Patrick Minton usually writes on his blog over at The NBA Geek. Today he brings us a familiar story about how NBA Decision makers think.
Last week, the Los Angeles Lakers attempted to trade Lamar Odom and Pau Gasol for Chris Paul (a third team was involved, but this was the trade from the Laker’s viewpoint). Since that trade was vetoed, the ”other” Los Angeles team has reportedly been trying to acquire Chris Paul. The trade has (again, reportedly) reached an impasse because the Clippers are willing to part with only two of the following three pieces/players: Eric Gordon, Eric Bledsoe and/or Minnesota’s first round pick.
In these two stories, we’re seeing the classic story play out. It’s a story we repeat on the Wages of Wins a lot:
- Decision makers consistently undervalue efficient scoring and net possessions (i.e. rebounding and “not turning the ball over”)
- Decision makers overvalue scoring totals
- Decision makers overvalue draft picks
- Decision makers tend to ignore the short supply of tall people (or perhaps they just wish it didn’t exist, so they pretend it’s not a problem)
The last point is particularly important. One generally has to be about 6’8″ or taller to be able to play power forward or center in the NBA. What most people don’t seem to be aware of is how exceedingly rare this is. The average American male is about 5’10″. A person 6’8″ tall is somewhere between 3 and 4 standard deviations from the mean. What this means is that there are probably less than 100,000 6’8″ men in the entire US, and with each inch this decreases exponentially; there are probably only about 3-4,000 American men that are at least 6’10″, and fewer than 50 are 7’0″ or taller (statistics quoted here). And I don’t need to explain that only a tiny fraction of those men have the athletic skill necessary to play basketball at all, and an even tinier fraction will have enough skill to play professional ball. There is a reason that NBA scouts love to say that “You can’t teach a guy how to be tall.”
The upshot of this is that finding a 6’4″ player that shoots the ball very efficiently and doesn’t turn the ball over may not be easy, but it is vastly more difficult to find a 6’10″ person that fits that description, and finding a 7’0″ player that skilled is (statistically speaking) a once-in-a-lifetime event. Dre brought this up last weak, but these numbers demonstrate that trading both Odom and Gasol for Chris Paul was probably not a “fair deal” for the Lakers (and yes, this means that Dan Gilbert’s whine about the unfairness of it all is unintentionally ironic).
The reverse of this, of course, is that the Clippers are being highly irrational by balking at trading two guards and a draft pick for Chris Paul. There are three reasons that this confuses me. First, neither player is tall. There are plenty of wing players on the free agency market (or available for trade) every year. It makes no sense to treat either player as a precious commodity. Second, Eric Gordon is probably going to get paid a lot of money soon. And that leads me to my third point: neither player is a particularly good player.
The following table shows the production of Eric Gordon and Eric Bledsoe, along with the average players at their position in 2010-11 (note, all stats are per 48 minutes, and are from the comparison engine at my site The NBA Geek, with the exception of WP48, which I took from the Wins Produced 2011 section of this blog, because my site hasn’t updated the formula yet, but you can read up on it here!):
| WP48 | PTS | REB | AST | TO | BLK | STL | PF | |
| Bledsoe | .006 | 14.2 | 5.8 | 7.5 | 5.1 | 0.7 | 2.4 | 3.4 |
| Average PG | .100 | 19.8 | 4.6 | 8.6 | 3.5 | 0.2 | 1.6 | 3.3 |
| Gordon | .110 | 28.3 | 3.7 | 5.5 | 3.4 | 0.4 | 1.6 | 2.6 |
| Average SG | .100 | 21.1 | 5.1 | 4.0 | 2.3 | 0.4 | 1.5 | 3.2 |
| FG% | 2FG% | 3FG% | FT% | eFG% | TS% | FTA | |
| Bledsoe | 42.4% | 47.0% | 27.6% | 74.4% | 45.7% | 49.9% | 3.5 |
| Average PG | 43.2% | 47.7% | 35.6% | 82.5% | 47.8% | 53.2% | 4.8 |
| Gordon | 45.0% | 48.8% | 36.4% | 82.5% | 50.6% | 56.6% | 7.9 |
| Average SG | 44.0% | 48.2% | 36.3% | 80.1% | 49.4% | 54.5% | 4.6 |
As we can see, Gordon was above average in assists, personal fouls, getting to the line (which is a consequence of the fact that he shoots a lot), and scoring points (and again, this was not because of his efficiency, which was average, but because he shoots a lot). He was below average in rebounding and turnovers. Bledsoe was below average in shooting efficiency, getting to the line, assists, turnovers (badly so) and scoring points (this latter is actually a good thing, if he shot more at this efficiency he’d be even worse). He was above average only in steals, rebounds and blocks, but didn’t excel in any of them. Thus, neither player posted an exceptional WP48, and Bledsoe was nowhere near average.
Now let’s take a look at Chris Paul:
| WP48 | PTS | REB | AST | TO | BLK | STL | PF | |
| Paul | .375 | 21.1 | 5.4 | 13.0 | 2.9 | 0.1 | 3.1 | 3.3 |
| Average PG | .100 | 19.8 | 4.6 | 8.6 | 3.5 | 0.2 | 1.6 | 3.3 |
Shooting comparison
| FG% | 2FG% | 3FG% | FT% | eFG% | TS% | FTA | |
| Paul | 46.3% | 48.2% | 38.8% | 87.8% | 50.2% | 57.8% | 6.4 |
| Average PG | 43.2% | 47.7% | 35.6% | 82.5% | 47.8% | 53.2% | 4.8 |
In contrast to Eric Gordon, my opinion of Chris Paul won’t surprise any readers: he was really, really good. He was above average in every category but blocks and fouls, in many spectacularly so (assists, steals, turnovers). He is, quite simply, one of the top 5 players in the league.
Finally, there’s the draft pick. Arturo has broken down the draft before. Benjamin Morris has also written great stuff. The upshot is that if it isn’t the overall #1 pick, it’s a bit of a crapshoot. And although Minnesota was terrible, and likely to be so again, it would be foolish to rely on the pick becoming the #1 pick in the draft. As such, holding on to it as if it were a precious commodity is foolish; one assembles draft picks precisely so that one can use them to nab superstar players! Why does it matter if you draft the superstar or you trade the pick for one? It’s the proverbial “two in the bush” fallacy to cling to this pick.
So revisiting: the Clippers don’t want to trade Bledsoe, Gordon, and Minnesota’s first pick (and filler) for Chris Paul (who is a superstar), because Bledsoe “might become a star” and that pick “might become a star”. And presumably because Gordon scores a lot (but just about any NBA guard who takes 17 shots a game would, too). A better solution might be to trade for Paul and be happy with winning. If the Clippers want higher scoring totals they could just try having Chris Paul and Blake Griffin shoot more.
-Patrick
I love the WP48 metric for comparing players, but I think there is a need to better examine the circumstances involving these players. The potential of rookie guards (especially PGs) tends to be undervalued in WP48. Substantial WP48 increases for young guards within a year or two are not uncommon. Now before I give you examples of big name players, know that I am certainly not expecting Bledsoe to become a star, but definitely an above average producer.
Many guards in the upper echelon of Wins Produced had humble beginnings:
Chauncey Billups, 2000: -.03, 2001: .067, 2002: .149
Billups continued to improve, and his streak of productive seasons is still running
Baron Davis, 2000: .067, 2001: .172
Deron Williams, 2006: .023, 2007: .13, 2008: .213
Derrick Rose, 2009: .087, 2010: .09, 2011: .161
Keeping in mind that the players mentioned above were all high draft picks, one must observe that WP48 undervalues potential for young point guards. If you exclusively use WP48 to measure a player, John Wall’s .068 puts him at the same level as his former teammate Bledsoe (.06).
Measuring Gordon’s productivity using Gordon’s season numbers from last year as a whole is a bit deceiving as his efficiency took a big hit after his wrist injury in January. During the beginning of last season, Gordon made great improvements in making his game more efficient. He shot at a higher percentage and got to the free throw line at a higher rate. Assuming his wrist injury has healed 100% as he says it has, his pre-injury stats are a better predictive measure of his productivity. I wish I had his pre-injury WP48, but the difference in his season before and after the injury are notable with a glance at split statistics.
One last tidbit I would like to add is that CP3′s knee issues have the potential to substantially handicap his team talent-wise, as well as their cap flexibility. Say the Clippers traded all the pieces asked for by the Hornets, CP3 and Blake have a good few productive months as a dominant duo. CP3 signs a four-year max contract extension and soon after his knee needs operation. CP3, already in decline for the last couple years, loses a lot of his productivity. Blake considers the marginal talent left on the Clippers and decides to sign elsewhere. I know this is all speculation, but the Clippers could lose everything they have been building to gain relevance.
http://www.csnne.com/basketball-boston-celtics/news/Celtics-concerned-about-Pauls-knee?blockID=603168&feedID=3945
Joey,
I don’t disagree. But I’ll note that we don’t “undervalue” potential at all; it’s more accurate to say that WP48 ignores it completely. In other words, as soon as you can predict what factors will indicate whether a player will make a giant leap from one year to the next, we can have a discussion about how to put that into WP48, but until then, “potential” might as well be random (you forgot Kevin Durant in your list, by the way).
I’ll note that for every example you give of players who went from bad to good around their third year, I can cite many that either remained terrible or who improved only very marginally.
So my point still stands: why would you cling so tightly to a player who is not good now, who *might* become good later, when you can trade them for a 26-year old who you already know is not just good, but truly great!? Again, you’re playing the two-in-the-bush game when you could just field a basketball team RIGHT NOW that wins 50 games (of a 66 game season). You are essentially saying “I don’t want to give up this player that might later become Chris Paul for Chris Paul.”
I will also point out, for about the thousandth time, that Chris Paul will not sign an extension ever, under any circumstances, for financial reasons. See http://www.thenbageek.com/articles/paul-or-howard-won-t-sign-an-extension
Even if he wants to stay with the team, he’ll opt out and re-sign instead, as it nets him about $50 million more dollars.
It’s possible if he got injured that he suddenly might be willing to sign an extension (because his value on the market would go down), but in that case there is nothing forcing the team to give him one.
So if I understand the league’s position, trading Chris Paul for the two best players on the Lakers isn’t good enough, but trading him for a bunch of random guys and a couple rookie question marks – to a Clippers team that gets to keep their two best players – is a great deal?
Charles – I think they might actually be right if they’re goal is to get some sucker to buy the Hornets. I’m sure Stern would rather be selling limitless potential than a couple years of .500 ball followed by a lot of uncertainty.
Shawn,
That may be the goal, but as I have stated many times, and as Arturo has pointed out on this blog, the only reason that the NBA is having trouble finding a buyer is simple: New Orleans can’t support an NBA team profitably. There just isn’t enough discretionary income in the community to support one.
So, my guess is that any potential buyer will give two or three rat’s asses about the players under contract, and will put enormous value on whether or not he/she is guaranteed the permission to move the team from New Orleans to some other, more profitable location. My guess is that the NBA is reluctant to guarantee this, and as long as they maintain this stance, they’re going to have trouble finding a buyer.
Congratulations! You clearly made a good case because Clippers have just agreed to this trade ;-)
Point well taken, that there is a shortage in good tall players… However, referring to population statistics is not that helpful. Maybe you should count 7’0″ players in the NBA (I read on answers.com that in 2008 there have been 40 players 7’). And the number of 6’8″ players is much higher given that the average height in the NBA is about 6’7″. If you remove the guards from the statistics you are probably averaging 6’11″.
I read the article again, and it seams that your main point is, that big player are from much worse quality than small players… That is probably true, but at least you can train them to get some skill :)
btw. in that context I would wonder, if big players produce less wins than small ones, and whether there are only a couple of PF/C how are performing well in your statistics.
Why do you list Gordon’s WP48 as .011 when the Wins Produced page has him at .11? That’s a pretty significant difference. If Gordon plays 3000 minutes it’s the difference between 1 win produced and 7. It doesn’t make Gordon a star but it sure changes the rationale for throwing him in to this trade.
The Clippers obviously decided you are right, a point I’m not necessarily trying to debate the point but the article clearly understates Gordon’s actual value.
Paulmuell,
Your first post displays a pretty depressing lack of understanding of statistics. The standard deviation of height in the NBA is not going to be anywhere in the same universe as the standard deviation of height in the general population, for the obvious reason of selection bias. The general population is applicable because we are talking about the overall short supply of tall people. Just because 7’0″ men are more common in the NBA than in the general population isn’t going to magically make more 7’0″ men appear on earth every year.
I also very much doubt there were 40 7 footers in the NBA in 2008. More likely 40 6’10″ guys in big shoes.
Josh,
Wow, you’re right. You know as I was typing this I was thinking “wow the new WP48 calcs really ****ed over EG” Because he was .069 in my database, and his stats are VERY average across the board.
Big typo on my part, I’m fixing the text. Thanks for the HU.
What a win for the Clips!
Kaman (negative), Gordon (average), Al-Farouq Aminu (zero) for the best PG in the league (.309 Wp48) PLUS les salary (2 Million LESS).
Jordan, Griffin and Paul are all well above average, and the support cast of Diogu, Butler, Williams, Gomes, Bledsoe and Warren should be good enought to be, what, a .500 team Maybe slightly more?
If the Clips can trade Mo Williams, for a SG that is average, they’ll have a monster team. Depth is an issue, especially up front, but they really do look good, and superstars certainly are the hardest thing to get, and now the Clippers have 2.
Billups – I forgot Billups! He adds another average to above average player.
@ TheNBAGeek
It is not a lack of statistics, I just doubt that its relevant. If there are only 50 7″ people in the USA, but there are 40 in the NBA (just an assumption), why would I care how many there are in the overall population??? I understand, that it is theoretical difficult to find new big man, but the NBA was pretty good in finding them in the past. And I don’t see why that would change in the future.
More importantly, the hypothesis that size is important and scarce should show up in your wins produced statistic. If there is a shortage in big qualified man (hence PF/C), than there should be a couple of super effective PF/C in the NBA (your one in a lifetime guys). I count 40 PF/C in your top 100 which is exactly the share they should have. And they are fairly distributed.
So your measure does not suggest a shortage of big man in the NBA (or that the shortage is relevant)
That is what I don’t understand about the argument. If you take your measure serious, there is no reason to bring the size into the argument. Either they produce the wins or not.
” why would I care how many there are in the overall population???”
Because, sir, that’s the number that determines supply. Supply and Demand determine PRICE.
This is the reason that an average big man free agent costs so much money.
And note that there are nowhere near 40 7 footers in the NBA today, but that isn’t the relevant number. The question is how many 7 footers there are that shoot efficiently, rebound well, and don’t turn the ball over. There are, like, THREE. And this scarcity of big men has been the case in the NBA for decades.
> The question is how many 7 footers there are that shoot efficiently, rebound well, and don’t turn the ball over. There are, like, THREE.
I get that height is value, because centers have a much greater standard deviation (meaning the bad are much worse than the worst SGs), but what an NBA team needs, ideally, is to have marginal value at every position, and massive marginal value somewhere. But short of that, you want to have maximum marginal value SOMEWHERE, irrespective of how many poor players you get stuck surrounding the star with.
As an example, the two man units of Chris Paul (.309) and Robin Lopez (-.096) is better than an average center and point guard (.100 each) – not by a lot (.309 + -.096 is .215 vs .200) – but Lopez was horrifically bad last year.
Paul is 3 times as good as an average player, and players like that are near impossible to find – as impossible as finding 7 footers. Players between .000 and .075 are a dime a dozen, so any trade that gets a .300 player is a golden trade, irrespective of the position they play, and then it comes down to finding cheap role players who can produce.
Wait wait wait — you concede that star big men are near impossible to get, then defend the trade because Paul is 3x better than the average guard? Are you trolling?
Why not keep Pau (who is 3x better than the average PF) and Odom (who is 2x better than an average PF and even better as an SF) and pair them both with an average PG? You know, the kind that grow on trees in the NBA?
How is pairing a very expensive PG who’s 3x better than average with an (expensive) average big man better?
> Wait wait wait — you concede that star big men are near impossible to get,
I concede MORE THAN that – I conceded that ANY star player is near impossible to get. Does that help?
> Why not keep Pau (who is 3x better than the average PF) and Odom (who is 2x better than an average PF and even better as an SF)
Ah, OK, you are stuck on the LAKERS trade, and we aren’t discussing the relative merits of players. I missed that part, so apologies.
That wasn’t a great trade for the Lakers, no. I don’t think anyone thought it was, did they? I can’t see how trading Odom (13th in WP48) and Pau Gasol (6th) for number 1 makes sense, no. Kobe for Chris Paul straight up would’ve been a fascinating test of the mettle of the NBA, though…
Anyway, your point seems to hinge on Big Men, and especially 7 footers, having far more value than little men. In other words, you think D12 is better than Paul, even if Paul has a better WP48, because there is more chance of an signing an average PG than an average Center, and the cost of tall players is higher (in dollars paid) . Is that summing your position up well?
I’m not sure how to respond to that. I think D12 is probably the first player anyone should choose if the NBA was a fantasy league, where everyone was draftable every year, for the very reasons you gave. But I’m not sure that one can make the blanket argument that it always holds that a 7 footer is better. Who would go second in such a draft – a non-D12 center or Lebron?
And what about, say, Marcin Gortat. Where would he rate – as a .176 WP48 center – vs, say, Manu Ginobili as a .204 SG. Who would you rather have?
That is the real question – how much is height worth when there is a clear difference in production? That, and doesn’t the team you have matter? Paul or D12 for the Clippers, and why?
Yes, I’d rather have a .176 center than a .204 SG. The reason is that you can always find good SGs on the market that the NBA as a whole does not appreciate. A classic example is Chicago bitching about their problems at shooting guard, even though a) they had a perfectly good one in Thabo and traded him to OKC and b) they had a perfectly good one in Ronnie Brewer, but they are replacing him with the (terrible) Rip Hamilton.
Then there’s MIA grumbling about Mike Miller, Aaron Afflalo STILL unsigned after bad players like Butler, Crawford, Barea, etc are grabbed up by one GM after another. (FWIW if I were Denver I wouldn’t rush to sign him either, until a different GM forces you to match a bid, but my point is that somebody should have done that a week ago).
Now, name a 6’10″+ guy with a WP48 of .175+ from the last ten years who had to sign cheaply because nobody wanted him.
@theNBAGeek
I crunched the numbers for the 2010/2011 season.
There have been 42 7 footers in the roosters of the NBA teams. However, many of them were actually not playing, or only limited minutes. Only 23 of them played at least 500 minutes. So I guess you are right there.
However, if you don’t look at size, but at the relevant positions (PF/C), you can see almost no difference in the Salary or WP distribution in comparison to the rest of the NBA.
The few large talents seam not to effect the distribution at the upper end at all. Nevertheless, around the 15 WP mark, there is a small peak of 7 footers, which might support your theory.
http://www.flickr.com/photos/72212715@N05/sets/72157628444508873
Just to be clear, I don’t doubt, that it is extremely rare to have 7 footers with good ball handling even within the group of NBA players. I just think you blew that out of proportion with your 6 SD away from the mean thing. In any case the price is not just determined by supply, but also by demand. So if these super rare people don’t outperform their smaller competitors, they won’t get the money for their rarity.
If you compare the salary for the upper half of the relevant 7 footer (+500min) with the relevant smaller players, you see, that they earn more than their smaller counterparts until the 90th percentile.
50% 60% 70% 80% 90% 100%
big players
4,050,499 5,587,493 7,540,000 11,480,000 13,480,000 17,823,000
other players
4,000,000 5,000,000 6,883,800 9,300,000 13,200,000 24,806,250
Furthermore, the WP are worse for the big players; thus, the “average” 7 footers are indeed overpaid.
50% 60% 70% 80% 90% 100%
big players
0.990 1.744 4.744 7.020 8.524 14.810
other players
3.230 4.140 5.425 7.420 9.170 18.450
Given, that this changes in the top group, makes Gasol indeed more valuable if you were going to replace him with another 7 footer.
I’ll re-iterate my belief (which is of course hard to prove/test) that a large percentage of those players probably add an inch (or two). It’s a widely-held assumption in the NBA that most teams pad their players’ heights for marketing reasons.
I also cannot resist commenting on this: “So if these super rare people don’t outperform their smaller competitors, they won’t get the money for their rarity.”
Then you go on to explain how the average 7 footer is overpaid, and that big men are paid more than guards until the 90th percentile.
The facts clearly demonstrate that being tall does, in fact, get you paid, even if you do not outperform your smaller competitors.
Of course, in the very top performance levels, the reason they aren’t overpaid (more than smaller “great” players) is because of the max salary rule. If you honestly believe that Chris Paul and Dwight Howard would earn the same salary if there were no max salary, then I have a 2-bedroom house here in Seattle I’d like to sell you for half a million.
I totally agree with everything you that in your last two comments (now). However, I am not sure what you mean with the Howard Paul comparison. If you mean that it would be rational to pay Howard more, I would disagree assuming WP is a perfect measure for the performance of a player.
Again, the WP distribution for PF/C is almost identical to that of the other group, as is the salary distribution. Now Assuming that the club owners would be rational, it is hard to claim that a tall talented C with WP 15 should be much more important than a PG with WP 15.
“If you mean that it would be rational to pay Howard more, I would disagree assuming WP is a perfect measure for the performance of a player.”
It would be completely irrational to play a good guard as much as a good center. Why? Because there are more good guards in existence. This is supply and demand. This is why average big men are much more expensive than average guards.
This is super standard economics and I’m having a hard time believing you don’t get it. The fact that the proportion of big men in the NBA is greater than the general population does not, in any way, increase the supply of big men (and in fact, this is the core problem: each team needs a few big men, but there are not enough talented big men in existence. Demand outstrips supply, price goes up. It’s that simple).
Your argument might make sense if it were a valid (competitive) strategy to field 5 guards. Then, we’d just rank players by WP48 and those with the highest would get the most money, regardless of height. But that ISN’T a valid strategy. If Paul played Center his WP48 would be negative. If I tried to field a team of 5 guys 6’5″ or shorter, I’d get crushed (although it would be fun to watch a team of Paul, Wade, Rose, Williams, and Westbrook, they’d get destroyed).
“Then, we’d just rank players by WP48 and those with the highest would get the most money, regardless of height. But that ISN’T a valid strategy.”
No, I would suggest to do that for each position, but “independent” of size.
“It would be completely irrational to play a good guard as much as a good center. Why? Because there are more good guards in existence.”
I thought this should show up in the distribution of WP as well. However, I read the FAQ again and saw that the measure is somehow normalized for each position. So I have to admit that you are probably right again…
To be clear here, everyone that is playing in the NBA is a rare physical talent. Yes, to play center in the NBA you might need, say, 4 sigma height – but you only need 1 sigma athleticism. The guys playing shooting guard might only strictly need one sigma of height, but they absolutely need to be a 4 sigma athlete to stand out. You’re paying for rare talent at every position; and that should be obvious when you think about it.
While I think there are good statistical arguments for paying more for a big man than a guard (based on replacement level production), I don’t think any of that is actually driving NBA salaries. I think it does come down to the short supply of tall people, but in a somewhat different light. People are remarkably good at bullshitting themselves, and executives are very good at convincing themselves that there are a lot of high impact perimeter players; every rookie guard has a lot of potential and can be a star, even though only a handful of them ever will be.
It is very easy to overlook performance, in terms of shooting percentage, or taking care of the ball, or what have you, when it comes time to evaluate whether or not someone is actually a good guard.
It is very difficult to overlook whether or not someone is tall.
Height is easy to measure, and thus gets paid for. Actual productivity, as the story goes, is non-trivial to measure (and even when measured, is remarkably difficult to convince people of the accuracy of said measurement), and thus is not particularly well compensated.
Again, you are misunderstanding basic statistics if you think 4-sigma athleticism amongst 6’5″ individuals is more rare (or anywhere close to as rare) as 1- or 2-sigma athleticism amongst 6’10″+ individuals.
Without any other assumptions, you would assume +4 sigma athleticism alongside +1 sigma height would have a similar rarity to +4 sigma height with +1 sigma athleticism. That’s just simple math; it’s a totally symmetric claim. You can think of height and athleticism forming a 2 dimensional probability distribution for the overall population (fixing all other variables); professional level athletes are skimmed off the high edge of athleticism, and in the case of the NBA, of height.
Of course the two aren’t going to be totally uncorrelated (though you would expect the correlation to be positive, and I would guess highly non-linear), but you might as well presume they are for the toy model, it doesn’t change anything if there is a skew. It probably isn’t Gaussian either; I’d expect a higher 4th moment, but again, it changes little unless it really warps the shape.
The point being, the two are equally scarce.
The argument I’m making is that it is very, very difficult to distinguish a +1 sigma height / +4 sigma athleticism from a +1 sigma height / +3 sigma athleticism. Athleticism has a lot of intangibles, and these things are very hard to measure when you get far from the mean.
But it is very easy to distinguish +4 sigma height / +1 sigma athleticism from +3 sigma height / +1 sigma athleticism. You just stand them on their heels and use a ruler.
I would wager that +4 height / +1 athleticism is much, much more common in the NBA than +1 height / +4 athleticism. I base this on two ideas. First, that height is easier to objectively measure than athleticism, so general managers do a better job identifying the tallest athletes than the most talented athletes. Second, there are many other professional sports, and all of them poach from the most talented athlete pool – they all want +1 height / +4 athleticism guys – but *all* of the +4 height / +1 athleticism guys are basketball players; and all the +5 height / +1 athleticism guys are in the NBA.
I like the thought that the NBA hoards all the height while other sports peel offany of the exceptional athletes. BUT, Paul isn’t an exceptional athlete by NBA standards. He’s not a leaper, not exceptionally fast or quick by NBA standards. Like Steve Nash his exceptionality is his skill level. A third dimension that confuses your debate.
IMO, one of the reasons teams seem to “pay up” for good big men is that there is general feeling among NBA teams that you practically NEED one to compete for a title, but you can get away with competent players at any other position if the rest of the team is very good.
Other than the Bulls (who had superman), most of the NBA champions had terrific or even a dominant big man (Russell, Chamberlain, Reed, Kareem, Parish, Shaq, Walton, Duncan/Robinson, Wallace, Chandler, Hakeem etc..). So if a team is in building mode and has an opportunity to get a good big man, they are going to bid harder for him than just about any other position.