99447    0.18518   5.370 8.75e-08 ***
    mpg          0.07715    0.01731   4.456 8.79e-06 ***
    ---
    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
    
    Residual standard error: 4.871 on 2052 degrees of freedom
    Multiple R-squared: 0.2803,     Adjusted R-squared: 0.2761 
    F-statistic: 66.61 on 12 and 2052 DF,  p-value: < 2.2e-16 
    

    That's not horrible -- there definitely wasn't as big a drop-off in fit as I thought there'd be.

  48. Neil Paine Says:

    Also, I'll have to run those other regressions you requested later. Sorry I keep putting it off.

  49. DSMok1 Says:

    Let's see: biggest movers positively with this new change (dropping versatility) are all pure post players.

    Team	Player		SPM	Minutes	Difference
    CLE	Leon Powe	-1.63	6.0%	6.63
    MIA	Jamaal Magloire	-1.14	9.0%	3.38
    OKC	Etan Thomas	-6.04	8.1%	2.50
    POR	Jeff Pendergraph-0.33	10.2%	2.48
    PHO	Robin Lopez	-0.59	25.0%	2.25
    POR	Joel Przybilla	0.38	17.1%	2.21
    OKC	Serge Ibaka	-0.92	33.4%	2.15
    WAS	Brendan Haywood	1.34	40.7%	2.07
    NJN	Sean Williams	-5.34	5.7%	1.74
    DEN	Chris Andersen	2.69	42.8%	1.69
    CHA	Tyson Chandler	-1.40	29.3%	1.67
    TOR	Reggie Evans	-0.56	7.9%	1.58
    CLE	J.J. Hickson	-2.50	42.7%	1.54
    ORL	Marcin Gortat	-0.33	27.6%	1.52
    HOU	Kevin Martin	0.81	21.6%	1.35

    And the ones who dropped:

    Team	Player		SPM	Minutes	Difference
    MEM	Hamed Haddadi	-6.56	6.0%	-1.80
    LAC	Craig Smith	-0.84	31.3%	-1.78
    NOH	Aaron Gray	1.23	6.6%	-1.69
    MIN	Brian Cardinal	-0.75	6.7%	-1.43
    NJN	Eduardo Najera	-3.66	5.2%	-1.40
    WAS	Fabricio Oberto	-3.10	16.4%	-1.40
    IND	Roy Hibbert	-1.82	51.6%	-1.35
    NOH	Hilton Armstrong-3.13	6.0%	-1.32
    CLE	LeBron James	12.51	75.0%	-1.29
    NYK	David Lee	1.39	75.9%	-1.24
    CLE	Shaquille O'Neal-0.59	31.3%	-1.23
    GSW	Mikki Moore	-4.96	10.3%	-1.17
    SAS	Tim Duncan	5.00	61.6%	-1.16
    PHI	Jason Smith	-3.32	16.6%	-1.16
    TOR	Hedo Turkoglu	0.79	57.4%	-1.15
  50. Anon Says:

    Going back through the Rockets' games in the '95 playoffs, I think part of the reason some people are so up in arms about Drexler being compared to Hakeem is because Hakeem's best performances came later in the playoffs, which also featured his "high-profile showdowns" with the Admiral (league MVP) and Shaq (the "future" of the league)...those games will tend to stick in fans' memories more vividly. Drexler had some STELLAR performances in the first two rounds though; his problem was that he slowed down a little just as Hakeem got himself going in the WCF and Finals.

  51. James Says:

    There is no way Clyde Drexler was as good as Hakeem Olajuwon in the 1995 playoffs. This is blatant revisionism. Clyde Drexler would be quite embarassed at such a laughable claim. That's the playoff run that catapulted Hakeem into all-time great status. He outplayed two of the best centers in the league, led the Rockets to 4 straight series wins without HCA. The main reason why Drexler played so well in those playoffs is because of Hakeem and Drexler said that himself. He repeatedly insisted Dream was the best player in the league, he's never seen anyone play as well as he did in those playoffs, there should be a reballot for the MVP etc. Glide was rejuvenated playing with Hakeem, these two had a special bond going back to their PhiSlammaJamma days. Hakeem was the key cog in the Rockets offense. Not Drexler. Hakeem was the one who drew all the defensive attention that the shooters and Glide benefitted from. There's a reason Seattle went after Hakeem in 1996 and tripled teamed him on every possession, something tells me they knew a thing or two about the game.

    Clyde Drexler was maybe half the player Hakeem was in those playoffs.