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 ’95 Rockets

Posted by Neil Paine on April 19, 2010

Over in the comments of an earlier post about the 1990s Knicks, a discussion is raging about who the best player on the 1995 Houston Rockets was -- Hakeem Olajuwon, or his old college teammate Clyde Drexler? At the core of the back-and-forth is whether Drexler's 120.1 offensive rating (using 23.8% of Houston's possessions when on the court) was more vital to the offense than Hakeem's 109.8 ORtg (using 34.1% of possessions when in the game)... In other words, the old usage-efficiency debate. On one side, Drexler clearly contributed more points per possession to the Rockets' effort than Olajuwon -- but on the other side, Hakeem had to create offense on a significantly higher % of the Rockets' possessions than Clyde, and if you subscribe to "skill curve" theory, this means Clyde's ORtg was artificially enhanced by the extra defensive attention Hakeem drew -- as well as the fact that his shot selection didn't have to include the offense's toughest shots, which were presumably going to Hakeem (at least in a larger proportion), in turn dragging down Hakeem's ORtg.

We've been through all of this before at APBRmetrics, so this isn't going to tread new ground or even settle the Hakeem-Drexler discussion, but here's some more fuel to pour onto the fire...

In 2005, Dean Oliver (inventor of "skill curves", at least in the way I discuss them here) ran a quick study that began to quantify the usage/efficiency trade-off at 0.6 pts/100 poss for each 1% increase/decrease in possession%. So the average player in 2005, with an ORtg of 106 on 20% possession usage, would drop to a 103 ORtg if forced to take on 25% possession usage. Another fascinating finding of Dean's simple study was that the effect was amplified for low-usage players and diminished for high-usage ones. "If you run the regression on players averaging high or low use," he wrote, "you see that the low use players (I used 18% as a cut off) are more sensitive to increases than high use players (23%). But both are still very significant. This implies that increasing Fred Hoiberg's possessions 5% causes a bigger decline (about twice the size) than a similar increase in, say, Kevin Garnett. Or, from an optimization perspective, taking Garnett's possessions (who increases in efficiency only a little) and giving them to Hoiberg (who declines in efficiency a lot) has a pretty big cost in even this crude analysis."

That was a great starting point for me, and led me to develop what I called WARP (not to be confused with Kevin Pelton's stat of the same name), which subbed a player for one with replacement-level production and tracked the difference in expected team wins, using Dean's trade-off formula to measure the effects of swapping players on lineup efficiency. I suspected that the +/-0.6 tradeoff was not strong enough, as evidenced by mid-usage/high efficiency players like Jose Calderon ranking ahead of Kobe Bryant in WARP for a brief period during the 2008 season, but I went with Dean's original study until something better came along.

That something came in March 2008, when Eli Witus conducted his own study on usage-efficiency tradeoffs using lineup data, which was a breakthrough because it eliminated many of the "chicken-and-egg" issues that had plagued earlier studies. Eli found in 2008, a league with an offensive rating of 107.5, that for each 1% a player increased his usage, his efficiency dropped by 1.25 points per 100 possessions.

For this post, I want to create a simple lineup efficiency model that combines Dean and Eli's findings -- specifically Eli's tradeoff for average players (+/-1.25 in a 107.5 ORtg league), but Dean's distinction between high-usage, mid-usage, and low-usage effects on personal efficiency (the effect on low-usage players is twice the effect on high-usage ones). What we in essence have, then, is a simple algebra problem: let x be the tradeoff for low-usage (<=18%) players and y the tradeoff for high-usage ones (>=23%). (x + y) / 2 = 1.25, and x = 2*y. What are x and y?

x = 1.6667, y = 0.8333

This means that in a 107.5-ORtg environment, the efficiency trade-off for increasing or decreasing usage by 1% is as follows:

Player Type Tradeoff
High Usage (>=23%) 0.833
Mid Usage (18-23%) 1.250
Low Usage (<=18%) 1.667

We can also adjust each of these appropriately as a proportion of the league average when applying them to different environment (i.e., the tradeoffs would be .782/1.173/1.564 in 1978, when the league's ORtg was 100.9).

With information in mind, let's look at the Rockets' primary playoff lineup in 1995:

Player Tm ORtg %Pos
Smith HOU 119.7 16.7
Elie HOU 125.4 13.1
Drexler HOU 120.1 23.8
Horry HOU 123.4 15.2
Olajuwon HOU 109.8 34.1

Those are their playoff-wide stats, and the Poss% don't add up to exactly 100%, so we have to adjust the usages (and the efficiencies) accordingly. If we assume every player would take on 20% of the possessions, you get a team efficiency of 117.6:

Player Tm ORtg %Pos
Smith HOU 114.0 20.0
Elie HOU 113.6 20.0
Drexler HOU 123.4 20.0
Horry HOU 115.2 20.0
Olajuwon HOU 121.9 20.0

Now, that's obviously not how this lineup operated in real life; rather, the best guess is that they divided possession% up according to their playoff-wide rates, proportional to 100% total possession%:

Player Tm ORtg %Pos
Smith HOU 120.5 16.2
Elie HOU 126.1 12.8
Drexler HOU 120.7 23.1
Horry HOU 124.1 14.8
Olajuwon HOU 110.6 33.2

That lineup yields an expected ORtg of 118.5, which is significantly better than the 117.6 we saw from the "perfectly fair" 20%-each lineup. But knowing the assumptions I laid out above regarding the various tradeoffs (and remembering that the league environment for the 1995 playoffs was 110.6 pts/100 poss.), can we further redistribute the possessions in this lineup to achieve an even higher offensive rating?

Player Tm ORtg %Pos
Smith HOU 121.4 15.7
Elie HOU 121.2 15.6
Drexler HOU 117.5 26.8
Horry HOU 122.0 16.0
Olajuwon HOU 116.8 26.0

Actually, yes. The lineup above yields an offensive rating of 119.2, even higher than the "realistic" lineup that divvied up possessions according to playoff-wide Poss%. And if you optimize a lineup with Cassell at the point, you see similar results (actually, even better -- a 120.3 ORtg):

Player Tm ORtg %Pos
Cassell HOU 118.3 22.9
Elie HOU 123.3 14.4
Drexler HOU 119.6 24.4
Horry HOU 124.1 14.8
Olajuwon HOU 118.9 23.6

Which means that, if you agree with the general ground rules I set at the beginning of this experiment, it's not unreasonable to think the '95 Rockets' best strategy was to divert possessions away from Olajuwon and give more to Drexler, to the point that Drexler would actually be the highest-usage player in the lineup (and he'd still have a higher offensive rating). Let me be clear that I'm not saying Olajuwon wasn't the better all-around player in those playoffs -- he had a defensive rating of 107.6 and saved 0.77 pts/100 poss vs. the league average according to DPA; Drexler's DRtg was 111.5 (worse than the league avg), and gave up 0.29 pts/100 more than avg by DPA.

So there's a good chance Hakeem's defensive edge offset Clyde's edge on offense. But the take-home point is that Clyde did have an edge on offense, at least according to the skill curve assumptions I laid out, and that Houston may have been better off allocating more of Olajuwon's possessions in Drexler's direction. This is a highly simplified model of the game (as Dave Lewin said, "players often affect team efficiency differently than you might expect from their offensive rating and possession rate"), but as a very general rule it holds according to Dean and Eli's studies, so at the very least these results can't be dismissed out of hand.

ShareThis

17 Responses to “Optimizing the ’95 Rockets”

  1. KLM Says:

    This is the Parker/Duncan 2007 Finals conundrum. Hakeem MADE Clyde look good. Teams were concentrating on Hakeem and that's what freed Clyde to do his thing, with more efficiency. You can throw all the statistics you want but at the end of the day there is no effin' way that you can say Clyde was better than Hakeem in '95. None.

  2. Mike G Says:

    "... there's a good chance Hakeem's defensive edge offset Clyde's edge on offense. "

    Didn't the debate start when it was pointed out that Drexler's playoff WS/48 was some 17% higher than Olajuwon's, in the '95 playoffs?

    Wouldn't it have been a hoot if Drexler was named Finals MVP ?

  3. Jason J Says:

    Neil - this is really well stated for the interested layperson to understand the skill-curve breakdown.

    I do think KLM has a point though.

    Something that I tried to point out in our Andrian Dantley discourse was that the specifics of what each player does matters. Obviously you didn't set out to breakdown film and do a play by play study of how each Rockets play was able to get his shots off. Did Hakeem's ability to draw double teams allow Drexler to score unhindered? Would diverting possessions away from Hakeem have made things significantly more difficult for Clyde than the normal skill-curve would account for? I'm not sure.

    OT - There is one play that took place in the finals that year that always sort of sticks out as a real classic case of the stats not telling the story. At the end of game 1 in Orlando, Clyde drove down the right side of lane and drew Shaq and Grant over for the contest on a tough layup attempt. Nobody boxed out Hakeem who tipped the ball into a completely undefended rim. End result - Clyde with a missed field goal - Hakeem with an offensive rebound and two points. Here's the thing - maybe five or six players in the league that year could have done what Drexler did, blowing by his man, drawing full rotation from Shaq and Grant actually out of the paint, and still getting the ball on the rim in a reboundable position. Just about any front court player in the league could tip the ball in. But the stats think Clyde had a terrible possession, and Hakeem had a great one. (Gonna try to embed the film, but I don't know if it will work - sorry if it looks like a bunch of code)

  4. AYC Says:

    To the naked eye, Hakeem decisively outplayed DRob, Shaq and every other player in the 95 PO; he also put up the best unadulterated postseason stats of his career, leading the playoffs in scoring with 33.0 ppg (only MJ avgd more on a championship team), avg double figures in rebounds, and 4.5 apg, plus almost 3 blocks per game; he also shot .531 from the field.

    Will I trust the evidence of my own eyes, and traditional stats, or should I trust WS, which says Robinson was more productive in 95? I think you know the answer...

    Statistical formulas like win-shares or PER are only as good as the results they produce; I believe in adjusted OPS because the all-time leader list is populated by exactly the players that a knowledgable fan would expect. Basketball doesn't have anything equivalent; when your formula says Clyde and DRob were better than Dream in 95, that's a sign that your formula still needs work

  5. Neil Paine Says:

    1. Maybe you should, you know, read the post.

    2. What you said about OPS+ is not how science works. You can't just say, "these results don't match what I expect/want, so I'm dismissing them." Otherwise, we'd still think a flat Earth was at the center of the universe.

  6. Neil Paine Says:

    Jason, over the course of a big enough sample, those plays even out -- sometimes Hakeem will get credit for a play where Clyde did most of the work, and sometimes Clyde will get credit for a play where Hakeem did most of the work. But if you play enough games/minutes/possessions, the proper credit will be allocated the majority of the time and you'll have a quality dataset. This is part of why basketball players are more consistent year-to-year than any other athletes, more so than even baseball players.

    Also, is there any evidence that Clyde's tradeoff would be significantly different from that of any other 24% usage guard, or that Hakeem's would be different than any other 34% usage center? Absent any kind of specific evidence that they would have a different skill curve than other players of their ilk, I see no reason to assume anything other than the typical skill curve, the existence of which we have plenty of evidence for.

  7. ryan. Says:

    This is one of those debates where revisionist statistics will not solve the questions (As Neil appropriately pointed out). We need tape, and play by play analysis. There is no question that Hakeem was the focal point of all opponents, and there is no question that this freed up Drexler. Having said that, perhaps the statistical side of the fence on this is the only way we can begin to approach it - as what played out in 1995, is exactly what played out. We ultimately cannot answer exactly as to how Clyde would have performed shouldering a larger load and seeing that defense slowly move away from Hakeem to the Gylde.

    Funnily enough, I recently watched a couple of games from this series and had these few intoxicated comments to make

    "I just watched 1995 Finals Games 2 and 4, on VHS (which completely sucks on a 52 inch plasma)again.

    I have a few drunken comments to make.

    1) Clyde, you bastard (for getting that ring while Jordan wasn't around).

    2) Was Clyde ever faster? This guy was faster off the dribble than anybody I can think of in the league right now, and he was an old fart.

    3) ROFLZ@the 2009 NBA Finals.

    4) Nobody could ever defend Shaq better than Olajuwon did. His offensive numbers may not have been the most efficient, but my God did he do a great job on a prime Shaq. "

  8. ryan. Says:

    BTW, I realize that my comment in reference to "Prime Shaq" could cause a slight amount of disdain. I stand by it, measuring his prime not by his peak.

  9. Anthony Coleman Says:

    I posted this as my final response to Anon, but its more appropriate here:

    """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
    In fact the whole argument is about the playoffs and while doing some research I noticed something: over the last 19 playoffs for all of the players who have won an NBA title and averaged at least 30 points (I'm going to include Kobe's 2001 because he averaged 29.4 a game), not one of them had a true Shooting Percentage as high as Drexler's. Here is the numbers (note: I'm not correcting for the pace because the shot attempts are pretty much the same)

    Jordan 1992: 34.5 points per game/ 57.1 TS%
    Jordan 1993: 35.1 PPG/ 55.3 TS%
    Jordan 1996: 30.7 PPG/ 56.4 TS%

    Shaq 2000: 30.7 PPG/ 55.6 TS%
    Shaq 2001: 30.4 PPG/ 56.4%
    Kobe 2001: 29.4 PPG/ 55.5%

    Kobe 2009: 30.2 PPG/ 56.4%

    also lets add more to the mix: D-Wade's 2006 was 28.4 and his True Shooting percentage was 59.3.

    Also because of his greatness in the postseason and his higher average in the first two titles, Tim Duncan
    Duncan 2003: 24.7 PPG/ 57.7%
    Duncan 1999: 23.2 PPG/ 57.3%

    So here is the breakdown: For all the ones that averaged at least 29 points per game not one of the max is 57.1 held by Michael Jordan. After that the rest were hovering around 55.5-56.5 percent. Then we had Duncan, who was less than thirty points, but had a higher average than Drexler, his percentage was in the 57%. There is only one player who had a higher scoring average, won a title, and had a higher TS% and that was Wade (and that was fueled by an absolutely crazy efficient final two series). But the point is this: in the playoffs when the average reaches the mid 20s, and certainly nearing 30 points, the drop in TS% is precipitous.

    This is why I am so surprised that there isn't so much skepticism when it comes to Drexler's high efficiency and just because of that he'd continue to be anywhere near effective with more shots. The data we have suggests that the likelihood of that happening when you're facing the very best teams in the league in a seven (well back then the first rounds were 5) game elimination is very, very, very low. It is very difficult to maintain that kind of productivity when you're shooting that often in the playoffs. Plus ask yourself that question: do you honestly, in your mind, feel that at his age Drexler was as athletically dominant as all of those all-time greats (and if Wade's body doesn't fall apart he will certainly join those ranks)? I think that answer is a definitive no.
    """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""

    We could also search through players who played significant numbers of games in the postseason too. I don't have the time now, but I would love to see it.

  10. Neil Paine Says:

    Follow-up post:

    http://www.basketball-reference.com/blog/?p=5519

  11. AYC Says:

    Neil, I did read the post

    I know how science works; this isn't about me rejecting objective stats, it's about rejecting your SUBJECTIVE interpretation of those stats; when a supposedly scientific metric produces a result that is clearly wrong to anybody who understands objective stats, that metric needs to be tweaked.

    These are the stats I trust:
    33.0 ppg, 10.3 rpg, 4.5 apg, 2.8 bpg, .531 fg%, .681 ft%

    One thing that is starting to annoy me is people claiming a 53% shooter from the field was "inefficient". Are you kidding me? Does the fact that Dream had a sub-par PO from the line matter more than his overall dominance? I don't think so, not when he still shot FT better than Shaq ever has

  12. Neil Paine Says:

    That's right, I forgot how subjective it was to create rational models based on evidence. So basically, you want to tweak the method until it produces the result you want to see, is that it? Are you sure you know how science works?

  13. AYC Says:

    You're using a straw-man argument by trying to portray me as a flat-earther; but as I said in my last post, my opinion is based on objective stats. I think a 33.0 ppg scorer on 53% shooting is a better offensive player than a 20.5 ppg scorer (on 48% shooting) from the same team. Is that irrational?

    Science is not monolithic; different scientists come up with different theories, and often disagree with each other vehemently. You remind me of the economists who worshipped EMH even as the economy collapsed...

  14. AYC Says:

    PS I do like the results produced by defensive WS; even though DRob rates ahead of Hakeem, DWS is by far the best stat I've seen for measuring that side of the ball. Unlike OWS, there are only acouple head-scratchers for me aon the DWS list (Bird is overrated, GP underrated)

  15. Jason J Says:

    Neil - I understand that on a large enough scale those types of stat discrepancies even out, but I wonder if there aren't exceptions (I had this conversation with Dave Berri re: PAWS once as well).

    Does a guy like Horace Grant give his teammates' better stats? He helps them win games, no doubt. But he's not a great passer. He doesn't draw help attention. He spaces the floor, but he's not a Robert Horry where you absolutely can't leave him on the perimeter, and he's not a Shaq where you can't help off him around the rim. So if Pippen or Jordan or Penny or Kobe drove to the paint, and Grant was there, would he in any way make it easier for them to score? He would grab an offensive rebound if they missed, but that goes back to my Clyde / Hakeem example.

    He's an absolute beast at taking advantage of every instance where his teammates create opportunities. When his man does rotate because he's not Shaq or Horry, he gets that offensive board or hits that 16 foot jumper. Which is exactly what a team needs but not necessarily going to make a teammate's metrics pop, especially given the paltry importance that is placed on the assist.

    I just wonder over the course of a career if he gives as many opportunities to amass stats to others as he receives from them. Of course the simple fact that he's low usage generally gives opportunities to others, but you know what I mean. It's not an important question, just a question.

    And I didn't mean to imply that I actually thought the Clyde / Dream dynamic was such that Hakeem's presence dramatically changed Clyde's efficiency. I actually think of all the Rockets that year, Drexler was probably the least impacted by Olajuwon (or maybe Cassell). I just thought it should be considered.

  16. AYC Says:

    "What you said about OPS+ is not how science works. You can't just say, "these results don't match what I expect/want, so I'm dismissing them." Otherwise, we'd still think a flat Earth was at the center of the universe."

    One last thought on this matter; science is based on experimentation, the purpose of which is to provide falsifiable results for a givern theory. So results do matter, and odd results may indicate a methodological shortcoming. And advanced stats (of any kind) have no predictive value (like EMH) so they aren't falsifiable. So there's no way to show that your methodology is actually the best way to interpret stats

  17. Neil Paine Says:

    That statement is completely, 100% untrue. Sabermetrics/APBRmetrics are absolutely falsifiable, they absolutely create testable hypotheses, and their practices absolutely conform to the scientific method. What do you think Hypothesis Testing is?