Tuesday, January 11, 2011

Project Defensive Score Sheet: Kansas@Michigan

As I mentioned a couple weeks ago, I just read (most of) Dean Oliver’s Basketball On Paper for the first time.  A few of the chapters focus on defense, and there’s one specifically about individual defensive stats.  Oliver laments the lack of useful defensive data, and talks about a WNBA pet project of his: Project Defensive Score Sheet.  This was (is?) an effort to keep track of individual defensive credit or blame for all of the shots and turnovers a team allows.  After reading the chapter, I rushed to the internet in hopes of finding the results of his efforts, but was disappointed to find very little information available, and very few people attempting to continue or expand on the project.  [See the end of this post for a list of what I did find.]

I thought it would be fun, and possibly illuminating, to keep track of Oliver’s individual defensive stats for some college basketball games.  In a happy little coincidence, the top defensive team in the country happens to also be my favorite team, so I decided to try to chart as many Kansas games as time and TV coverage would allow, starting with this past Sunday’s game against Michigan.

It’s amazing how different the game-watching experience was when I was forced to pay close attention to defensive players.  I would never have otherwise noticed how active – and cagey – Jordan Morgan is.  More on that later.  Anyway, at this point, I don’t have any brilliant ideas on what to do with the numbers, so I’ll simply start by posting the results of each game.

Here’s the table (click for larger view); the explanation is after the break.



  • Taken from the box score
    • Min – Minutes played
    • DREB – Defensive REBounds
  • Tracked by me
    • FM -  Forced field goal Miss – when a defender forces an offensive player to miss a shot from the field.  Oliver separates FM from Blocks, but I’ve lumped them together here.
    • FTO – Forced TurnOver – when a defender forces an offensive player to turn the ball over.  Again, Oliver separates out Steals, but I’ve combined them, partly because because I don’t know which plays the official scorekeeper would actually count as steals.  One thing to note here is that a player who draws an offensive foul is always credited with a FTO, even if it’s just a moving screen.
    • FFTA – Forced missed Free Throw Attempt – missed foul shots resulting from a defender’s foul
    • DFGM – allowed Defensive Field Goal Made – when a defender allows an offensive player to score a field goal over him or by dribbling by him
    • DFTM – allowed Free Throw Made – made free throws resulting from a defender’s foul
  • Calculated Tallies
    • Stops – the credit a defensive player gets for actions that contributed to ending an opponent possession.  This isn’t as simple as adding FM + FTO + 0.4*FFTA, because the credit for a missed shot has to be shared with the defensive player who rebounds it.  The formula is more complex than you might think, and includes a sliding weight for FM vs. DREB, based on how difficult those actions seem to be in each particular game, so I’ll just refer you to Appendix 3 of Basketball On Paper.
    • ScPos – Scoring Possessions allowed by a player.  This is essentially just DFGM plus a FT-related factor.  I’ll again refer you to Basketball On Paper for details.
    • DPoss – [Stops + ScPos] – total Defensive Possessions that were credited to (or blamed on) a player.
  • Calculated Metrics
    • Stop% – [Stops/DPoss] – the fraction of an individual player’s credited defensive possessions that ended with 0 points. Essentially the inverse of offensive Floor%.
    • %DPoss – [(Min/40)*DPoss/TeamDefensivePossessions] (for a non-OT game) - the percentage of team defensive possessions faced by an individual defender.  Analogous to %Poss on offense.
    • DRtg – [(1–%DPoss)*TeamDRtg + %DPoss*(100*TeamDefPtsPerScPoss*(1-Stop%))] – individual Defensive Rating.  Gives a player credit for stops and scoring possessions he was directly involved in, then assumes a nebulous team-average performance in the other possessions.  This is the analog of offensive rating.


1.  I’m sure you spied all the decimals in the “tracked by me” stats.  Why are they there?  Well, because defensive actions aren’t nearly as discrete and well-defined as offensive ones.  The player who touched the ball last gets 100% of the credit for a made basket, but who gets credit for forcing a turnover when a two-man trap causes a player to travel?  I gave each trapping player half credit, because that seemed to be Oliver’s original intent.  But I found some plays where even that didn’t cut it.  I can’t remember the specific players involved at this point, but there was one play on Sunday where a Michigan player dribbled into the lane and was immediately confronted with a two-player wall blocking him from the basket.  He turned to his right, ran into a third Kansas player, bounced backwards and turned further rightwards, and a fourth KU player stripped him of the ball while he was concentrating on not falling over.  I’m fairly sure the official scorer gave Jayhawk #4 a steal, but I split it 4 ways.

2.  Speaking of the official steal being credited to only one player, Tyrel Reed’s official line from Sunday gives him 4 steals, while I only give him 2.6 forced turnovers.  I’m guessing the play above accounts for 0.75 of that difference, but that still doesn’t get us all the way there.  I believe there was another play where a Michigan player simply threw the ball past his teammate, into Reed’s hands.  If Reed hadn’t been standing there, the ball would have gone out of bounds – Jayhawk ball either way.  I credited that play as a “team” forced turnover.  If an opponent takes a shot or makes a turnover with no player defending him, it’s credited to the team as a whole. 

3. As the above notes indicate, these numbers are extremely subjective.  Luckily, changing a couple plays doesn’t make as much difference as you might think.  Sticking with Tyrel Reed, if I change his 2.6 turnovers to 4, his DRtg changes from 76.9 to 75.0.  Yes, that’s a noticeable difference, but it won’t change a good game to a bad game, or vice versa.  However, the subjectivity makes it unlikely that I’ll try to do any real analysis on these. (That, plus I’m not recording WHO took the shot, which is pretty important.)


1. You can see above that about 12% of Kansas’s defensive possessions, and 10% of Michigan’s, were ended by the action of an unguarded player.  You can also see that Michigan made 5 of 6 unguarded shots, while Kansas only made 3 of 7.  Both teams committed 3 unforced turnovers.  I’m curious to see this numbers going forward, since it seems like a low fraction of FGA credited to “Team” is a sign of good defense.

2. Looking at Kansas’s individual stats on kenpom.com, you might wonder why Elijah Johnson isn’t getting more playing time, as he has the highest offensive rating on the team.  Well, this is only one game, but the fact that his Stop% was lower than the unguarded “Team” number can’t be a very good sign.

3. Notice that Brady Morningstar had the lowest %DPoss among Kansas players.  He’s generally regarded as one of the team’s best defensive players, but he didn’t seem very involved this game.  I have a feeling that might be misleading.  A good off-ball defender may be underrated by these numbers, because ball denial should result in a lower %DPoss, meaning more of the player’s DRtg will come from the team-average portion of the calculation.

4. Kansas’s highest %DPoss players were their worst 2 defenders, while Michigan’s highest %DPoss players were among their best.  Just throwing that out there.

5. This doesn’t show up in the above table, but it’s amazing how many of Kansas’s forced turnovers were the result of teamwork.  Only 3 of 14 turnovers were solely credited to one player, compared to 9 of 14 for Michigan.  I’ll be curious to see if this trend continues.  I would assume (with absolutely nothing to back this up) that better defensive teams would have more shared credit on both shots and turnovers.

6. I credited Jordan Morgan with 5 forced turnovers, and they were all individual efforts.  A couple of them seemed very … professional (over-selling the amount of contact on a Thomas Robinson screen, and using his hip to subtly knock over an off-balance Kansas player and draw a travelling call).  He’s a guy I would definitely want on my team if we’re both playing at the Y.


As I mentioned before, I found only a few references to Project Defensive Score Sheet online.  Here’s the rundown, if you’re interested in reading more:

I’ll at least track these stats for a few more games, simply because I enjoyed the alternative viewing experience of focusing on defensive details.  If anybody has any suggestions on how to use the numbers (or insight into how useless they are - save me the effort!), please chime in.


  1. I remember thinking the exact same thing when I read Basketball on Paper. I wanted individual defensive stats in the worst way. I'm glad to see you following through on the notion.

  2. Anyone find a way to use these stats ad a high school coach? Suggestions?