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Thinking About NBA Statistics: A Proposal

http://www.depressedfan.com/img/iguodala.jpg[Note: I'm just as anxious to get to the draft and next season as everyone else, but it's a long way off.  Here's something different to think about in the meantime ...]

In many of the discussions we have here at Depressed Fan and other "hardcore" NBA blogs, people quote and then debate the meaning of different statistics.  Defensive statistics, in particular, are often thought to be misleading, and with good reason.  For example, if Lou's man blows by him and Brand goes over to help but Sammy doesn't rotate to Brand's man, does the resulting dunk by Brand's man count against Brand?  Or on offense, if Jrue beats his man, draws a defender, and dishes to Jason Smith who fumbles it out of bounds, is the turnover solely Jrue's responsibility?  Somehow, there has to be a better way of assigning credit and blame.  I thought about this for a while and came up with a system that I'll describe after the break ...
The system is based on points per possession, with the initial observation being that teams in the NBA average around 1 point per possession (PPP).  Actually, the average number among all NBA teams is closer to 1.05, but my system converts easily to PPP and its relatives, offensive/defensive efficiency (which is points per 100 possessions).  So the idea then is to score each possession relative to the average 1 PPP.  An empty possession is worth -1, a 1-point possession is worth 0, a 2-point possession is worth +1, and a 3-point possession is worth +2.  But how are the points assigned?

On offense:
  • A made 2-point basket is +1 and might be divided into +0.5 for the passer and +0.5 for the shooter if the pass was responsible for the shot.
  • A made 3-point basket is +2 and might be divided +1.5/+0.5 or +1/+1 for the passer/shooter if the pass resulted in an open shot.
  • 2 made free throws is +1 but might be divided +0.5/+0.5 for the passer and shooter if the pass set up the foul shots.  1 of 2 free throws is a 0.
  • A turnover is -1 and might be divided -0.5/-0.5 for the passer and catcher if the responsibility is partly the fault of the catcher.
  • A missed field goal attempt resulting in an opponent defense rebound is -1 for the shooter.  The one exception would be if someone else dribbled the clock down and gave the shooter only a desperation attempt (in which case it would be divided -0.5/-0.5).
  • A missed field goal attempt resulting in an offensive rebound is -0.5 for the shooter and +0.5 for the offensive rebounder.
On defense:
  • A made basket is either -1 or -2 (for a 3-pointer), with blame assigned partly to the defender nearest the shooter and partly to the defender whose lack of defense resulted in the shot.
  • 2 made free throws is -1 and is assigned to the defender who fouled the shooter, unless another defender's poor defense resulted in the foul (in which case blame is divided -0.5/-0.5).
  • A turnover is +1 and is credited to the defender who forced the turnover.  An exception is if the turnover is "unforced" (e.g., an opponent dribbles the ball off his foot) in which case the team is credited with a +1.
  • A missed basket resulting in a defensive rebound is usually a +0.5 for the defender and +0.5 for the rebounder.  If exceptional defense results in a poor shot and easy rebound, it might be +1 for the defender.
  • A missed basket resulting in an offensive rebound is +0.5 for the defender and -0.5 for the person who gave up the offensive rebound.
Currently, I don't divide up partial credit into anything smaller than halves, but in theory partial credit can be assigned to whatever precision the scorer wants.  At the end of a game, the individual numbers on offense and defense can be summed to get the total relative to 1 PPP.  For example, if the Sixers win 90-82 and there were 80 possessions for each team, the sum on offense should be +10 and the sum on defense should be -2. The interesting part would be how the sums come about.

As an example, I went back to the 4th quarter of the Sixers' win over the Lakers on 3/17/09.  Now, before the Iguodala Haters start complaining that it isn't a representative game, please note that this is one of the few Sixer games I still have on my DVR and it's just an example.  The Sixers came into the quarter trailing 73-62 and outscored the Lakers 32-20.  Each team had 20 possessions, so the Sixers were +12 on offense and 0 on defense.  Here's the play-by-play and how I "scored" each play according to the above system.  Laker possessions are in purple, Sixer possession are in red.

  • Lou caught in traffic, Farmer hits open 3 (Lou -2)
  • AI9 penetration and score (AI9 +1)
  • AI9 steals pass (AI9 +1)
  • AI9 pass to Lou for lay-up (AI9 +0.5, Lou +0.5)
  • KB penetrates, passes to Gasol for open 16-ft jump made (AI9 -0.5, Evans -0.5)
  • AI9 missed 23-ft 3-pt, Sam off. reb. (AI9 -0.5, Sam +0.5)
  • AI9 draws shooting foul, 1 of 2 FT (0)
  • [Ivey and Marshall in for Sam and Miller]
  • Marshall steals pass (Marshall +1)
  • Lou pass to AI9 for dunk (Lou +0.5, AI9 +0.5)
  • KB misses jumper, loose ball foul on Marshall rebound (AI9 +0.5, Marshall +0.5)
  • Lou pass to Marshall for open 3-pt made (Lou +0.5, Marshall +1.5)
  • Gasol penetrates, passes to JPowell for lay-up (Evans -1, overplay set up score)
  • AI9 penetrates for layup plus foul, 1 of 1 FT made (AI9 +2)
  • KB misses 3-pt, Gasol off. rebound (AI9 +0.5, Evans -0.5)
  • Farmar missed 3-pt, Gasol off. rebound (Lou +0.5, Evans -0.5)
  • Gasol missed hook, Evans def. rebound (Evans +1)
  • Ivey scoop pass to Evans for lay-up (Ivey +0.5, Evans +0.5)
  • JPowell missed 5-ft hook, JPowell off. reb. (Marshall +0.5-0.5=0)
  • JPowell traveling (team +1)
  • Ivey penetration score (Ivey +1)
  • Marshall steals from KB (Marshall +1)
  • AI9 transition lay-up (AI9 +1)
  • KB missed jumper, Evans rebound (AI9 +0.5, Evans +0.5)
  • Lou missed jumper, Evans off. rebound (Lou -0.5, Evans +0.5)
  • Evans rebound basket (Evans +1)
  • Odom missed wide-open 3-pt, Evans def. rebound (team +0.5, Evans +0.5)
  • Lou passes to Marshall for 3-pt made (Marshall +1.5, Lou +0.5)
  • Ariza 3-pt made off Farmar penetration (Ivey -1, Lou -1)
  • Ivey 10-ft jump blocked, JPowell rebound (Ivey -1)
  • Farmar missed 3-pt after good AI9 defense on KB, Laker team off. reb (AI9 +0.5, team -0.5)
  • Ivey steals KB pass (Ivey +1)
  • Ivey pass to Lou for lay-up (Ivey +0.5, Lou +0.5)
  • KB missed 3-pt, Gasol off. rebound (AI9 +0.5, Evans -0.5)
  • Gasol rebound basket (Marshall -1)
  • Ivey missed 3-pt, KB rebound (Ivey -1)
  • Gasol fouled by Marshall, 2 of 2 FT (Marshall -1)
  • [Miller returns for Ivey]
  • Miller missed 3-pt, KB rebound (Miller -1)
  • Odom 7-ft hook made (Marshall -1)
  • Lou draws 2 defenders, passes to Marshall for open 3-pt made (Lou +1, Marshall +1)
  • Fisher missed 3-pt after KB bad pass, Odom off. rebound (team +0.5, Evans -0.5)
  • Gasol fouled by Marshall, 2 of 2 FT (Marshall -1)
  • Lou missed penetration, Ariza reb. (Lou -1)
  • KB missed 3, Evans defending on switch, Lou rebound (Evans +0.5, Lou +0.5)
  • Miller pass stolen by Gasol (Miller -1)
  • Gasol missed lay-up, Evans rebound (Evans +1)
  • Lou lay-up blocked, Gasol rebound (Lou -1)
  • KB 22-ft jumper made (AI9 -1)
  • AI9 3-pt made (AI9 +2)

Sixer totals for the quarter were as follows.  On offense: Iguodala +6.5 (+7-0.5), Marshall +4 (+4), Evans +2 (+2), Lou +1 (+3.5-2.5), Sam +0.5 (+0.5), Ivey 0 (+2-2), Miller -2 (-2), Total=+12.  On defense: Iguodala +2 (+3.5-1.5), Evans 0 (+3.5-3.5), Ivey 0 (+1-1), Marshall -1.5 (+3-4.5), Lou -2 (+1-3), Team +1.5 (+2-0.5), Total=0.

A couple of comments.  First, this quarter was relatively easy to score defensively because the Lakers attempted zero transition shots.  It's harder to assign credit or blame in transition.  It was also relatively easy to score because the Lakers rarely made more than one pass after a switch.  As we all know, the Sixers this past year switched a lot, and it was sometimes hard to keep track of who was supposed to be guarding whom.  Second, there is some subjectivity to this scoring method, but I claim that all NBA defensive statistics involve some subjectivity.  Finally, it should be noted that 0 is actually a good defensive team score and a poor offensive score.  If Iguodala, guarding primarily Kobe, put up a 0 on defense, that would be an excellent result, because in most Laker games, Kobe contributes heavily to their positive team offensive score (i.e., their offensive efficiency comes in large part from him).

So, let me know what you think, especially if you have any suggested tweaks to the scoring system (I just came up with it, so there certainly could be improvements).  If it's an interesting idea, I might try it on selected games this upcoming year.

by Statman on Jun 2 2010
Tags: Basketball | Offseason | Sixers | Statman |