Andres Alvarez graduated from Colorado State University with an M.S. in Computer Science. He is currently a GIS Analyst who likes to work on geeky stat side projects for fun, including the automated Wins Produced website (which we all appreciate). He has been a Colorado resident his entire life and a Nuggets fan for most of it.
Last year the Denver Nuggets were two bad inbounds passes away from the finals. Many believed we were on track for a repeat performance and maybe one trade away from being crowned champions. This year the Nuggets regressed to a first round exit, raising a few interesting theories.
The first popular theory is that Carmelo needs help. This was accentuated by the fact that Melo said he needed help right before the Nuggets were bumped by the Jazz. The Wages of Win’s Journal, a typical detractor of Melo, stood up and pointed out that he was right. At least if you were just counting this year’s playoffs. So we need to get Carmelo help, but where?
Another popular theory is the Nuggets needed George Karl’s leadership. Last year with him on the bench, the Nuggets made it to the Western Conference Finals. This year they won the division with him at the helm, but he had to step down for health reasons before the playoffs. The theory is that George Karl is a huge part of their success and his absence hurt them in the playoffs.
Well Melo’s help can be addressed in a very Wizard of Oz way. It was there all along! If only Melo had clicked his heals together three times and looked to his bench, maybe the team would have overcome their problems both this year and last. As for George Karl’s leadership, the answer is not as happy. In fact, maybe it was never there to begin with.

The answer to both Melo’s Help and Karl’s leadership starts by looking at minute allocation. Looking at Table 1 we see that Denver had 6 players with at least 1,986 minutes this year. On the bench were three above average players in Andersen, Lawson, and Carter. Andersen played much better than starters Martin and Nene. And in the backcourt, Smith and Afflalo both posted below average WP48 for their 2000+ minutes, while two above average guards in Carter and Lawson sat on the bench. To be fair, Lawson did have some injury troubles. Even a slightly below average Balkman, though, would have been a welcome change to an abysmal J.R. Smith (who apparently played at SF part of the time).
What was Karl’s leadership plan in 2010? He actually followed a very simple formula for his minute assignment. If you were paid more than $5 million you got at least 2,000 minutes of play. After that your minutes were assigned based on the coach’s assessment of you. In this case Afflalo got more minutes for being a “defensive presence”, Andersen for being an “energy player” and Balkman was put in the dog house for not learning the team’s offensive schemes.
What about 2009? Surely Karl must have had the Nuggets stocked full of leadership to get so far. Perhaps, but he still left a lot of Melo’s help on the bench. Looking at Table 2, we notice that 7 players played 1,750 minutes or more. Andersen, though, played fewer minutes than Nene, Martin and Kleiza. Not only that, Renaldo Balkman played a meager number of minutes despite having the best WP48 of all the players on the team! Finally JR Smith played well last year, but we notice he split a lot of his minutes with Dahntay Jones, whose net contribution to the Nuggets wins was zero.
Essentially, Karl’s method in 2008-09 was the same as we saw in 2009-10. If you were paid 4.985 million dollars or more, you got more than 2,000 minutes. After that you were again assigned minutes based on the coach’s assessment of you; Kleiza was an “offensive threat off the bench”, Carter was a “smart veteran presence”, Dantay Jones was a “defensive presence”, Andersen was still an “energy player” and Balkman had a bad attitude limiting his minutes.
Karl’s leadership seemed to amount to two things. First and foremost was pay. In an almost stubborn attitude of “We paid for it, we may as well use it”, he heavily relied on the second or third best option for at least two positions in both 2009 and 2010. His next method was if the player had a good role player term. It was maddening as a Nuggets fan to see Balkman, a WP48 powerhouse, benched for not being an “offensive threat”; while seeing Dahntay Jones and Aaron Afflalo get minutes for being “defensive presences”. What is worse is that Karl’s nice coaching terms for his bench player’s minutes did not actually seem to correlate with their performance.
So despite Melo’s help being there all along, it is possible that Karl’s leadership stopped it from seeing the light of day. Dantley apparently stuck to this plan and potentially hurt the Nuggets. However, the West was crazy this year with only Portland – because of significant injuries — actually being an easy first round opponent. It is impossible to know if the Nuggets fortunes would have changed with a better record.
In closing there is some light at the end of the tunnel. Carmelo may seek his help elsewhere if the Nuggets do not improve this upcoming season (and Melo is really doesn’t produce enough to justify his pay). A healthy Portland, OKC and LAL could ensure this. Kenyon Martin’s contract also comes off the books at the end of the year. The Nuggets can therefore potentially free up cap room for next summer or get a good deal from a team looking to dump salary.
All of this, though, might require Coach Karl to allocate minutes differently. At least that’s what I hope as a man behind the curtain.
Please note the author does not hold any ill will towards George Karl, and wishes him a full recovery.
- Andres Alvarez
The WoW Journal Comments Policy
Andres,
First off, your page rocks. Is your argument that if Karl had a rational GM he’d be a great coach;-)
Seriously, we seem to see Pay=Minutes way too often in the league.The best lineup for the nuggets based on talent would be:
Chris Andersen (PF)
Chauncey Billups (SG)
Nene Hilario (C)
Ty Lawson (PG)
Carmelo Anthony (SF)
with melo being the worst player on the floor according to WP48.
Arturo,
Actually Warkentien has been amazing as a GM. He picked up Andersen, Billups, Lawson and Balkman ( a heck of a line up). Really Karl has had an odd choice of favorites, including Afflalo and Jones.
Frighteningly Warkentien’s name is being tossed around as the next Portland GM. They already have Miller and Camby. Their strategy seems to be to take good pieces the Nuggets let go. . .
A lot of cum hoc, ergo propter hoc here.
Does pay=minutes, or do minutes=pay?
For what it’s worth the Nuggets were a juggernaut at home and a weak sister on the road. Not sure what impact that may have had in the post-season, but it wasn’t consistent with other similarly seeded teams. What characteristics go into the making of a successful road team? Road records seem to separate the players from the pretenders.
Somehow paragraphs 7 and 8 were duplicated, the second instances should probably be edited out.
The question of sub-optimal minute allocation on teams that have a quantitative approach to finding players to employ has boggled me for a while. I’m sure Dean Oliver can demonstrate that the minute allocation on the Nuggets isn’t what it should be, but these people often don’t seem to have much sway when it comes to who plays from night to night. Adelman, McMillan, and Karl (the most immediate examples in my mind) all seem to be of more common mindsets than of their respective teams’ GMs, yet they often seem to be deferred to on matters of minute allocation, and end up undermining the good construction of their teams.
Thanks Shawn. Duplicate paragraphs tells us the editor doesn’t know what he is doing. Andres didn’t submit it that way.
Shawn Ryan,
Wasn’t Adelman coaching the Rockets when Ming and McGrady(both avg the most minutes) got hurt and then the team went on a 20 game win streak after struggling for a large part of the season.
Adelman also coached some extremely talented, underachieving teams in Portland. Bill Laimbeer claimed the Blazers made no adjustments from one half to the next during the finals.
Shawn Ryan,
Your point on minute allocation is interesting. The Nuggets GM has built a good team talent wise. But the players’s minute allocation by his coach (based on conventional wisdom- Yay!Points! anyone). I did a optimization sort (using the year end roster and assuming no injuries)
WinsP WinsP optimized Wins left on the table
POR 49.4 77.5 28.1
LAC 24.0 48.9 24.9
SAC 29.7 49.3 19.5
CHA 44.0 60.9 16.9
GSW 31.7 48.1 16.4
CHI 36.7 49.9 13.2
WAS 28.4 41.3 12.9
MIN 15.4 27.8 12.4
HOU 39.9 52.1 12.2
OKC 49.8 61.9 12.2
NYK 31.3 42.2 10.9
TOR 36.3 46.7 10.5
NOH 34.7 44.9 10.2
SAS 54.3 64.4 10.1
IND 33.1 42.7 9.7
BOS 50.5 59.7 9.2
DAL 48.4 57.4 9.0
NJN 16.5 25.0 8.5
MEM 36.5 45.0 8.5
DET 27.2 35.4 8.2
DEN 51.1 59.1 8.1
ORL 60.1 67.7 7.5
CLE 57.9 65.4 7.5
MIL 46.6 52.3 5.7
PHI 30.9 35.8 4.9
PHO 53.8 58.6 4.8
UTA 55.0 59.7 4.8
LAL 53.1 57.4 4.3
MIA 47.2 50.3 3.1
ATL 53.3 54.9 1.6
Most of these can be explained due to trades or injuries (and in Portland case the sort suggesting they play three centers :-)). Denver didn’t actually leave that much on the table.
Michael,
Excellent point! And in Latin no less. For this year and last I believe Pay was the driving force. However, the two definitely go hand in hand. Melo, Nene, Billups and Martin were all drafted top 10, got lots of minutes as rookies. Minutes + draft position = higher pay AND more minutes.
JR Smith was drafted lower, BUT got lots of minutes his rookie season. Higher pay(put not top 10 draft pay) AND more minutes. Balkman and Andersen were drafted lower AND played fewer minutes. Less pay, fewer minutes leads to fewer minutes.
Marparker,
Yes, he did coach over that stretch for the Rockets, but you have to understand that the Rockets really don’t have negative contributors like most teams do, so the damage he can do through improper management of minute allocation is limited. He did however play Kyle Lowry for 24.3 MPG, and Aaron Brooks for 35.6 MPG last season, which is clearly a mis-allocation.
Absolutely ace Arturo. Funny that Mike Brown is out of job considering it seems he’s done a very good job at assigning minutes. So all the Cavs can hope for is that they take on one of those rare coaches who can eek an improvement out of his players.
Arturo,
I’m working with the Rockets, so I’ll use them as an example. Like I alluded to in my follow-up to Marparker, Adelman played Aaron Brooks for 35.6 MPG. He played Kyle Lowry for 34.3 MPG. Brooks played all 82 games, while Lowry only played 68. If, only for the 68 games that Lowry played, the two players minutes would have been inverted, which would be very doable, the Rockets could have picked up 2 games by my calculation. And that’s just reallocating minutes for one position.
With the Nuggets, I know that Balkman, who has played significant minutes in previous years, and has, has until this year (in which he has played the fewest minutes since being drafted, a paltry 92, hardly a significant sample) has consistently been well above average in terms of WP48. Kleiza has been below average most of his career, yet gets more minutes. I’d be willing to wager that if you inverted their minutes, that (other things being equal) the Nuggets would pick up some wins.
Arturo,
Didn’t really mention it, but I was responding to your concluding paragraph. Really, if you’re leaving any wins on the table as a team, you’re leaving too many (wins = ticket sales = $, see Wages of Wins, Stanford Business Books (May 9, 2006)). And while your algorithm is interesting, I question its robustness, but also your conclusion from its results. Assuming it is perfect (for the sake of argument), I would say that it’s pretty damning of improper minute allocation by most teams, including the Nuggets. The fact that they are less backward than much of the rest of the league is not a compelling endorsement.
Shawn,
I feel Arturo is being the messenger here. A common theme on this site is that decision makers in the NBA(and other sports leagues) behave irrationally.
Arturo is showing something interesting. I wrote a harsh article of the Nuggets on their minute allocation. Arturo shows that actually they aren’t any where near the worst in the league.
Only 6 teams in the league are leaving fewer than 5 wins on the table. Now again this leaves out injury, etc. Still given the West was won by 5 wins, this is pretty frightening news.
I believe the WP48 minutes statistic to be seriously flawed. Take the concept that Carmelo is not Denver’s most productive player according to WP48: In any game of basketball, one player’s contribution is contingent upon his role on the team, who is on the floor when he is, and what type of treatment he receives from the opposition. How do you think the WP8 for the Nuggests would be impacted if these roles were reversed, say so that Renaldo Balkman or Kenyon Martin received the lions share of shots, usage, and the opposition’s defensive scheme was strategically built purely to foil his specific skill set. I think we need a means of measuring how beneficially impactfull a player is under these circumstances, i.e. how does player x perform in role of superstar and how are teh historical stats of his teammates impacted. Clearly, this is why we see certain players stats inflated when they are coupled with superstars who garner all of the defensive attention.
Hey Dre, nice article.
I agree that Arturo’s comment was interesting, and said as much. In fact, it inspired me to write 279 words of extra analysis. I appreciated his comment, and certainly wasn’t trying to attack him. I don’t know if I came off as snarky, or something, but that was not my intention.
Really, he commented on what I had said, and drew different conclusions, so I intended to offer a response, and to elaborate on my prior point with a concrete example based on the numbers that I’ve been working with, and I feel that I did that successfully.
Also, I’m not dismissing the optimization algorithm, I’m merely skeptical that it is robust enough to draw conclusions from, as all that is given is the output, and not the methodology, so I can’t agree that “Arturo shows that actually they aren’t any where near the worst in the league”. That may be the case, but I don’t believe that the model shows that, at the moment.
Finally, I’m treating this as an intellectual forum. Disagreement, in my mind does not equate to disrespect, and quite the contrary, I offer my views in the utmost respect. If I did not respect the commenters on this blog, then I wouldn’t waste my words, and I wouldn’t have offered to write for it. It is precisely because of the fact that I respect Arturo’s contribution to the discussion, and yours for that matter (better cover all my bases :P) that I chose to respond in such depth.
(Sorry for talking about you in the 3rd person Arturo. I do value your input, and certainly do not mean to imply otherwise.)
Let me chime in for a moment…
I really enjoy the fact there is extensive back and forth on these posts. When the sports economists meet in a few weeks I can assure you that we will not all agree. Good to see that happening here as well.
Shawn,
Arturo takes no offense :-) . I was trying to do a quick and dirty calculation to show that irrational minute allocation is the norm and not the exception in the NBA.
As for the method used, it was decidedly non-optimal:
1.Sort the players for each team using WP48 (ignoring those who played less than 400 minutes)
2.Sort the minutes assigned for each team
3. Multiply WP48 *Minutes /48 for the two ranked tables
4. Pivot and compare
I did not account for position or for actual final composition of the roster (it would take me a little longer than 10 minutes to do). Writing a robust optimization algorithm would be an interesting exercise and would provide some interesting insight. I’d rank players by position and look for historical samples for player playing less than 400 minutes. I’d also try to work in trades (roster configurations). Any other suggestions?
This analysis assumes WP48 to be an independent variable. It isn’t. It tries to be and it MAY be the closest thing one can construct to approximate an independent variable, but it isn’t one. Analysts must face the fact that everyone, all the time, acts irrationally. Perfect rational action would require the causes of all events to be known.
In essence, perfect rationality would let us predict the future. That seems to be rather difficult, in my estimation.
Arturo,
I think the main thing is that you have to have some mechanism for ensuring that the best players aren’t assigned 48 MPG. That part gets pretty dirty. For instance, Iverson was well known for averaging in the 40MPG range, but few players could play for that long, it would seem.
I would say that, in general, if a player is being consistently played more than 30 MPG, then whatever his MPG might logically be assumed to be that player’s ceiling, but then that says nothing for players who play fewer than 30 MPG, and really those are the players that this whole process is about anyway.
Perhaps you could take an average MPG for starters at each position (eliminating any outliers, such as starters who have to share a substantial number of minutes with a non-starter, etc.) and set that as the maximum number of minutes that any player can be allocated for that position (with the exception of players who have proven that they can play above average minutes).
Arturo, cont.
Also, if it’s robustness you seek, then historical WP48 would be important, e.g. I suppose your algorithm assigned Renaldo Balkman to 0 minutes because he didn’t make the minute total cut (400 min) this year, yet he has in each of his prior seasons.
BTW, I’m pretty certain that you’re right about irrational minute allocation being the norm. I think that those GMs do help the situation by providing fewer bad options for coaches to use, but it seems all the more tragic when a GM/stat dept. has found a bunch of gems who are working for peanuts, and then the coach doesn’t utilize them.
Arturo, cont.
And I don’t know how to codify this into an algorithm, but as I’m sure most readers of this blog are aware, it generally seems very beneficially to put players in the smallest position they are capable of playing. Rashard Lewis is obviously not playing the correct position because he is capable of playing SF. Perhaps this doesn’t happen often enough to worry about algorithmically, but it would seem that it would at least be an important caveat to keep in mind when looking at the output.
I will agree that coach Karl failed to allocate minutes efficiently. The nuggets best two lineups in terms of win % are (from 82games) :
Lawson-Smith-Melo-Andersen-Nene
Lawson-Afflalo-Smith-Andersen-Nene
Those two lineups are also top three in terms of +/-, yet they are 10 and 11 in terms of minutes played. Based on that, coach Karl deserves some blame but the Denver was still second in the west while he was coaching. So Im not sure how much blame he should get.
Given that the nuggets still lost in the first round where they had HCA, i don’t think it would have mattered what lineup he played during the season. I do think that the nuggets missed his leadership in the playoffs. The playoffs is more about matchups and adjustments and your best lineup during the season isn’t necessarily the one that should be playing major minutes. That’s where Dantley failed to make the correct adjustments.
Interestingly, Smith shows up in both of those lineups, yet, according to WP48, he is a below average player. Maybe Smith is another of those players where WP48 craps the bed.
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I think your view on this subject almost has to be correlated to your view on whether certain lineups work better than others because of the skill sets of the individual players.
Much as we all seem to agree that you can’t build a championship team with all great Cs or all great PGs, at a less extreme level coaches are trying to mix and match players while paying attention to their individual skill sets in order to get the greatest productivity from the whole.
For example, if a team has two above average players, but they have identical skills and weaknesses, he may start one and use the other off the bench instead of playing them together.
The assumption he is making (or drawing from practical experience in games or in practice etc… ) is that the combination of the two above average players will produce worse results than one above average and one average player because of some kind imbalance in the line up when the two of them are together.
When viewed from afar, it may seem like he mis-allocated their time, but perhaps not.
Arturo, I find your data quite interesting (a Laker fan), and would like to ask if you could somehow compare that data with how many minutes starters play on each team.
I know that the Lakers really taxed Gasol this season, and Kobe plays heavy minutes as well. So your data might actually show coaching tendencies (seeding or health?) and not coaching prowess.
Of course, if the team in question was at the bottom of your list and didn’t make the playoffs, that’s something else entirely…
Looks like there will need to be a “Does the Wizard have Kobe’s Help,” because these Lakers are getting killed and surprisingly, Kobe isn’t the problem.
Harold,
I think Phil is a basketball genius. The only real change in the numbers is that it assumes Bynum was healthier and suggests giving Shannon Brown Fisher’s minutes which might not be realistic.
I hope this renders well:
Name Position Minutes WP48 WinsP Minutes WinsP(optimized)
Pau Gasol PF:32% C:67% 2403 0.310 15.5 2835 18.3
Lamar Odom PF:100% 2585 0.279 15.0 2605 15.1
Andrew Bynum C:100% 1977 0.176 7.3 2585 9.5
Kobe Bryant SG:89% 2835 0.164 9.7 2403 8.2
Ron Artest SF:100% 2605 0.064 3.5 2227 3.0
Shannon Brown PG:15% SG:84% 1700 0.056 2.0 1977 2.3
Jordan Farmar PG:100% 1474 0.047 1.4 1700 1.7
Sasha Vujacic SF:100% 575 0.045 0.5 1474 1.4
Derek Fisher PG:100% 2227 0.010 0.5 581 0.1
Josh Powell PF:100% 581 -0.137 -1.7 575 -1.6
Luke Walton SF:88% PF:11% 272 0.017 0.1 355 0.1
Didier Ilunga-Mbenga C:100% 355 -0.028 -0.2 272 -0.2
Adam Morrison SF:100% 241 -0.095 -0.5 241 -0.5
Speaking of Adam Morrison, isn’t it ironic that he was one of the worst all-time WP48 players in his rookie season, hasn’t done much better since, and will most likely be out of the league once his contract ends, yet he could walk away with a championship ring this year!
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Best, most objective analysis I’ve seen. This is a problem thoughout the NBA. Balkman should have have been playing ahead of Smith any day
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