Saturday, April 19, 2014

2013-14 Rookie Player Impact Estimates

Among the many measures aimed at capturing a player's overall value to a team (i.e., PER and WARP), NBA Stats uses Player Impact Estimate (PIE)*. The statistic combines a range of conventional stats and standardizes them per game. With the regular season complete I wanted to take a retrospective look at rookie performance and do some simple forecasting to see which players might excel in their sophomore season. I pulled PIE data from NBA Stats for all rookies that played at least 10 minutes per game. The first chart presents the results. Interestingly, based on PIE, top overall pick Anthony Bennett was actually the worst rookie in the 2013-14 season, and seventh overall pick Ben McLemore wasn't much better. The top performing rookies included Gorgui Dieng, Mason Plumlee, Michael Carter-Williams and Victor Oladipo. The latter two were effective consistently throughout their rookie years, Diegn and Plumlee came on strong during the last two months of the season.

Next, I wanted to get an idea of how PIE might predict performance among the 2013-14 rookies in their 2014-15 sophomore season. I collected data on the April PIE for 2012-13 rookies (i.e., the Anthony Davis class) and compared it with their full season PIE from their 2013-14 sophomore season. I captured only players from the 2012 draft class that played registered a PIE in April 2013 and registered a PIE for 2013-14, which resulted in 56 players (actually 57, but I dropped Robert Sacre and his -200% PIE for April 2013, which reflected 1.6 of the worst minutes of basketball in the 2012-13 season). 

My thinking is that by April, the last month of the regular season, rookies have become accustomed to the NBA game. As a result, it represents a good focal point to project performance into their sophomore year. (I'm hesitant to project anything over the long-term based on rookie performance as their are players, like Steve Nash, that need a few years to adjust to the NBA game.) I included a linear regression line, which indicates a positive correlation between rookie year April PIE and sophomore season PIE. (The anomalous point that is about 15% for his rookie season and 16% for last April is, of course, Anthony Davis.)

Finally, I pulled April PIE data for this season's rookies. The top twenty are listed below. If April's performance holds, we can expect that Carter-Williams, Plumlee, Olynyk, Diegn and Oladipo to lead next year's sophomore class. (In April, Dieng averaged a double-double in points and rebounds plus two blocks per game; Olynyk averaged almost 17 points and 7 rebounds a game while shooting 55%.)

Friday, April 4, 2014

Conventional Stats that Matter

With a growing focus on advanced statistics and measures, some analysis disregards conventional playing statistics, like steals, points or field goal attempts. But many "advanced" stats are based largely on conventional measures. For example, effective field goal %; (eFG%) simply places greater weight on three point made baskets to account for their value. More complex advanced stats, like PER, combine a range of individual and team conventional statistics, like assists, rebounds, steals, FG%, etc.

Now this isn't to say that advanced stats are deficient in any way. In many cases they are superior measures of performance--because of their ability to account for more than a single measure of play, like just rebounds, or just points--but conventional statistics are of intrinsic value.

I collected team data from the last three full NBA seasons (2011-12 was cut short 16 games by a collective bargaining agreement work stoppage) and included all conventional team stats from (for example . . . ). Next, I cheated and ran a correlation matrix to determine those conventional statistics most correlated with winning and most correlated with losing. Below are charts that show the two conventional statistics most correlated with winning and the one conventional statistic most correlated with losing. (Wins over these three seasons are plotted on the horizontal axis for the first two charts; losses are plotted on the horizontal line for the third chart.)

For each chart I included a linear regression line (blue line) with a 95% confidence region (grey area). The line and grey area give some indication of the relationship between wins and each conventional statistic. The upward slant of the regression line indicates a positive correlation between blocks (first plot) and assists (second plot) with wins. In other words, blocks and assists, rather than FG%, points, or rebounds might represent the most important indicator of a team's success (as measured by regular season wins) 

When I ran the correlation matrix, the conventional statistic most highly correlated with losing was fouls. While the association between blocks and assists with winning and fouls with losing does not necessarily hold with individual players, there is some evidence that at the team-level these are critical conventional statistics.

Sunday, March 23, 2014

2013-14 Player Salary per Win Share (as of March 22)

I wanted to update the list of most cost-effective contracts in the NBA through so I pulled player advanced stats and salary data from on March 22. As a rough measure of player efficacy I used Win Shares (WS), which attempts to estimate the number of wins a player contributes to his team in a given season (read this for Basketball-Reference's detailed explanation of the measure). I divided the player's 2013-14 salary by WS to determine, which player contributes the greatest number of wins to his team at the lowest cost to the organization. For some reference, the average cost per WS was $1,551,542 and the median cost per WS was $1,427,214.

Typically, I standardize statistics as per minute or per 48 minutes of performance to take into account for the fact that players that play more minutes also are likely to accrue more statistics than players that play fewer minutes. ( does provide WS per 48 minutes.) But taking salary into account changes the dynamics because a player receives his salary regardless if he plays 30 minutes a game or if he plays 2 minutes a game. As a result, the organization benefits from total WS (as opposed to WS/ 48) because the player receives his full salary and not some prorated amount based on performance.

I filtered the population of 2013-14 NBA players to those that have played 100 minutes or more, which left me with 422 players. The chart below shows the full spectrum of those 422 players: Ekpe Udoh is the most expensive per WS and Isaiah Thomas is the least expensive per WS. Among the 39 qualifying players with a negative WS, Kobe Bryant comes at the greatest cost to his team (i.e., his contract in 2013-14 is very burdensome and when he plays he has a negative effect on his team's chances of winning a game--this is a bad thing.)

First, the good--the table below lists the 10 most cost-effective contracts this season in reverse order. When taking salary into account, this table suggests that Isaiah Thomas, Lance Stephenson, and Chandler Parsons are the best players this season. To give you some context of cost/ WS of other notable players, consider: LeBron ($1.45M), Durant ($1.05M), Deron Williams ($4.01M), Kevin Love ($1.13M), and John Wall ($1.04M).


The five least cost-effective contracts of players with a positive WS are listed below. Ekpe Udoh and Charlie Villanueva have the most cost-ineffective contracts. But they're not the worst . . .

While the 5 most cost-ineffective players listed above prove burdensome on the financial well-being of their organizations, they all at least contribute to WS. Among players that have played at least 100 minutes in the 2013-14 NBA season, there are 39 players with a negative WS. In other words, when they are on the floor they actually hurt their team's chances of winning. It's one thing to be Jason Terry or Aaron Gray and to be paid a lot to help a little, it's another thing to be paid a lot and to hurt one's team. The table below shows that Kobe, Derrick Rose and OJ Mayo are the greatest offenders of this latter group. Ignoring injuries to players, like Bryant and Rose, from a cost-efficacy standpoint there is evidence to suggest that through March 22, OJ Mayo is the most burdensome player in the NBA.

Sunday, March 2, 2014

Blocks, Defensive Rebounding & Defensive Rebounding %

I've always assumed that defenders--centers, in particular--that focus more on blocking shots sacrifice opportunities for defensive rebounds as an attempted block puts the defender out of position to box-out opponents and secure defensive rebounds. To measure this assumption, I pulled blocks (Blk), defensive rebounds (DRB), and defensive rebounding percentage (% of DRBs a player grabs while on the floor) for centers from NBA stats (games as of February 28). I focused on centers that played at least 50 minutes and appeared in at least 5 games during the 2013-14 season (which resulted in a population of 103 centers).

I standardized blocks and DRBs both per minute played. DRB% was already standardized. Below are two charts. In the top one, I plotted Blks/ minute (vertical axis) against DRBs/minute (horizontal axis). In the bottom chart, I plotted Blks/ minute (vertical axis) against DRB%. For both I included a linear regression line (blue line) with a 95% confidence region (grey area). The line and grey area give some indication of the relationship between blocks and defensive rebounding. The anomalies in the upper right hand corner of each chart are Javale McGee in the top chart--indicating that he is exceptional as a defensive rebounder and shot blocker--and Cole Aldrich in the bottom chart--indicating that he is an exceptional shot blocker and grabs a disproportionate % of his team's DRBs. Both players present anecdotal evidence that shot blocking and defensive rebounding are unrelated.

If players with more blocks were poorer defensive rebounders then the blue line and grey area would start at the top left of the plot and slope down toward the bottom right of the plot. But that doesn't happen. In both plots the blue line is effectively horizontal, which indicates that there is no relationship between blocks and DRB or DRB%. In other words, blocks have no effect on a player's defensive rebounding.

There are some limitations to this approach to measuring the relationship between defensive rebounding and shot blocking. First, it would be better to have a measure of attempted shot blocks rather than just shot blocks. Unfortunately, the NBA does not collect this statistic (they do collect the number of shots a player has had blocked), and even if they did, it would be difficult to capture what qualifies as an "attempted shot block" as most field goal attempts are contested and, thus, could potentially be blocked. (In other words, does an attempted shot block only occur when a defender leaves his feet? Should the defender also have to have a hand raised in contesting the shot?)

Second, this approach only measures the relationship between shot blocking and two measures of defensive rebounding separately. It ignores intervening factors in the relationship, such as the DRB and shot blocking ability of teammates or a team's defensive scheme. (If there were a scheme where Kevin Love is only supposed to grab defensive rebounds and his teammates should focus on contesting shots--as often appears to be the case with the Timberwolves--then shot blocking could be indirectly related to DRB. As evidence of this Love is second to last in blocks per minute but second to best in DRB%.)

Sunday, February 16, 2014

Net & Defensive Team Rating

This chart helps explain why the Pacers are so dominant--they strap. I collected team data on Feb 13 from NBA Stats on offensive rating (points scored per 100 possessions), defensive rating (points allowed per 100 possessions), and net rating (offensive rating minus defensive rating). I measured offensive rating with the size of the circle next to the team (larger circles equate to greater relative offensive efficiency), defensive rating on the horizontal axis, and net rating on the vertical axis.

With respect to net rating, a team wants to be above the horizontal bar because that signals they score more points than they allow per 100 possessions . With respect to defensive rating, the further left the team falls on the chart, the better as that signifies that the team allows fewer points per 100 possessions. As the chart shows, only four teams--Pacers, Thunder, Warriors and Bulls--allow fewer than 100 points per 100 possessions. The Pacers, however, are anomalous--and exceptional--in just how few points they allow per 100 possessions (93.6). To give some scope of this defensive efficacy, the Jazz, who have the worst defensive rating, allow 107.3 points per 100 possessions.

Saturday, February 8, 2014

The best teams don't need second chances

Two things you would think successful NBA teams do well is score second chance points and have a high effective field goal percentage (a measure that takes into account the value of three point shots). I took team data from NBA Stats as of February 7th's games and plotted second chance points (vertical axis) against effective FG % (horizontal axis), and captured each team's winning percentage based on the size of the red circle (the bigger the circle equals the greater the win % for each team). The chart presents some evidence that the best teams don't really rely on second chances but are very effective shooters (in terms of eFG%). The exception being the Portland Trailblazers, who benefit from LaMarcus Aldridge and Robin Lopez, who average the 9th and 15th, respectively, most second change points per game this season. Of course, bad teams, like the Bucks and Celtics, do both poorly.

Friday, January 17, 2014

Most Clutch: 2013-14 (so far)

If I'm going to measure who has been the least clutch it makes sense to look at who has been the most clutch this season. (Aside: In light of the growing obsession with statistics, there has been thoughtful, recent discussion about the inaccuracy of assigning "clutch" as a quality to players. As far as we know, there isn't a clutch gene, thus some humans are not more inherently clutch than others. Despite this, some people and NBA players moderate stress--i.e., critical moments in games--better than others. And, while no compilation of basketball statistics will perfectly define a psychological state, we can look at a set of statistics and say that given the circumstances, like a close score and few minutes left on the game clock, some players are associated with better performance than others. Of course, if an exceptional player, like LeBron, shows up as "clutch", it just means that LeBron is exceptional regardless of the score or game clock.)

To measure clutch I pulled 2013-14 per game data (as of last night's games) from NBA Stats on 'clutch play', which I defined as consisting of a player's team being ahead or behind two points or fewer in the last two minutes of a game. To narrow the 338 players that met these two criteria, I focused on only those players that had had played at least five games in such situations. Further, I eliminated players that played at least five games but averaged fewer than one minute per game. That narrowed the sample of players to 166.

I measured "clutch" based on three factors: effective field goal % (eFG%), win percentage (Win %; % of qualifying games that resulted in a win for the player's team), and net rating (NetRtg). Net rating is the difference between offensive rating (points scored for a team/ 100 possessions while the player is on the floor) and defensive rating (points allowed by a team/ 100 possessions while the player is on the floor). A positive net rating indicates that the player's team scored more points than they gave up while he was on the floor (so, like a positive plus-minus). The 15 best players as measured exclusively by eFG% (or all players with an eFG% of one or greater) were:

Courtney Lee (MEM) 1.50
Ray Allen (MIA) 1.25
Patrick Patterson (TOR) 1.25
Robin Lopez (POR) 1.00
Dwyane Wade (MIA) 1.00
Norris Cole (MIA) 1.00
Draymond Green (GSW) 1.00
Jason Thompson (SAC) 1.00
Ryan Anderson (NOP) 1.00
Marcin Gortat (WAS) 1.00
PJ Tucker (PHX) 1.00
Dwight Howard (HOU) 1.00
Miles Plumlee (PHX) 1.00
Jonas Valanciunas (TOR) 1.00
Michael Kidd-Gilchrist (CHA) 1.00

The 11 best players as measured exclusively by Win % were (the fact that 8 of the 11 players were from the Spurs or 76ers indicates that those two teams have fared well when the score was close and there was less than two minutes in the game):

Player Win%
Marvin Williams (UTA) 100.0%
Marc Gasol (MEM) 100.0%
Kawhi Leonard (SAS) 88.9%
Michael Carter-Williams (PHI) 87.5%
Kenneth Faried (DEN) 83.3%
Evan Turner (PHI) 80.0%
James Anderson (PHI) 80.0%
Spencer Hawes (PHI) 80.0%
Manu Ginobili (SAS) 80.0%
Thaddeus Young (PHI) 77.8%
Tony Parker (SAS) 77.8%

The ten best players as measured exclusively by NetRtg were:

Wesley Johnson (LAL) 100.3
Marc Gasol (MEM) 76
Pau Gasol (LAL) 75.8
Dwyane Wade (MIA) 59.3
Norris Cole (MIA) 54.9
Kenneth Faried (DEN) 53.5
Tyreke Evans (NOP) 52.7
Robin Lopez (POR) 49.8
Steve Blake (LAL) 48.2
Marvin Williams (UTA) 46.5

And the ten worst were (the fact that 8 of the 10 players were from the Timberwolves or Bucks indicates that those two teams have fared poorly when the score was close and there was less than two minutes in the game):

Nikola Pekovic (MIN) -110.4
Corey Brewer (MIN) -107.2
Kevin Love (MIN) -106.9
Ricky Rubio (MIN) -102.1
Kevin Martin (MIN) -94.1
Glen Davis (ORL) -61.5
O.J. Mayo (MIL) -56
Brandon Knight (MIL) -47
Taj Gibson (CHI) -45.7
Ersan Ilyasova (MIL) -43.7

Next I standardized each category to select the 40 players that performed best across all three measures of "clutch" play. To illustrate the results, I created the chart below, which captures Win % on the X-axis, NetRtg on the Y-axis and eFG % is measured by the size of the circle next to the player's name. Of this subset of "clutch" players, the most clutch have larger circles next to their name (no circle indicates an eFG% of 0%), and are located in the top right of the box, which indicates that they win a greater percentage of qualifying games, and are on the court when their teams scores more points per 100 possessions than they give up. 

Based on NetRtg, Wes Johnson and the Gasol brothers stick out as exceptionally effective. With respect to Win %, after Marc Gasol and Marvin Williams, who have won all games based on the defined scenarios, Kawhi Leonard, Michael Carter-Williams, and Kenneth Faried appear to have anomalously high percentages. In terms of eFG%, Dwayne Wade, Robin Lopez, Jason Thompson, Ray Allen and Draymond Green are all exceptional. Taken together it is fair to say that through almost half of the 2013-14 season based on NetRtg, eFG% and Win % in the final two minutes of a game when a player's team is above or behind by two points or fewer, Marc Gasol, Marvin Williams, Dwayne Wade and Robin Lopez are among the most "clutch" players in the NBA.

Friday, January 3, 2014

Least Clutch: 2013-14

Anyone who watches the Wizards or any average to marginally better than average team recognizes that the difference between a 10, 15 and 20 win team right now is largely determined by play in the second half of the fourth quarter. From competitive high school basketball up to the NBA winners know how to close games out and losers tend to collapse in the closing minutes. Average teams waver between those two poles. To get a better understanding of players that might adversely affect their teams in these clutch scenarios, I attempted to identify the least clutch players this season.

I pulled 2013-14 per game data (as of last night's games) from NBA Stats on 'clutch play', which I defined as consisting of a player's team being behind four points or fewer up to being tied in the last four minutes of a game. (More succinctly--trailing closely in the final few minutes.) A total of 336 players met these first two criteria.

I wanted to winnow the group further to focus only on players that have received somewhat significant time in these circumstances so I eliminated players with fewer than five games played (126 players). From this group I eliminated players if they had averaged fewer than one minute per game (16 players). This left me with 194 players.

I measured individual clutch player based on three factors: effective field goal % (eFG%), turnover ratio (TO ratio; # of TOs/ 100 possessions), and defensive rating (DefRtg; points/ 100 possessions while the player is on the floor). Based on these three metrics a "clutch" player should have a high eFG% and low TO ratio and DefRtg. To further reduce the group of 194 players I first eliminated those with an eFG% greater than 50%. This eliminated 59 players. Those with the best eFG% that met the previous criteria are identified below:

Gerald Wallace (BOS) 125.0%
Manu Ginobili (SAS) 125.0%
Spencer Hawes (PHI) 121.4%
Iman Shumpert (NYK) 116.7%
Shawn Marion (DAL) 110.0%
Chris Bosh (MIA) 105.6%
Jordan Hill (LAL) 100%
Robin Lopez (POR) 100%
Miles Plumlee (PHX) 100%
Derrick Favors (UTA) 100%
Dwight Howard (HOU) 100%
Ekpe Udoh (MIL) 100%
Norris Cole (MIA) 100%
Andre Drummond (DET) 100%
Trevor Booker (WAS) 100%

Of the remaining 135 players I focused next on TO ratio and I eliminated those with a TO ratio less than 10. This eliminated 83 players, 60 of whom had a 0 TO ratio. Finally, of the last 52 players I focused on DefRtg and removed those with a rating below 100. This included 23 players. The ten players with the lowest DefRtg that met all previous criteria are identified below:

Jimmy Butler (CHI) 71.4
Jarrett Jack (CLE) 71.9
Tristan Thompson (CLE) 72.3
Trevor Ariza (WAS) 72.5
DeJuan Blair (DAL) 73
Marcin Gortat (WAS) 73.8
Courtney Lee (BOS) 75.2
Carlos Boozer (CHI) 76.1
Luol Deng (CHI) 79.6
John Wall (WAS) 80.3
The chart below captures TO ratio on the Y-axis, DefRtg on the X-axis and eFG% is measured by the size of the circle next to the player's name. Of this subset of relatively unclutch players, the most clutch of the unclutch (i.e., the better players) would have larger yellow circles next to their name (no circle indicates an eFG% of 0%), and be at the bottom left of the box, which indicates that they turn the ball over infrequently, and allow relatively fewer points per 100 possessions. 

The chart shows that most in this subcategory of unclutch players are lumped largely in the same area with a few exceptions. Tyreke Evans is noteworthy for his abysmal defense, but is an effective offensive player in the sense that he has relatively few turnovers and he shoots the ball pretty well. Most significant--and least clutch--are Zaza Pachulia, Channing Frye then Kyle Singler. These three, led by Pachulia, turn the ball over at an anomalously high  rate, shoot 0% eFG, and are among the five worst defenders based on DefRtg.