NBA Free Agents: PER and Salary

According to basketball-reference.com there are 60 unrestricted free agents (UFA) in the NBA that played during the 2012/13 season and remain unsigned. I was interested in understanding the most cost-effective UFA so I collected data on two categories for each of the 60 players: their 2013-14 salary or salary cap hit, and their 2012-13 PER--a standardized per-minute measure of offensive and defensive performance where 15 represents the average performance for a given season.

I divided each player's 2013-14 salary or salary cap hit by PER to capture a salary cost per PER point. Basically, teams would want to look at UFAs with the lowest salary dollar per PER point because they would be paying less for better performance (at least based on 2012-13 and assuming a player's salary remains at the reported level).

Based on this approach the 5 most cost-effective available UFAs are Brandan Wright, Malcolm Thomas, Earl Barron, Antawn Jamison and Chris Wilcox--all of whom had above a 15 PER (Cole Aldrich is the only other player on the list with a PER above 15). The five least cost-effective available UFAs were Hedo Turkoglu, Daniel Gibson, Tyrus Thomas, Joel Pryzbilla and Drew Gooden. The chart below ranks the players based on 2013-14 salary per PER point starting with Brandon Wright.

Player	13/ 14 Salary or Cap Hit	12/13 PER	13/14 Salary/ PER
Brandan Wright	$884,293	21	$42,109.19
Malcolm Thomas	$884,293	16.7	$52,951.68
Earl Barron	$884,293	15.4	$57,421.62
Antawn Jamison	$884,293	15.3	$57,796.93
Chris Wilcox	$884,293	15.3	$57,796.93
Mo Williams	$884,293	14.4	$61,409.24
Kenyon Martin	$884,293	13.9	$63,618.20
Leandro Barbosa	$884,293	13.5	$65,503.19
Alan Anderson	$884,293	12.6	$70,181.98
Damien Wilkins	$884,293	12.5	$70,743.44
A.J. Price	$884,293	12.4	$71,313.95
Louis Amundson	$893,500	11.7	$76,367.52
Keyon Dooling	$884,293	11.2	$78,954.73
Jamaal Tinsley	$884,293	10.6	$83,423.87
Juwan Howard	$884,293	9.9	$89,322.53
Cartier Martin	$884,293	9.7	$91,164.23
Mike James	$884,293	9.5	$93,083.47
Richard Hamilton	$1,000,000	10.6	$94,339.62
Marquis Daniels	$884,293	9.2	$96,118.80
James White	$884,293	9.1	$97,175.05
Ronnie Brewer	$884,293	9.1	$97,175.05
Lance Thomas	$1,005,000	10.1	$99,504.95
Jerry Stackhouse	$884,293	8.5	$104,034.47
Tracy McGrady	$884,293	8.5	$104,034.47
Anthony Tolliver	$884,293	8.4	$105,272.98
Royal Ivey	$884,293	8.1	$109,171.98
Sam Young	$884,293	7.5	$117,905.73
Derek Fisher	$884,293	7	$126,327.57
DeJuan Blair	$2,002,600	14.6	$137,164.38
Devin Harris	$2,003,339	14.6	$137,215.00
Vladimir Radmanovic	$884,293	6.3	$140,363.97
Mickael Pietrus	$884,293	6	$147,382.17
Dahntay Jones	$884,293	5.4	$163,757.96
Sebastian Telfair	$2,037,750	10.7	$190,443.93
DaJuan Summers	$884,293	4.3	$205,649.53
Terrence Williams	$2,678,640	12.3	$217,775.61
Daequan Cook	$884,293	4	$221,073.25
Jannero Pargo	$3,340,920	14.1	$236,944.68
Cole Aldrich	$3,857,040	15.7	$245,671.34
Nolan Smith	$1,793,520	7.1	$252,608.45
Johan Petro	$2,897,976	11	$263,452.36
Jason Collins	$884,293	2.9	$304,928.62
Elliot Williams	$4,469,548	12	$372,462.33
D.J. Augustin	$4,200,000	11	$381,818.18
Luke Walton	$4,320,000	11.3	$382,300.88
Mike Miller	$6,200,000	13.5	$459,259.26
Luke Babbitt	$4,508,504	9.4	$479,628.09
Marcus Camby	$4,383,773	8.6	$509,741.05
Lamar Odom	$5,607,240	10.9	$514,425.69
Roger Mason	$5,568,333	10	$556,833.30
Linas Kleiza	$4,600,000	8.2	$560,975.61
Corey Maggette	$4,500,000	7.9	$569,620.25
Beno Udrih	$11,058,300	14.9	$742,167.79
DeSagana Diop	$5,016,960	6.6	$760,145.45
Xavier Henry	$6,344,164	7.6	$834,758.42
Drew Gooden	$6,687,400	7.7	$868,493.51
Joel Przybilla	$2,897,976	3.3	$878,174.55
Tyrus Thomas	$10,300,000	9.6	$1,072,916.67
Daniel Gibson	$9,105,431	7.7	$1,182,523.51
Hedo Turkoglu	$12,000,000	3.4	$3,529,411.76

Win Shares per Salary Dollar

I pulled data from the basketball-reference.com on players' 2012-13 win shares (WS), which reflect an estimate number of wins that a player contributed to his team last season, and on salary for the 2013-14 season. If a player's salary is not yet determined then I used the amount he will be charged against his team's salary cap. I divided 2013-14 salary by 2012-13 WS to get some rough estimate of the dollar per win a team can expect from a player assuming he performs identically next season as he did this season (and plays the same amount of games and minutes).

First a few points on win shares. The more a player plays the more likely he is to accumulate a larger WS. The statistic is not standardized thus injuries that cause a significant loss of game time or general low playing time adversely affect WS. (Basketball-reference.com does provide a standardized WS per 48 minutes of play where the top 5 are: LeBron [.322], Durant, [.291], CP3 [.287], Jeremy Evans [.208], and Tyson Chandler and Chris Andersen [.207]. Darko Milicic has the lowest--an astounding -.779--which suggests that extrapolating his 5 minutes of play in 2012/13 to a whole game, his presence on the court would virtually guarantee a loss for his team.)

Dividing WS by salary $ is important because it gives an idea of low cost players who disproportionately contribute to wins. The worst of the worst consists of big name players with negative win shares, like Danny Granger, Drew Gooden, Thomas Robinson, Quentin Richardson, Hedo Turkoglu, Ben Gordon, and Michael Beasely. The next group, the not quite worstest of the worst (but still awful), include players with a 0 WS, like Marcus Camby, Michael Pietrus Al Harrington and Miles Plumleee. Next the five players with the greatest salary to positive WS (basically, the least efficient players in terms of payroll besides those just listed). The dollar value next to the name reflects salary dollar per win:

1. Andrea Bargnani ($118.6 million)
2. Linas Kleiza ($46.0 million)
3. Kevin Seraphin ($27.6 million)
4. Brendan Haywoon ($20.5 million)
5. Daniel Gibson ($18.2 million)

The six (sixth place was added for obvious reasons) most valuable players in terms of salary per WS are:

1. Chanlder Parsons ($132.4K)
2. Nate Robinson ($149.9K)
3. Jimmy Butler ($159.0K)
4. Kenneth Faried ($175.3K)
5. Isaiah Thomas ($176.9K)
6. Andray Blatche ($180.5K)

Another way to look at this is where as to buy (with salary) 10 wins from Andrea Bargnani a team should expect to pay about $1 billion, Chandler Parsons could return the same 10 wins for a little more than $1 million. 

All D v Not All D (1989-90 to 2011-12) per 48

The charts below (click to enlarge) break out conventional offensive and defensive statistics for All Defensive players versus all other players by position category (i.e., PGs, wings, and post players) for every season from 1989-90 to 2011-12. The statistics are standardized on a per 48 minute performance, which gives some indicator as to how these groups would perform over an entire NBA game. (Although fatigue, injury, etc. would likely result in declining play--significantly for some players--as minutes played  approached 48. Thus, this should be viewed as a rough estimate of full-game performance.)

The charts show that over 48 minutes, All Defensive players are better in virtually every offensive and defensive category than are non-All Defensive players. The exceptions are all All Defensive positional categories are slightly more likely to turn the ball over than their non-All Defensive counterparts (which makes sense as they are more likely to possess the ball), and that All Defensive wings average slightly fewer offensive rebounds than their non-All Defensive counterparts. The difference is most stark with post players, where All Defensive post men far outperform their non-All Defensive counterparts, whom over 48 minutes average almost six and a half fouls. These statistics simply present more evidence that All Defensive players are all-around superior players, which should not come as a surprise but may give reason to believe that offensive performance could influence NBA coaches' decision to vote a given player to the All Defense team.

Last 15 #1 Picks WS & WS/ 48

In preparation for this Thursday's draft--where if Alex Len is drafted first overall the NBA, the sport of  basketball, the concept of competition, physical activity will all mutually implode as that signals that some mysterious dark matter is going to instantaneously subsume all of the galaxy--basketball-reference reported the Win Share and Win Share/ 48 minutes of the last 15 number one picks.

What's interesting from the chart? Despite being injured for much of his rookie year Anthony Davis has about tripled Michael Olowokandi's career contribution and almost exceeded that of Greg Oden (who it's obviously unfair to compare to without taking injuries into account). It's also surprising that over the entire course of his career,  Elton Brand has had more of a contribution than Dwight Howard. Taking Brand's longer tenure into account however, Howard has contributed more per game (as indicated by the higher WS/ 48).

Of course, no draft analysis, no matter how basic, can be complete without troubling results for Wizards' fans--John Wall and Kwame Brown share the same WS/ 48 thus far in their career, and the only two players with lower ratings are Olowokandi and Andrea Bargnani, the latter of whom ended the debate re: the question: If there isn't strong domestic talent in a given draft (i.e., 2005, 2013), do you just select the foreign player most often described as "the next Dirk Nowitzki"?

Per Minute Performance: All D v Not All D (1989-90 to 2011-12)

While previously addressed factors, like age, make sense when considering the qualities of superior defensive players--as measured by being voted to an All Defensive team (ADT)--it is also important to look at conventional performance measures (i.e., points, rebounds, etc) to understand other potential correlations. Below is a heat map of a range of performance measures (listed in the bottom columns) standardized per minute of play* for ADT players and non-ADT players grouped by type of position (i.e., PG, wing, post) from every season between 1989-90 to 2011-12.

A heat map is basically a matrix that illustrates, in this case, how well the ADT/ non-ADT position groups performed in a specific standardized category. As the legend in the top right illustrates, superior performance is indicated by red, and from there more moderate performance is indicated by orange-red then orange then yellow . . . down to white, which indicates inferior performance. (In other words, more red = good; less red/ more white = bad.)

Not surprising, Post ADT were the highest in rebounding categories, FGM, FGA, FTM, and FTA. While it may come as a surprise that they ranked so high in FTM as post players are typically not considered successful FT shooters (in terms of %), it likely reflects that playing the post results in them getting fouled more and, thus, getting more FTA than other positions. This is supported by the fact that this group has a relatively low FT% (indicated by "FT_Per"). Post non-ADT performed the best at fouling and were abysmal at FT%, both of which are expected considering the position.

PG and Wing non-ADT (middle two groups) were mediocre to poor across categories except that the PG group was among the highest in TOs and the two groups performed just marginally worse than their respective ADTs in 3FG, 3FGA and 3FG% (all indicated by "ThP" in the place of "3FG"). PG ADT (the second to bottom group) ranked exceptionally high in steals, assists and TOs--again, which all makes sense considering the position is inclined to accrue those stats relative to other positions--and Wing ADTs led in FGM, FGA, points and FTM. 

So what does all this mean? Basically, that over the last 23 seasons, ADT nominees also dominate those offensive categories associated with their position, which suggests that ADT players tend to be well-rounded players (i.e., effective defensively and offensively). Conversely, it could present problems for using nomination to an ADT as an indicator of superior defensive ability if the coaches that vote these players to the ADTs confuse or belie offensive aptitude for defensive skill.

* Statistics are standardized per minute to account for the fact that players that play more minutes accrue more stats so playing time tends to positively affect most measures. (Of course, there are measures that a player does not want to accrue, like TOs, that would also be higher with greater playing time.) Failure to account for performance per minute would likely benefit averages of players in the ADT groups on account of the fact that they are all starters and, thus, average more time than non-ADT players, which is a compilation of starters and (many) non-starters/ low MPG players.

Age, Defense & Position

From the 1989-90 until 2011-2012 players selected to an All Defensive Team (average age 28.5) were about 1.5 years older than all other players (average age 27.0) in the NBA. The median difference was slightly larger at 3 years (29 for All Defense, 26 for all others). The question then becomes--Does the difference hold by position?

To measure this I categorized players over the last 23 seasons (excluding the 2012-13 season) into three positional groups based on their positions assigned in basketball-reference.com. 'Point Guards' captured any player that was classified at one point as a point guard regardless of any other position he played during a given season. 'Post players' captured any player that was classified at one point as a center or power forward regardless of any other position he played during a given season. (Note: During these 23 seasons there were no players that were classified as point guards and power forwards or centers.) Finally, 'Wings' captured all other players (i.e., shooting guards and small forwards) that were not captured in the other two groups.

Admittedly, this isn't a perfect approach as there are players in a given season that played in more than one of these three categories. Examples include players, like Jalen Rose (2003-04) who played PG and SF, Mike Dunleavy (2006-07) and Kyle Korver (2007-08), who were assigned the positions of shooting guard and power forward, and any number of shooting guard-point guard combos, like Jarrett Jack, Kirk Hinrich, Bobby Jackson, Terry Dehere, and Shammond Williams. That being, said the approach represents a reasonable method for aggregating defensive players based on the offensive positions they are most likely to guard.

The first two charts below break out the mean and median for 'Point Guards'. It shows that for every season All Defensive PGs were at least the same age or up to 3 years older than all other PGs until a precipitous decline starting in the 2007-08 season, after which there is a gradual increase in All Defensive PGs over the next four years until last season where the two groups were about the same average and median age. (The sharp drop in the age of All Defensive PGs reflects that at the time third year players and 23 year olds Chris Paul in 2007-08 and Rajon Rondo in 2008-09 became regular All Defensive PGs.)

The next two charts break out the mean and median for 'Wings' (i.e., SGs and SFs). They show that except for the 1993-1994 season All Defensive wings were almost always older, and by quite a bit in the late 1990s, than all other wings. (The drop in 1993-94 is most explained by 23 year old Latrell Sprewell receiving his first and only All Defensive [Second] Team nomination.)

The final two charts show the mean and median for 'Post' players (i.e., PFs and Cs). Similar to Point Guards and Wings, All Defensive post players appeared to be older than all other post players except for about a 5 year stint starting with the 1999-2000 season, which reflects the beginning of a ten-year Tim Duncan and Kevin Garnett reign as first or second team PF and C. (The 1999-2000 season was Duncan's third and his third time on an All Defensive team and Garnett's fifth season and first on the team. Where Duncan entered the NBA after a four year college career and, thus, started his career at a later age than Garnett, Garnett entered the league straight out of high school but was only a month younger than Duncan despite his additional NBA experience.) Taken together the charts on the three groups suggest that with the exception of the emergence of a few precocious superstar defenders, across major defensive positional categories players nominated to an All Defensive Team tend to be older than all other players.

Age & Defense

Of the many factors that might explain a successful NBA defender, his age is one worthy of consideration. To measure it I collected data from basketball-reference.com on full season stats for every NBA player from the 1990-91 season until the 2011-12 season. Because qualifying a player as a 'successful' defender demands subjectivity, I also categorized players based on if they were voted 1st or 2nd All-Defensive Team in a given season or if they were not voted to an All-Defensive team.

A few things to note about the All Defensive Team. First, while this seems like a reasonable measure of defensive aptitude, it's worth noting that head coaches vote for the team. As a result, there could be bias in the voting process. For example, if a coach harbors ill will toward an opposing player for personal or competitive circumstances he may consciously or subconsciously disregard that player when casting his vote. There's also the issue that popular players may possess greater relevance in a voter's memory. As a result, coaches might continually vote for Kobe Bryant not because he was a top ten defender in a given year, but they recall his name quicker than less popular and less offensively capable players or because Kobe's defensive achievements from prior seasons affect perceptions on his defense for the current voting season. In other words, this isn't a perfect measure but it is reasonable. Also, most seasons ten players--five for the first team and five for the second team--are selected to the First and Second All-Defensive Teams. In other seasons, like 1998-99, 2004-05 or 2005-06, there is a tie in voting so 11 players are selected.

Before introducing some basic analysis it's important to identify why age would affect defensive ability. On the one hand, successful man-to-man defense (which is the dominant scheme of the NBA) demands exceptional athletic ability because the defender must react to the cuts, bursts and moves of another world class athlete. As a result, we might expect younger players to have an advantage as defenders because youth better serves athleticism than the time, wear, and injuries experienced by a rugged veteran. On the other hand, defense also demands intelligence and guile to read an opponent's tendencies, to process and predict offensive schemes, and to understand how to best neutralize an opponent's offensive strengths. These are qualities one might expect a veteran to possess from his year's of competition and, thus, would suggest that older players serve as better defenders.

Below are two charts. The first shows the mean and the second shows the median (or middle age of the group) of all All-Defensive First and Second team players and all other players (i.e., those that weren't voted to an All-Defense team)*. The top chart on average age shows that for every season since 1990-91 except for the 1999-00 season the average age of the All-Defense team was greater than the average age of the rest of the NBA.

The second chart shows that the median age of All Defense players is greater than or equal to all other NBA players in every season except 2009-10 when the two groups had the same median age. Therefore, looking at data from the last 22 NBA seasons it appears that defensive aptitude, at least in terms of being measured by whether a player was voted first or second team All-Defense, increases as players age and gain experience. (Of course, only up to a point as All-Defensive Team players' age seems to hover in the late 20s/ early 30s. There likely comes a point in the mid-30s where despite the knowledge and guile of these defenders, age compromises athletic ability to too great a degree.)

*The reason for looking at the mean and the median is because very large or very small values can skew the mean but won't skew the median. In other words, if you took a sample of five players and their ages were 24, 25, 25, 26 and 41 then looking just at average would make us think that the average age of the group was greater than the rest of the population of players because of the anomalous 41 but the median, 25 in this example, gives another perspective on the 'central' age. Because NBA player age is usually at most a total variance of 20 years between the youngest and oldest player, anomalous ages would only affect small groups, like that of ten or eleven players voted into All-Defensive Teams.

Marc Gasol & Advanced Defensive Stats

With Marc Gasol receiving Defensive Player of the Year he becomes the third straight center to win the award, which since Jordan won it in 1987-88 has only been won by centers and power forwards except for Gary Payton in 1995-96 and Ron/ Meta Artest/World Peace in 2003-04 (thus, giving some idea of the value of frontcourt, help defenders). What's interesting about Gasol's winning is that he's a relatively unimpressive nominee based on conventional defensive measures.

Looking at the performance of all players in the 2012-13 season that played at least 100 minutes and standardized over 36 per minutes of play (which simply helps take account for the fact that some players play more than others so we're interested in performance per minute of play rather than total performance, which would benefit players that play more minutes), Gasol is 127th in defensive rebounds (tied with Kawhi Leonard and Antawn Jamison), 75th in steals among just PFs and Cs, and 46th in blocks (to give some context, in both steals and blocks he is tied with Ronny Turiaf). Even among the more basic advanced statistics,  like DRB%, STL% and BLK% (basically, all just estimate the percentage of DRBs/ STLs/ BLKs that player achieved while on the floor), he's unimpressive. For DRB% Gasol is 105th, for STL% he's 60th among PFs and Cs, and for BLK% he's 45th among all players.

It is perhaps the two most advanced defensive stats (among popular advanced defensive stats) that signal Gasol's value as a defender. Gasol's defensive rating (DRTG), which is an estimate of the number of points a player gives up per 100 possessions, is 98, which is 4th in the league--one point behind Hibbert and Paul George and 3 points behind Tim Duncan, the leader. Based on defensive win shares (DWS), which is an estimate of the number of wins the player's defense contributes to his team, Gasol was second with 5.4 behind only Paul George's 6.3.

But, why if George leads Gasol in these two advanced measures did he not receive the award? (More so, how did he finish 7th in voting?) Perhaps that's the case because 5th in DWS was Roy Hibbert and much like George's high DRTG (which Hibbert shared) it may be the case that voters feel George's defense is bolstered by Hibbert's (and other phenomenal Pacer defenders, like David West's) defensive contribution. (Interestingly, LeBron, the runner-up for Defensive Player of the Year, didn't finish in the top ten of DRTG or DWS.)

Syracuse 3FG Defense

During the NCAA Men's tournament Syracuse received much publicity and warranted praise for its 2-3 defense. (In fact, it received such recognition that even NPR ran a segment on it.)  The movement and the length of the defenders seemed to receive most of the credit for the zone's success. But there's something equally important that Jim Boeheim understands as well as anyone--college kids are not good jump shooters and the further from the basket you make them shoot the worse they get. Blame it on the 'AAU-I gotta do me' culture or Youtube dunk contests or whatever but what Boeheim gets so well is that if opponents do something poorly then make them do a lot of it.

Among division 1 college basketball teams over the last season, Syracuse had the third best opponent three point field goal defense percentage at 28.4%. (The two teams ahead of them--New Hampshire and Weber St--were sub 80 RPI teams and didn't play close to the competition that Syracuse did.) Among the top 100 division 1 basketball teams in terms of opponent three point field goal defense percentage Syracuse averaged the 7th highest opponent 3FGA per game at 21.7 (all 6 teams ahead of them allowed a higher opponent 3FG% and were from much lower-tier conferences than the Big East).

One way to look at this is--what was the value an opponent should expect for each shot attempt against Syracuse. For threes it was 0.852 points (28.4% opponent 3FG% x 3 points) and for twos it was only slightly higher at 0.854 points (42.7% opponent 2FG% x 2 points). But considering that two point attempts are far more likely than three point attempts to incur fouls and, thus, free throws (Syracuse's opponents averaged 19.1 FTA against them per game), opponents would have benefited even more by relying less on threes.

What became clear during the tournament was that not only did Syracuse's guards play excellent perimeter defense but the zone forced opponents to take a seemingly irrational number of contested threes--if history shows opponents that they have a low probability of making the shot then don't take it, or at least minimize the number of attempts. It wasn't just that their 5 tournament opponents shot 19% from the three, but the fact that their opponents averaged 23 3FGA while they should have known the three point attempt was an exceptionally low probability method for scoring points. (To give some reference, Montana took 31 3FGA, and Marquette and Michigan each took 24.) So what happened in the loss to Michigan? After shooting around 36% from threes in the first four tournament games, Syracuse shot 21%.