In the wake of my last few posts on diminishing returns in rebounding, a lot of people have suggested looking at how diminishing returns applies to scoring. This is a more complex issue, but I think some of the same methods can be used to try to understand what’s going on in this part of the game of basketball. For rebounding, we were just looking at the relationship of player rebounding to team rebounding. For scoring, we have to look at the relationship of player efficiency and player usage to team efficiency. Diminishing returns for scoring is really just another way of framing the usage vs. efficiency debate which has been going on in the stats community for years. Does efficiency decrease as usage increases? By how much? What, if any, value should be placed on shot creation? Are coaches using anything near to the optimal strategies in distributing shot attempts among their players? Is Allen Iverson wildly overrated? Was Fred Hoiberg criminally underutilized? The big names in basketball stats like Dean Oliver, Bob Chaikin, John Hollinger, Dan Rosenbaum, and Dave Berri have all staked out positions in this debate. For some background, see here and here and here and here and here and so on and so on. A lot of words have been written on this topic.
The major difficulty in studying the usage vs. efficiency tradeoff is the chicken-and-egg problem - does a positive correlation between usage and efficiency mean that players’ efficiencies aren’t hurt as they attempt to up their usage, or just that in seasons/games/matchups where players are more efficient (for whatever reason) they use more possessions? For instance, if a player is facing a poor defender (which will increase his efficiency) he (or his coach) might increase his usage. But it could be that this positive correlation is drowning out the presence of a real diminishing returns effect. If players go from low-usage, low-efficiency against a good defenders to high-usage, high-efficiency against poor defenders, it still could be the case that if they tried to increase their usage against average defenders their efficiency would decrease. Defender strength is just one of the factors that can cloud things - another confound comes from game-to-game or season-to-season variation in a player’s abilities (e.g. a player being “hot” or having an “off game”, a player being injured or tired, or a player using more possessions as his skills improve from year to year).
By using the method from my last study on diminishing returns for rebounding, it’s possible to largely avoid this chicken-and-egg problem. This method looks at situations in which some or all of the players on the court were forced to increase their usage (relative to their average usage on the season). And on the other side, it looks at lineups in which some or all of the players on the court were forced to decrease their typical usage. By looking at these forced cases the method minimizes the confounds from players increasing or decreasing their usage by choice in favorable situations.
Following up on my last post, I’m going to look at the issue of diminishing returns for rebounding from a different angle. The new method I’m going to use has several advantages over the previous one (and some disadvantages). What I like best about it is that it does a great job of presenting the effect of diminishing returns visually, rather than just through a table of numbers.
The approach I will use was first suggested to me by Ben F. from the APBRmetrics forum. But before I got a chance to try it out, another poster, Cherokee_ACB, presented results of his own using a similar method. So this post can be seen as building on the ideas of both of these posters.
Instead of comparing individual players’ rebounding percentages to the rebounding percentages of the lineups they played in, this method takes into account the rebounding of all five players on the court for a team. Instead of just speculating about how well a team would rebound if it put five strong rebounders on the court together (or five poor rebounders), it looks at what has actually happened in such situations in the past.
There has been a lot of discussion in recent months about the importance of rebounding on the player level. Much of this debate has been in reaction to the high value that Dave Berri’s Wins Produced player rating puts on rebounds. On Berri’s blog there have several posts with long, insightful debates in the comments about the issue (that is, if you ignore the unfortunate mudslinging often directed at those with differing points of view). In particular, I would recommend the comments sections of “The Best One-Two Punch in the Association”, “Chris Paul vs. Deron Williams, Again”, and “How Has Texas Survived the Loss of Kevin Durant?”. There have also been some good debates on the topic in the APBRmetrics threads, “Current season Win Scores/Wins Produced” and “Can some one explain the ‘possession cost’ scheme?”.
These are wide-ranging debates, involving such issues as the relative value of rebounding versus scoring and the apportioning of credit for a defensive stop between the defensive rebounder and his teammates. The issue that I want to pick up on is the extent to which the law of diminishing returns applies to rebounding.
It’s taking longer than I anticipated to compile and analyze the context-dependency of various player stats by the method I outlined in my last post, so in the meantime I would like to shift gears and introduce a method that uses team stats to try to understand whether the offensive or defensive team controls various aspects of the game.
There’s an old saying in baseball that “good pitching always beats good hitting.” I want to examine what a claim like this is trying to get at, look at a method that attempts to objectively analyze whether it’s true, and then apply that method to many areas of basketball and see what we can learn.
At that the end of my recent post on evaluating player ratings I said that the next step would be to take a step back from comprehensive ratings and look at how the component stats they are built from change in different contexts. That is what I will begin to look at in this post.
The methodology I’m going to use is pretty complicated, so instead of just presenting the results I’m going to use this post to explain in a step-by-step manner the techniques I plan on using. I’m also going to try to point out what I see as potential problems, but in many ways I’m learning as I’m going so I may miss some things. I’d welcome any critiques or suggestions from anyone who knows what they’re doing (or anyone who pretends to know what they’re doing, like me).
To test out the height ordering measure I came up with, and to try some of the methods described in recent posts on the Sabermetric Research blog, I decided to run some correlations to look at the relationship between a player’s height and his rebounding performance.
For the 2006-07 season, I looked at all players who played at least 200 minutes (which came out to 397 players, counting stints with different teams separately). I chose 200 minutes as the cutoff because the correlations seemed to stabilize at that level (at lower cutoffs the correlations were lower because of fluky low minute guys, and at higher cutoffs the correlations were very similar to what they were at the 200 minute cutoff). The explanatory variables that I used were height (in inches) and height ordering (which is on a 1 to 5 scale, with 1 indicating that the player played all of his minutes as the shortest player on the court for his team). The response variables were defensive rebounding percentage and offensive rebounding percentage. DRB% is an opportunity rate measuring DRB/(DRB opportunities), or more specifically, DRB/(team DRB while the player was on the court + opponent ORB while the player was on the court). ORB% is similar but uses ORB opportunities. The actual formulas, which estimate the on-court part, are as follows:
DRB% = DRB/((5*MIN/tmMIN)*(tmDRB + oppORB))
ORB% = ORB/((5*MIN/tmMIN)*(tmORB + oppDRB))
Last season, among players who played at least 200 minutes, Kevin Garnett led the league in DRB% at 30.7%. Earl Boykins finished last at 5.1% for his stint in Denver. For ORB%, Justin Williams was first at 17.6%, while Keith McLeod was last at 0.3%.
Identifying a player’s position is useful for all sorts of statistical analysis of basketball, but unfortunately position in basketball is not nearly as well-defined as position in baseball. The traditional breakdown into point guard (1), shooting guard (2), small forward (3), power forward (4), and center (5) works some of the time, but breaks down at the edges. Some teams’ offensive systems don’t differentiate between the roles for the two wing positions (SG and SF), or between the two post positions (PF and C). Some players play one positional role in their team’s offense yet typically guard an opposing player that plays a different positional role in his offense (e.g. Kirk Hinrich, who plays PG for the Bulls offensively but often defends opposing SGs). Many players play different positions at different times in the same game depending on which teammates they are on the court with. For all these reasons and more, having a list saying Player X is a PG, Player Y is a PF, Player Z is a SF, etc. is bound to be lacking.
How can positions be assigned in a more objective and informative manner?