Projecting Success

Reed —  October 22, 2008

Now that we’ve been talked off the Kobe ledge and feel reasonably comfortable with Odom’s role, let’s move on to something less fun … statistical analysis. What follows is my attempt to weed through stats from last year and projections for this year and draw a few conclusions about the team’s likely performance. I recognize there are numerous flaws, big and small, in my assumptions and analysis, but nevertheless press on in the hope of adding some piece to the puzzle.

PER Differential

There are numerous bottom line statistics that measure individual performance, but I will focus on one I think is particularly illuminating – PER differential. “PER” tells us how efficient a player is in scoring, helping others score, gaining possession of the ball, and protecting possession of the ball. “PER allowed” tells us how efficient a player is in stopping his direct opponent from doing the same. “PER differential” (PER minus PER allowed) tells us the net effect of a player’s production on both sides of the court. In doing so, it weeds out players who appear productive by piling on box score stats, but are ultimately liabilities because they do so inefficiently. For example, in fantasy circles Josh Smith and Gerald Wallace are known as elite defensive players given their high combination of steals and blocks, yet they both allow a relatively high 18.2 PER allowed. By way of reference, Tayshaun Prince, who gets very few steals and blocks, has a sparkling 12.4 PER allowed. PER differential also helps us distinguish between offensive wonders and more well rounded players. Amare Stoudemire, for example, was one of the best offensive players in the league last year, but also one of the worst defensively – with one of the highest PERs and PERs allowed (27.6 PER, 19.2 PER allowed, +8.4 differential). Bynum, by comparison, while less flashy overall and less dominant on offense, had a stronger net effect (22.6 PER, 13.1 PER allowed, +9.5 differential).*

*(Note: for reasons I won’t get into here, the PER ratings listed by Hollinger and are slightly different, with Hollinger’s always a fraction smaller. All PER references here are on Hollinger’s scale, so anytime I use data from I normalized to Hollinger’s lower scale).

Team PER Differential

What I want to focus on here is using individual PER differentials to predict team success, particularly when it comes to the Lakers. There is a close (and obvious) statistical correlation between a team’s win-loss record and the cumulative PER differential of its individual players (taking into account minutes allocation). lists the PER, PER allowed, and PER differential for each team by position. By adding up the five positional PER differentials, we can generate a total team PER differential. I did this and then mapped team wins as a function of team PER differential to measure correlation, as shown below.

Running a linear regression (not shown), we find the correlation coefficient between the variables is very high: .941. This is an obvious finding, as we already know that PER and PER allowed, given their focus on efficiency in scoring and preventing points, is a powerful statistic in tying individual to team success. Unsurprisingly, the Celtics and Pistons finished 1-2 in both team PER differential (+17.4, +14.4) and wins (66, 59). Also unsurprisingly, the Heat, Sonics, and Knicks finished bottom 3 in PER differential (-14.6, -14.3, -13.8) and with 3 of the 4 worst records in the league (23, 20, and 15 wins). The Lakers were third in the league in wins (57) and fourth in PER differential (+11.4). By calculating the slope of the regression line fitting the data, we can determine that each extra point of team PER differential is worth an extra 1.3 team wins (with a 0 differential tied to 41 wins, as we would expect).

What is more interesting than this obvious connection is the potential to use individual player PER projections to project likely team success. Recently, John Hollinger came out with his PER projections for every player in the league. By using these and forecasting minutes played for each Laker at each position, it is possible to come up with a rough estimate of total team PER for this season – and then use that to project wins. I did this. My methodology:

1. Project minutes played per game at each position for our 12 (likely) rotation players;
2. Use Hollinger’s PER projections and my minute allocations to determine the net PER for each of the five positions;
3. Because Hollinger does not project PER allowed, I used last year’s numbers for each player from (thinking that our unchanged roster would lead to basic stability in defensive numbers), and calculated net PER allowed for each position;
4. Using the projected PER and PER allowed, I calculated the net PER differential for each position, and then the team as a whole.

The following spreadsheet shows the results (and makes it easier to understand the process):

As you can see, the projected team PER differential is +15.1. This (a) would have been second in the league last year, (b) is a significant improvement over last year’s +11.4, and (c) results in a projected total of 62 wins. A few notes:

Changed Assumptions

I tweaked the numbers in just a few cases. First, Hollinger projects Odom as having a 15.93 PER (down from 16.9 last year). Looking back at past seasons, it is apparent that Lamar has a much higher PER at PF than SF, but he will split time this year between the positions. Thus, my spreadsheet reflects this as I give Odom a 13.73 PER at SF and a 16.89 PER at PF (which, taking into account that I project him playing 2/3 of his minutes at PF, leads to a net PER of Hollinger’s 15.93). Second, Ariza’s data from last year was too small a sample size so I used his defensive numbers from 2007 with Orlando when inputting his PER allowed.

Roster Thoughts

• The Lakers have great talent and depth. Thanks to Kobe, Gasol, and Bynum, we project to be very strong at three positions (SG, PF, C) and among the league leaders in two (SG, C). At SF, PF, and C we not only have a star starter (Kobe, Gasol, Bynum), but backups with positive PER differentials (Sasha, Odom, Gasol). This is a rare blessing.
• The main improvement over last year comes at PF and Center, which is unsurprising given that we expect a full season out of both Bynum and Pau at those spots.
• As expected, SF is a mess. There are simply too many bodies to give anyone meaningful minutes. Based purely on the numbers, we should focus our minutes there on Ariza and Kobe (and to a lesser extent Odom), especially as Sasha is very productive at SG and worthy of more minutes (shifting most of the SF minutes to Ariza and Kobe and giving more time to Sasha would lead to an increase in 2-4 projected wins). Ariza is the only true SF (Kobe excepted) with a positive differential (+2.19). However, based on the preseason, I am optimistic that Radmanovic can be more productive than projected. As we’ve all discussed, at some point Phil needs to ride the most productive players at SF and sit the others.
• If Hollinger is right and Fisher regresses while Farmar improves, more of the PG minutes should be transitioned to Jordan. Last year they split at 27 for Fisher, and 21 for Farmar; I projected an even 24/24 this year, but it might make sense to give Jordan a little more than that.
• Our best lineup on paper (Farmar, Kobe, Ariza, Gasol, Bynum) has an incredible PER differential of 28.0 (if that lineup played all 48 minutes of every game, the team would be projected to finish 77-5). Last year, the Spurs had the best 5 man lineup in terms of PER differential (Parker, Finley, Ginobili, Thomas, Duncan) at +31.3. The Celtics had the second best at +28.8 (Rondo, Allen, Pierce, KG, Perkins). The difference between those teams was that the Celtics’ production did not fall off the cliff when they went deep into their bench, and the Spurs did (in addition to the fact that PER really disfavors pure defensive specialists like Bowen). Clearly, this Laker team has strength in both being able to sport very effective 5 man lineups, and in having depth to not lose significant production when it goes 8-9 men deep in the rotation (we have seven players who project to have positive PER differential; many teams have multiple negative players starting). But, there also remains room to create a much more dominant 5 man lineup by improving (whether internally or via trade) at the PG or SF position.
Hollinger projects PER decreases for most of our players: Fisher (sizable), Kobe, Sasha, Radmanovic, Odom, Walton, Gasol, and Bynum. Basically every rotation player on the team except Farmar and Ariza. I buy his arguments for Fisher, Kobe, and (to a lesser extent) Sasha. Some of the drops are significant and puzzling: Gasol and Bynum. I understand that they will share responsibilities and numbers, but PER is also about efficiency. I’d be surprised if their mutual presence seriously harms each of their individual PERs, especially with Bynum young and developing. I think Walton bounces back from a poor showing last year and Radmanovic has room to improve. Overall, I think Hollinger’s projections are a touch on the low side for the team. If I’m right, and many of these players just hold steady with their production (in terms of efficiency) from last year, the team would project closer to 65 wins.

Methodological Problems

This analysis is obviously rough and there are a few problems with my analysis, including: (1) failure to take into account how roster changes will affect individual PERs (although I understand Hollinger’s projections did so, as shown by Pau and Bynum both having lower projected PERs than last year); (2) using last year’s PER allowed stats (there was simply no way to accurately project changes for this year, but I hope our basic roster and style stability will lead to a small error size); (3) my minute allocations do not take into account possible injuries (although I do try to project on the low side – e.g. Bynum may play more than 30 minutes a game by the end of the year, but he’ll also probably miss a few games); and (4) most importantly, statistics (including PER) have significant, inherent limitations and overlook things like chemistry, effort, health, attitude, style synergies, etc. This analysis is intended to be interesting and spark discussion, not be an end all projection of the team’s performance this year.


We don’t need statistical projections to tell us this is a very talented, deep Laker team. With health, the forecast of 62 wins is reasonable, even in the increasingly brutal West. How many wins do you predict? What players have the potential to make a leap in their production and efficiency this year (like Sasha did last year)? Who might regress? Is Hollinger right that both Bynum and Gasol will lose a little individual efficiency when playing together and see a drop in their PERs this year, or is it possible they could become more efficient (I, for one, think they could both shoot over 55%, which would make our offense historically dominant)?