Over the past couple weeks in this space I have explored the shot tendencies of the traditional positions.  I’ve set out to find the players who don’t shoot like their designated positions by comparing their shot location distribution to the average shot location distribution of their conventional position.

I’ve found some pretty interesting results. Point guards, shooting guards, and small forwards have nearly indistinguishable average shot distributions.  PG Rajon Rondo shoots like a Center, PF Ersan Ilyasova shoots like a guard, and Dirk Nowitzki is in a class all in himself.  No, these aren’t earth-shattering discoveries, not subjectively at least.  Statistically maybe.

I think these were worthwhile exercises but I wasn’t fully satisfied with the method I used to look at the shot distributions.

Why? Look at the average shot distribution for a center in the table below:

What this tells us is that 6 percent of the average center’s shot distribution comes from beyond the arc.  Does this sound right to you? Does the typical center have a small 3-point game?  With all the stretching that goes on with today’s big men, it may seem as though 3-point shooting centers are on the rise.  Channing Frye, Brad Miller, Rasheed Wallace, Andrea Bargnani, and Mehmet Okur are conventionally considered centers but they make up just a small subset of the center position.  I’d venture to guess that half of the NBA’s centers shot as many NBA 3-pointers last year as you or I did: zero.  So why does this table tell us that the average center shot a healthy dose of threes last year?

What we’re dealing with is a skewed sample distribution.  Not in shot location sense of “distribution” but the skewed shape of the underlying data.

Say you’re hanging out with your five of your buddies when one of them decides to take a poll.  How many Justin Bieber songs have you listened to in the past 24 hours?, your buddy asks.  The five of you write down their answers on a sheet of paper and hand them to the Bieber-curious poll administrator (we’ll call him Sean).  You, Pat, Steve, and Matt confidently write down that they’ve listened to exactly zero Justin Bieber songs. But Sean? Sean loves Justin Bieber. He confesses that he has listened to 10 Justin Bieber songs.  Sean collects the answers, smiles, and makes his big announcement: “The average guy in this room listened to  not one, but TWO Justin Bieber songs in the past 24 hours. I knew it! I’m not the only one!”

You see what Sean did there? He added up all the total songs listened by the group (10) and divided by the number of members in the group (5).  But Sean’s obsession skews the distribution and the sample average (mean) misrepresents the general song tastes of the group.

In cases of skewed distributions, it’s better to look at the sample median rather than the sample average (mean) because medians are less sensitive to the extremes.  For those who skipped the mean, median, and mode portion of fourth grade, the median tells us the middle observation in a sample.

Back to basketball.  The typical center didn’t shoot 6 percent of his shots from downtown, just as the typical buddy didn’t listen to 2 Justin Bieber songs.  Twenty regular centers in the 41 person sample didn’t even take a 3-pointer last year, making the median 3-point share among centers last season 0.5% from Clippers center Chris Kaman. That’s an important tweak.

So I wanted to run this tweak for all the positions and illustrate their distributions. I decided to display the data in the form of a box plot, also known as a box and whisker plot.   These plots pack a ton of information in a nice tidy graph: the median value for the sample, the smallest value, the largest value, where the bulk of the observations fell, and, if they exist, outliers in the sample.

Let’s take a look at one here that illustrates the at rim shot distributions of each traditional position:

So here we have 5 box plots. The top of the box tells us where the 75th percentile observation lies and the bottom of the box tells us the 25th percentile observation.  The box therefore, represents where half the distribution lies. The line in the middle? That’s the median value. I would have displayed the average line to give you an idea how the two descriptive statistics differ but I didn’t want to confuse. You can see the average values in the table above.  The lines that stick out are the whiskers, detailing the maximum and the minimum of the sample.

So what do we learn? Centers have the widest range of at rim tastes, both in the box and the whiskers. You have Channing Frye with 10.9 percent share at the bottom and Joel Przybilla who never ventures away from the basket (94.0 percent of his shots were layups/dunks).  You don’t see that range in the other positions.  For centers, Brook Lopez represented the median value of 48 percent while the sample average was slightly lower at 46 percent.  We can confidently say that layups and dunks make up half the shots of a typical center.

The other positions are more tightly packed, indicating that centers are unique in their varied shot tastes. Or it’s the other way around: centers are the most heterogeneous position because their center label has the least to do with their playing style. Who’s the tallest guy on the court? He’s the center.

What’s also interesting is that positions descend in their taste for shots at the basket from center to shooting guard but point guards jump up a bit.  Why? This is just my take but point guards are usually the quickest on the court and run the offense, and therefore can get to high-percentage spots more often than their taller teammates.  It’s hard to get a layup when you don’t have the ball in your hands or the quickness to evade defenders.

You’ll notice an upper outlier for both small forwards (Gerald Wallace) and shooting guards (Ronnie Brewer). We should flag these guys as players who probably don’t fit their positional label since they certainly don’t shoot like it.

Let’s move on to “short” shots, the attempts that were less than ten feet from the basket but not layups or dunks.

Here we see that guards rarely get a shot off in this zone and shooting guards especially have a compact distribution.  The floater makes up most of the shots that a guard would take in this zone.  They rarely have the chance to take a set shot or a post up in the further away in the paint.  Also, the positional “shape” mirrors the last zone where the shot taste descends to shooting guards from centers, with point guards exhibiting a slight up-tick.

Let’s take a look at the mid-range area which is 10-15 feet from the basket.

Not much doing here. Only five players shot over 20 percent of their field goal attempts from this area last season (Elton Brand, Shaun Livingston, LaMarcus Aldridge, Dirk Nowitzki, and Rip Hamilton).  Moving on.

Long twos:

Note that centers have the widest distribution as well as the lowest median, while shooting guards have the tightest distribution and the highest median value.  Power forwards and shooting guards have similar medians but a larger number of power forwards make long twos a big part of their shot palette.  Power forwards don’t like to shoot threes but they love taking long twos.  Keeps them close for the rebound.

Pretty much all point guards feature a long two game.  The most long-two resistant point guard last year was Chris Duhon and even he took more than the typical center did. Gotta have that pull-up jumper to keep the defender honest off the dribble.  (FYI, one out of every five of Rondo’s shots are from the long two zone despite shooting just 33 percent from there).

Let’s glance beyond the arc:

This is what I expected. Most centers have no 3-point game to speak of but the statistical mean suggested that the typical center has shoots a three once every 19 shots.  Power forwards, too.

Most wings have at least 30 percent of their shots coming from beyond the arc. Not exactly mind-blowing but shooting guards exhibit a much more compact box than small forwards. What does this mean? Small forwards are a mixed bag when it comes to 3-point shooting. You have Shawn Marion who barely shoots threes and you have James Posey who loooves shooting from downtown.  Shooting guards are more tightly wound around the 30 percent median, but plenty of small forwards have little  propensity to launch from downtown.  In fact, half the small forwards shoot somewhere between 14 and 41 percent of their shots from beyond the arc.  That’s their “interquartile range” from top of the box to the bottom, in case you were wondering.  Mixed bag throughout.

In general, the wider the box, the more varied the shooters.  On the flipside, a compact box indicates that there’s not much variance in the bulk of the distribution.  The biggest interquartile range of the bunch? Centers at the rim. You can’t definitively say, “A typical center should shoot X amount at the rim” when the distribution is so dispersed.  This probably indicates that there are wide variety of center subtypes at the rim.  3-point shooters, too, looking at the boxes for SF, SG, and PG.

Hopefully this reveals a little bit more about positional shooting tendencies.  It’s not the averages we should be so concerned with, but the distribution.

I’m currently working on some k-means cluster and PCA statistical analyses that I think will blow the lid off the positional revolution. As is, they’re not quite ready to publish yet. Consider this is an appetizer.

Lastly, I’m not sure why some of the outliers are wonky. I’m using a program to spit out these charts and some of the outliers pretty much sat on the whisker ends.  I’ll look into it.

Earlier this year, I published a post at Hoopdata that analyzed player’s who shoot like a position unlike their own.  (Too bad a virus gobbled up the article archive or else I’d link to it.) In that piece, Rajon Rondo, Channing Frye, and Kobe Bryant were featured as players who were contrarian shooters. Today, I’d like to update that post with a more rigorous statistical technique, z-scores, that I used in last week’s post.

So here’s what I’m asking:

Which players shoot like a particular position who are not actually members of that position?

As a refresher, here are the summary stats from my positional analysis.

I’ve noticed that the shot location makeup of point guards, shooting guards, and small forwards are very similar.  Take a look at their percentages under the share column.  Almost identical, right? What distinguishes the three positions is not their shot densities but their shot types (spot-up, dribble-drive, off-screen) and shot source (assisted or not).   You’ll noticed that on shots at the rim (layups and dunks) small forwards get assisted twice as often as point guards (55.5 percent vs. 28.4 percent).  The reason is obvious: point guards are usually the ones feeding not the ones being fed.  So, even though the shot location is in the same area, it’s a different kind of shot.

Why do I bring this up? You’ll see a lot of overlap in the next few tables.  Since the makeups are so similar, you’ll notice the same players will keep popping up for multiple positions.  O.J. Mayo was the most shooting guard shooting shooting guard from last week’s post and likewise, he shoots a lot like a point guard and small forward.

Nonetheless, you should learn a thing or two from these tables.

Some ideas for next time:

- Using median shot location shares instead of average shot location shares to correct some skew issues. For example, does the typical center shoot 6% (the statistical mean) or does the typical center shoot none (the statistical median).

- Since PG=SG=SF, separate into two groups: guards (PG, SG, SF) and bigs (PF, C). Lose some of the detail but more instructive.

- Player comps rather than positional comps.  Since Dirk Nowitzi doesn’t really ascribe to a traditional position, how about trying to find players who shoot like Dirk?  Suggestions for player comps are welcome.

- K-means clustering.  DSMok1 with another fantastic suggestion in last week’s comment section, asks if we could do a k-means cluster analysis.  I think we could, although it’s not my statistical proficiency.

- Heat maps using r, courtesy of chart genies Albert Lyu and Jeremy Greenhouse.

Hit me up on Twitter at @tomhaberstroh if you have any other ideas or just comment below as usual.

The positional revolution has gained a full head of steam over the past month.  Although talk of tearing down the walls of traditional positions has been going on for years, Drew Cannon’s brilliant article at Basketball Prospectus blew the discussion wide open and sparked a slew of articles from the game’s brightest writers and analysts.

Definition is the root of the issue.  What is a point guard? Besides height, what differentiates a power forward from a center?  Why do we call a player who can’t shoot a lick a shooting guard?

Here’s an attempt at quantifying those definitions from the shot selection standpoint. Using Hoopdata.com’s player shot location data, I’ve calculated the average shot location shares of each position (the positional designations on Hoopdata come from dougstats.com).

We want to outgrow the conventions of traditional positions but let’s see if we can observe divisions in the first place.  Hoopdata breaks down shot types into 5 buckets: at the rim (layups and dunks), <10 feet, 10-15 feet, 16-23 feet, and 3-point shots.  Here’s how the five positions look, in terms of percentage of shots in each location.  So what does a point guard’s shot makeup look like compared to a shooting guard? Where do we see the biggest disparities between positions?

Here we see that the typical point guard attacks the basket more than the typical shooting guard and then the basket attack trends upward with the following positions.  Most point guards work out of the pick-and-roll which lends itself to penetration to the rack or dishes to the rolling big.  They’re getting almost all of their at rim baskets on penetration as opposed to bigs who can get layups/dunks from offensive rebounds.

Looking further, we see that the mid-range jumper is the least populated area for shots but there isn’t much distinction between positions in the mid-range.  What’s also interesting is that point guards, shooting guards, small forwards, and power forwards all shoot the long two in similar doses, with centers only taking about 18 percent of their overall game from here.

From the 3-point line, it makes sense that shooting guards launch the most from deep and the centers the least.  Nothing too ground-breaking there.

Perhaps what’s most interesting is how similar point guards and small forwards are in their shot palette.  The blue and green bars are nearly identical with each other from zone to zone.  Below is the graph in table form along with the assisted percentages and field goal percentages from each shot location, courtesy of Hoopdata.

There’s plenty of good stuff in the table above but for now, let’s dig deeper and see which players get classified in a particular position but shoot nothing like their traditional brethren.  To get there, I calculated each player’s z-score (which, in simple terms, calculates the magnitude of deviation from the norm) compared to the positional mean from each shot location.  Then, I took the absolute value of those z-scores and summed each location together for the Zsum to get the final aggregated score.  Note: I only looked at players who averaged 20 MPG and played 20 games last season.

In the first table below, we find that Miami Heat point guard Carlos Arroyo deviates the most from the shot selection of a traditional point guard.  In particular, 65.3 percent of his shots come from long twos and he barely attacks the basket or launches from downtown.  His z-scores total to 8.19 which is the highest sum of the point guard bunch.  Perhaps is good that he doesn’t attack the basket, as he only converts on 47.8 percent of his tries which is far below new Charlotte Bobcat Shaun Livingston’s 71.4 percent success rate.

The first table displays the “Least Alike” players in the group and the next table shows the “Most Alike” which tells us who are the most protypical point guards in their shot selection.  Orlando point guard Jameer Nelson tops that list.  I’ll save the commentary for a later date but I found this to be a pretty interesting exercise.  Which players are positional contrarians? Find out below. (My apologies for the blurriness).

SHOOTING GUARDS

SMALL FORWARDS

POWER FORWARDS

CENTERS

Lost in the whole Free Agentpalooza of 2010 was the fact that the party could have been bigger. Outrageously bigger.

With the cap-slashing climate over the past few years, the writing was on the wall well before the calendar reached July 1, 2010: this class of free agents were due for an enormous payday.  Seeing the formation of the storm on the horizon, organizations wisely arranged meetings with their imminent 2010 free agents and their representation in effort to prevent their prized players from hitting the market at all.  The plan? Sign them to a contract extension.

Contract extensions can be mutually beneficial; the player receives job security  from the team and the team gets the player at a discount.  The latter part of the deal isn’t guaranteed by any means but the team doesn’t have to compete with other bidders to sign their player long-term.  And that exclusivity is a huge advantage for teams.  But how can we quantify that advantage?

Let’s compare some contracts.  Of course, every free agent’s situation is different but to responsibly compare apples to apples, let’s examine the 2006 draft class whose rookie scale contracts were generally due to expire after the 2009-10 season, allowing them to become free agents this past summer.

First, the guys who cashed in early.  Can you imagine if Brandon Roy, Rajon Rondo, and LaMarcus Aldridge joined the free agent sweepstakes? Believe it or not, each of these players could have waited to test the free agent waters but elected to sign long-term with their respective clubs in the fall of 2009.  But they weren’t alone; Andrea Bargnani and Thabo Sefolosha also agreed to contract extensions before hitting free agency.  How much did they sign for? Let’s take a look.

For each player, the first two columns after their name tell us the contract length and dollar amount, with the third column calculating the average salary over that contract. For example Rajon Rondo inked a contract extension with the Boston Celtics in early September 2009 for 5-years, $55 million for an AAV (average annual value) of $11 million.

Then, for each player, I included their 2008-09 Wins Above Replacement Player (WARP09) with the “09″ signifying the year.  I chose 2008-09 to reflect their output before they signed their contract extension.  The WARP numbers are courtesy of BasketballProspectus.com and the brilliant work of BBP author and Indiana Pacers consultant Kevin Pelton.  To be clear, this version of WARP is not his newest version, WARP2, which incorporates an added bonus for players who space the floor with 3-point shooting.  Why? The Basketball Prospectus site has not updated their databases with WARP2 yet so for continuity purposes I opted for the older version.

So, this chart tells us that Rajon Rondo received a $11M AAV contract extension after a 13.2-win season in Boston, meaning he was being paid $0.8 million for each win that he accrued that season.  To be sure, teams pay for future projected performance not past performance, but this provides a quick dollar-value conversion that I’ve outlined in previous articles.

Through some research, I found that teams roughly paid $2.25 million for each win in this past free agency period.  Using that standard, the contracts handed to Rondo, Roy, and Aldridge were incredible bargains for their respective organizations.  Sefolosha received a contract fairly in-line with the going rate and Bargnani’s salary hasn’t quite reflected his production in the eyes of the WARP model (although WARP’s opinion is not unique in the statistical nor the scouting world).

All in all, the players who received contract extensions were paid about $1.4 million per win which is far below the free agent price observed this season.  Rondo undoubtedly would have received a max contract had he tested free agency and a case can be made that Aldridge would have pulled one down as well, given his age and productivity.  They left money on the table for job security, ensuring that they’d be set long-term should a career-altering injury occur in 2009-10 (which happened to Roy to some extent).

But how much money did they leave on the table? To find out, I looked at the going rate for their fellow 2006 draftees who received at least three-year deals in free agency: Rudy Gay, Tyrus Thomas, J.J. Redick, Jordan Farmar, Ronnie Brewer and Kyle Lowry. (The three-year qualifier captures players in the same stratosphere as those worthy of an extension and excludes players like Shannon Brown.)

While these free agent deals aren’t all completely egregious, the free agent premium bears out in this small group with the average price for a win costing $3 million compared to the previous group’s $1.4.  In fact, according to this method, inking an extension gave the parent organization about a 50% discount on the commodity of wins.

The biggest difference? In free agency, it’s nearly impossible to sign a talent like Rondo at a clearance markdown price.  Rondo has nearly four times as much impact on the standings as Rudy Gay but the latter will earn about $25 million more over the next half-decade.

So how are teams able to convince players to sign extensions that are probably below their market value?  Well, it’s not easy.  It’s paramount for an organization to produce a winning attitude from the top on down.  That means not just winning in practice but also in style (right, Dan Gilbert?).  It’s the responsibility of the owner, front office staff, and the coaching staff to make the players feel like there’s no sense to risk losing the professionalism, commitment, and comforts they can enjoy at home.  In other words, make your lawn as green as green gets.

In my previous post here at Hardwood, I shed some light on the biggest bargains in the game last season. Superstars LeBron James, Dwyane Wade, and Dwight Howard found themselves in the top tier but also some young studs who were still paid on the rookie scale such as Kevin Durant, Rajon Rondo, and Brook Lopez.

To reiterate from that post, I found that teams spent approximately $2.25 million per WARP2 produced in 2010.  So, I converted each player’s WARP2 into a dollar amount by multiplying their production (WARP2) by the price for that production ($2.25M) to calculate a dollar value for their production.  Then, I simply subtracted their salary (source: Patricia Bender’s database) from their dollar value of production to find their net value.  Some players, like Kobe Bryant and Andrew Bynum, were paid a salary that matched their production value. But other players, well, didn’t live up to their pricetag, for various reasons.

Which contracts lead to the biggest loss last season? Last take a look.

Injuries. Injuries. Injuries.

It’s incredibly difficult to project how players will perform six years into the future.  But it’s even harder to foresee how injuries will plague their career down the line.

The cases of Tracy McGrady, Yao Ming, and Michael Redd illustrate the devastating effects that a serious injury can have on a team’s books.  The Rockets were set to receive nearly nothing for their $40 million investments in Yao and McGrady but a midseason deal with the Knicks handed McGrady’s albatross over to Jim Dolan in exchange for long-term cap relief. In general, $40 million equates to about 18 wins above replacement so the Rockets 42-win season becomes even more remarkable considering what they lost due to injury.

Boston’s signings of the O’Neals haven’t received a standing ovation from some fans and analysts largely due to the stigma of the $43.2 million they were owed last season.  At those prices, the O’Neal’s were undoubtedly poor investments by their respective teams but they still contributed about $14 million in on-court value.  Despite the 6-win production from Shaq and Jermaine, the contracts sank $30 million worth of deficit on the books, according to this method.  The Celtics will pay just $6.5 million for their services next year, which amounts to about one seventh their pricetag last season.

McGrady and the O’Neals aren’t the only ones who may go from albatross to asset overnight.  Brad Miller and Zydrunas Ilgauskas will see huge paycuts next season and their salary will more closely mirror their on-court production.

Again, I owe a huge thanks to Kevin Pelton for the WARP2 numbers.  Be sure to get your hands on the invaluable 2010-11 Pro Basketball Prospectus when it comes out in the early fall.

Over the past few weeks, I’ve been updating the free agent market value for a win, measured by Kevin Pelton’s WARP2.  Today, I’d like to apply the same method to a retrospective look at last season’s production.

Given the general rate for wins, who were the best bargains in the game last year?

In my salary research using Patricia Bender’s salary index, I found that teams “paid” approximately $2.25 million per WARP2 last season.  I framed that with quotation marks because for the most part, teams do not purchase players every summer but rather in contract intervals.  The $2.25M pricetag a quick and dirty rule of thumb when you’re looking at player worth.  The price reflects what I found researching the contracts handed out this summer as well.

So who were the best bargains last year?  To find out, I converted each player’s WARP2 into a dollar amount by multiplying their production (WARP2) by the price for that production ($2.25M).  Team loses on their investment if they pay more than what they receive in production.  On the flipside, teams enjoy a profit or surplus of value if their player provides more production than they were paid.  So if the general market rate for wins is $2.25M per win, how much surplus value did teams receive on their investments?

I present the 20 biggest bargains of last year:

I’m guessing most people would argue that Kevin Durant is by far the biggest bargain in the game. But even though LeBron gets paid $11 million more than Durant, he still provides about $5 million more in surplus value.  The difference of $11 million would generally buy about 5 wins on the open market so the 7.1 extra wins that LeBron produced wins out.

Rondo was the most valuable player on the Celtics last year and that’s even before we look through the bang-for-your-buck lens.  Remarkably, the Celtics paid Brian Scalabrine 50 percent more than they paid Rondo and yet, the latter produced nearly 15 wins more.  And next year, Rondo will still only rank as  the fourth highest paid Celtic.

How about geezers Jason Kidd and Steve Nash? The Mavericks and Suns have gone the extra mile to make sure these two players, 37 and 36 years old respectively, can stay on the court and the dollar investments have been absolute steals.

Notice the surplus value of rookie contracts.  Several of these bargains are still under the pay scale of their first NBA contracts.  This is why the draft and player development are the lifebloods of shrewd franchises.

Brandon Roy missed 17 games last season but still measured out as one of the best values of last year, getting paid $3.9 million for almost 10 wins of production.  Impressive.

In next week’s edition, we’ll take a look at the biggest wastes of 2009-10.  Any guesses?

Thanks again to Kevin Pelton for his player metric.  Be sure to get the new Pro Basketball Prospectus when it comes out in early spring.  Now that’s a bargain.

Richard Jefferson signed a few days ago which mean’s it’s time for another market update on the free agency price.  To recap, I’m comparing every newly-signed player’s salary to their WARP2 from last season. It’s a quick and handy measure of how much teams are willing to pay for talent this summer.  Last year, the going rate for free agents was $1.49M for each win.  This year? It’s risen to $2.2M.

Here’s the full run down:

To reiterate from last week, the last row on this table subtracts players who likely signed for lower than the free market rate (LeBron James, Dwyane Wade, Chris Bosh, and Dirk Nowitzki).  This takes a more accurate view of what teams pay free of cap spending restrictions.

$2.2 million per win is an increase since the last count because the newest additions have been sold at the rate of $3.3 million.  WARP2 didn’t think much of last year’s production of Ronnie Brewer, Joel Anthony, Richard Jefferson, and Marquis Daniels but teams were willing to pay more than the minimum and in some cases, much more than the minimum for these near replacement-level efforts.

Newly minted Matt Barnes looks like one of the best deals of the summer and should help bolster the Lakers’ chances of bringing home another championship.  It’s hard to imagine Ridnour posting another 5.3-win season but this objective method makes David Kahn look like a genius.

Next week, look for a team by team and position by position break down.  We’ll see if the summer’s $700,000 premium sticks.

Much thanks to Kevin Pelton of Basketball Prospectus.

Here’s the transcript–

David Kahn: “I have never– I haven’t seen a big man pass like [Darko].  He really does pass like Vlade, in that respect. Absolutely. He’s a Great Passing Big Man^TM. And, you know, Vlade will be the first person to tell you that.”

Chris Webber: “HA! Wow. Wow. Like Vlade Divac… Woah.”

I mentioned earlier on Twitter that Kahn’s declaration was full of fail. Darko has a very pedestrian 7.2 percent career assist percentage while Webber (20.2 ast pct) and Divac (16.0 ast pct) should be insulted by the insinuation that they’re anywhere close to being in the same class.  But it’s one thing for Kahn to make such a claim on TV, but it’s another thing to say it directly to Chris Webber who played with Divac for six seasons in Sacramento, not to mention Webber is one of the most gifted passing big men of all time.

To see the enormous divide between Darko and Webber, consider that Darko’s single best season in assist percentage (10.7 pct)  was far lower than Webber’s worst (16.4 pct).

But I didn’t stop there. I decided to switch directions and head down a more subjective path of research.  I hit up YouTube to find some evidence that Darko deserves to be mentioned in the same breath as Webber and Divac.  And this is what I found.

Divac to Chris Webber:

Webber to Divac:

Darko to… Kurt Rambis (seriously this is all I could find):

In last week’s post, I calculated the going rate for free agents this summer by applying the dollars-per-win method that others have used in the past.  If wins were a known commodity (which they aren’t), then this would represent the price.  To be sure, not all teams value wins at the same rate.  Some teams have an easier time swallowing risk or ignoring risks altogether.  But aggregating the talent and dollars gives us a good window into the pricing climate.

I found that teams were paying about $2.23 million per win according to Kevin Pelton’s WARP system.  Since then, Kevin has kindly pointed out that he made an updated version of WARP (referred to as WARP2) and they haven’t been published yet on the Basketball Prospectus player cards just yet.  Being the helpful gent that he is, I was sent the WARP2 numbers for last season (denoted 10WARP2) and those numbers are reflected below.

You’ll notice I have cited two prices here.  The $1.69 million pricetag reflects the entire free agency lot with the max guys included.  However, several high-end players had their salaries artificially capped due to the CBA rules that restrict the max salary to about $20million annually if resigned by their former club.  Moreover, we witnessed a rare circumstance where players took paycuts below their max cap (LeBron James, Dwyane Wade, and Chris Bosh) so that the team could have more money to fill out the roster. Consider that Joe Johnson will get paid more than James despite only being half the player James is.

There isn’t a perfect way to handle this designed deflation but I chose to ignore the players fulfilled the following qualifiers a) received the max allowable contract AND b) produced at least 10 WARP2.  This takes out Dirk Nowitzki, Bosh, James, and Wade —  all of which would almost undoubtedly receive bigger contracts if the CBA gave them that right.  It’s arguable whether someone would have paid higher than the max for Johnson, Stoudemire, and Rudy Gay, but their included in the Total w/o “max” price.

So, with that in mind, it seems as though the market rate has slid from $2.23 million per win to $2.01 million per win (or just $2 million) over the past week.  As I mentioned in my previous post, the 2009 summer going rate was approximately $1.49 million which means NBA teams a whole are paying about half a million dollars more for each win.

You could interpret this finding in a number of ways.  An argument can be made that agents are simply getting better at selling the product but that’s probably not something that happens collectively overnight.  It could also be a sign that front offices are desperate to pacify their anxious fans and thus, will use their enormous cap space to land someone of name-value.  Remember, fans have been promised the moon in the Summer of 2010 ^TM and that demand has pushed up the price.  But it’s also very possible that the impending lockout has caused more players to enter the free agency market to secure a long term contract.  In turn, the supply has been raised as well, but maybe not as much.

It’s also worth noting that the $1.49m price from 2009 was derived with the original version of WARP and thus, the price could change slightly.  However, I don’t have any reason to believe it would change the price significantly as the system adjustment was merely a minor tweak to allocate more credit to 3-point shooters for floor-spacing.

So the $750,000 premium we saw last week has been reduced down to a not-too-shabby $500,000.  The players will take it — while they can.

With Joe Johnson receiving a max contract and Darko Milicic taking in $20 million from David Kahn, it seems as though teams are recklessly showering free agents with money this summer. It’s a sellers market; teams are flush with cash and promising the world to their fans.

But what do we mean when we say that a team overpaid for a free agent?  Whether you know it or not, our minds gather bundles of basketball information (How good is this player?), transfers that to a dollar amount (What is that product worth?), and compares it to the price tag (Was it a good deal?).  The wondrous mind is able to perform this function in a matter of seconds.  But let’s try to slow it down and put it on paper.

One approach is to quantify player value on the court and then observe how much that product costs on the market.  The market prices stabilize only after several deals have been made and they change from year to year as player as new money enters the market (say, a Prokhorov arrives or salary cap threshold rises) and/or the product line changes.   The product line has never been stronger and the suit pockets have never been deeper.

There are several player metrics out there that attempt to quantify player value on a scale of wins: John Hollinger’s Estimated Wins Added (EWA), Dave Berri’s Wins Produced (WP) and Justin Kubatko’s Win Shares (WS).

The player metric I’ll use for these purposes is Kevin Pelton’s Wins Above Replacement (WARP) which applies the same framework in Baseball Prospectus’ WARP to the NBA.  To account for player value, I will use the player’s WARP for the 2010 season.

So far, the going rate this summer for one WARP is $2.23 million.  This means that in this climate, a 4 WARP player would generally command about a $9 million per annum contract.  Of course, this isn’t ironclad and as shown by Chris Duhon and Steve Blake, who both received four-year contracts after contributing sub-replacement level performance last year, this model will bend going forward.

Remember the Drew Gooden contract that people drew all sorts of insta-snark?  That measures out to be the best bang for the buck deal of the summer up to this point, along with Boozer’s deal.  The years may be long on Gooden but the Bucks got the veteran big man at a steep discount most likely because of his questionable motor and perception that a oft-traded player equals a flawed player.   If he continues to produce on the court, Gooden could be a steal at this climate.

Surprise, Surprise: Darko Milicic was one of the worst deals so far this off season.  The Timberwolves overpaid about $13 million ($2.23 x 0.8 x 4) on the fringe contributor and the signing did little to change David Kahn’s rep as a showrunner.

One shortcoming of this model, as you can see with the cases of Blake and Duhon, is that a straight $/WARP calculation can produce some wonky results off of a poor season.  I looked at adjusting the WARP input to reflect an average of the past two seasons but the going rate remained nearly unchanged ($2.23 per win vs. $2.1 per win).  With that adjustment, Duhon and Rudy Gay became the summer’s worst deals.

Another assumption that this model makes is that production is constant.  Joe Johnson’s contract doesn’t look nearly as bad as it would if we considered his career arc and likely depreciation.  It’s the length that’s egregious; a two-year, $20 million is a much better deal than six-years , $120 million.

So is $2.23m/win an inflated price?  Compared to last year’s free agency, yes.  In fact, teams are paying about a $740,000 premium per win this offseason compared to last summer.  Using the same system for last year’s free agency, teams paid $1.49 million for each WARP unit in 2009.

But there’s still plenty of time for the Grand Opening excitement to calm and the price will likely slide a bit.  The other capped max contracts have yet to be handed out (Wade, LeBron, and Bosh) and their contracts will actually drive the going rate downward since they’re not paid on the free market.  The near $1 million premium may drop down to $500K or $250K by the end of summer.

But right now, players are seeing green.