NBA stats have some definite, huge holes, particularly on the defensive end.  It has always been that way.  But does it have to be?  I say no.

After the jump is an analysis of where the stats are lacking, a proposal of ways to give fans more and better information in looking at individual player performance, and an application of the new stats to the Friday (10/9) Wiz-Mavs game, with an expanded box score.

I recently read Dean Oliver's Basketball on Paper.[i] 

Oliver has a lot of interesting things to say, but I found one particularly elegantly simple and thought-provoking:  the "Four Factors" of winning.  The bottom line of it is that there are four ways for a basketball team to win a game:[ii]

(1)        Shooting (efficiently/effectively)

(2)        Turnovers (minimize your own/maximize your opponent's)

(3)        Rebounding (create extra opportunities for your team/end opponent's possessions)[iii]

(4)        Free throws

If you want to read more about them, I highly recommend the book and won't get into them here, because I won't do it justice without either needlessly recasting what Oliver wrote or unfairly block quoting him.  In any event, I think the Four Factors view is very self-evidently true from a team perspective-if you look at how the two teams performed on the Four Factors, it should be apparent what they did that won/lost them the game.  Think about it for a moment.  If you know the results of those four areas, what else do you need to know?[iv]

This should make the Four Factors attractive as ways of evaluating individuals as well, right?  Well, while the modern NBA box score already gives us all the data we need *for teams,* it falls far short at the individual level.

What can we get from the current box score?

Offense is (almost-more on that in a moment) completely captured.  The box score gives everything you need to know about a player's shooting efficiency in the game, and it tells you exactly how many turnovers the player had, how many offensive rebounds the player got and how often they were at the line and how they did when they got there. 

(My only quibble: it seems to me that if we are giving free throws their own element, then, at the individual level, we should also look at how many fouls the player drew.  This becomes important because of the bonus.  To illustrate:  if a team's PG blows by his man four times in the first few minutes of the game, each time drawing a non-shooting foul, that has a huge effect on the team's opportunities at the line for the remainder of the quarter, not to mention how the defense has to play.  At the team level, this doesn't matter.  At the individual level, however, the player has achieved something that works toward the 4th Factor but that does not show up in the box score.  Is this worth expanding the box score for, from a Four Factors perspective?  I'm not sure.)

Defense, however, is a mess.  What does the box score tell you about a player's impact on the 1st Factor, shooting?  Little to nothing.  There is one category, blocks, that tells you how many shots a player made absolutely certain would be missed.[v]  Ok, fine.[vi]  And beyond blocks, what do we even have?  We can look at the other team's box score and speculate as to who was primarily guarding whom and look at how effectively the player shot.  That has very obvious limits, with lack of accurate matchup information, court time information, and defensive switching among the more prominent problems.  I suppose staring at plus/minus long enough might be worth something.  But that's about it.

Turnovers has a somewhat similar problem.  Here, on the defensive side, we are given steals.  Yes, that is, like blocks are to shooting, one way to achieve the end goal.  And steals are a bigger part of turnovers than blocks are of missed shots, so that's good.  But it leaves much else in the dark at the individual level.  What about forced bad passes that go out of bounds?  What about forcing your man all the way to the baseline so he steps out?  What about drawing the charge that prevents the shot and turns the ball over?  We are missing information here.  As with shooting, we can try looking at the opposite side's individual offensive stat, turnovers, and try to attribute things to individuals on defense, but I think this has at least as big an opportunity for error.

Defensive rebounds does its job without complication.  Of course, it still doesn't track many contributions to the team-wide cause.  For example, boxing out a good offensive rebounder and taking him out of the play is valuable for the team (and probably for one particular teammate) without generating credit for the individual player.  But, I think advanced stats can help enough with that problem.  Looking at how the player's team rebounds when the player is on the floor should, in the long term, round out the picture for us enough that bothering with quantifying such help with rebounding probably is not worth the time and space for the common box score.  (Though this might/should be a different story for a team/coach.)

Free throw line.  We do have fouls, which is good, but of course not all fouls are created equal.  Hacking a Shaq five times in a game could will likely hurt the cause a lot less than hacking a Nash the same number of times.  This is something like the opposite of the above discussion regarding offensive FTAM-A (FT Against Made-Attempted).  Maybe we shouldn't only track the player's fouls, but rather should also track the points-on-the-board impact.

Oliver and others have done work to estimate individual players' impacts by analyzing some of the defensive-side-of-the-coin factors.  The estimate, however, is generated using a combination of the flawed individual stats (blocks/steals) and opposing team or opposing player stats.  For example, you might look at how many blocks a player makes and how the opposing team shoots while he is on the floor to extrapolate the impact he's having on shooting.  For some players, there probably a correlation.  But by no means are blocks the only way to reduce the effectiveness of opponents' shooting, nor are steals the only way to generate turnovers.  I haven't seen anything that proves out how well these estimates compare to what is seen by actually tracking the individual player.[vii]  Without such proof, I have a hard time taking the estimates seriously on faith, when it is so easy to think of so many reasons they could be off.

What else could we get?

If we can agree that the Four Factors matter and that box score is deficient, particularly on defense, this begs the question:  can the box score do better?  I think "yes" is a likely enough answer that I've decided to give it a try.

For offense, there's nothing extra, versus the current box score, that really *needs* to be done.  I will, however, track fouls drawn to see whether that paints a picture any different from FTM-A.

For defense, we've identified three areas that need some work, while we can just accept rebounds as-is.

Shooting:  For this, I propose tracking FG Against Made-Attempted (FGAM-A), with a subset of 3PtAM-A.  Unfortunately, stating that is a lot simpler than knowing how to do it.  My plan is, in short, to credit to a player any attempts that take place where that player had responsibility for guarding the offensive player at the moment the shot was taken.  So, if Caron Butler is guarding Shawn Marion with Arenas on Kidd and they switch on a screen, leading to Marion hitting a jumper over Arenas, it counts on Arenas.  But, if, instead, Kidd penetrates and Haywood comes over to help and gets in front of Kidd and Kidd misses the layup, it is a miss and an attempt for Haywood.   

This will require judgment calls (though certainly no more than assists already do).  If the Center comes over to help/double on a driving SF, and both the SF's man and the Center both are in position to contest the shot, who gets the credit/blame?  That will necessarily be a judgment call.  Some ground rules, though:  (1) when a player gets blown-by or otherwise loses the guy he's responsible for without a teammate having a reasonable opportunity to take over, the play belongs to the first player; (2) if a defender clearly had responsibility to take over the defense of an offensive player, but doesn't get there because he just doesn't bother trying to, it counts against him (for example, if you get lost on the switch on a pick and roll and your man scores without someone else getting into position, it is on you; if you go weak under the screen and the ball-handler shoots, that's also on you); (3) not every shot will get allocated to a defender, for example end-of-half heaves and undefended leak-outs will both be "team" FGAA, as would a 3-pt attempt where the defensive help/rotation just gets beat and the would-be defender has no reasonable chance to get to the shot; (4) offensive put-backs will generally be counted on the defender who was responsible for blocking that player out.  That's a start.  I expect this approach will trigger some questions, and I've tried to anticipate them below, in their own section. 

Turnovers:  This should be easy.  Instead of only counting steals, also tally other actions that directly cause a change of possession without a shot/free throw taking place.  This would include taking offensive fouls, forcing bad passes that are picked off, forcing double dribbles or travels and forcing offensive players out of bounds. (Taking a charge would show up in both the fouls drawn and the turnovers created categories.)

Free Throws:  As was already touched on, while we're already given the raw number of fouls, we can also track the FTM-A outcomes of the fouls.

And that's it.  Five "new" stats to track in-game to fill out the Four Factors in looking at individual players:  Fouls Drawn, FGAM-A, 3PtAM-A, TOC (turnovers created), and FTAA-M.[viii]

Applying the expanded "Four Factors" to a game performance

Here, then, is the "expanded" Wizards' box score for Friday night's Wizards-Dallas game.[ix]

(I welcome feedback on the best way to present the information.  You'll see I put all Offense together and then all Defense together.  Maybe it would be better to present Scoring O/Scoring D right next to each other for easier comparison? Etc.)

Some individual player Four Factor game notes:

• Haywood got off to a great start; it would have been spectacular if he'd hit any FTs
• As it was, the player of the game was probably Blatche.  While Blatche committed too many fouls, he also generated even more and created some turnovers.
• The Big 3 got a lot of FGAA.  The Mavs went at Butler and Jamison quite a bit.  Marion particularly caught Butler out of position too many times.  Arenas's FGAA is so high because spent most of the game daring his man to shoot.  Sometimes that worked out, too often it didn't.  He allowed enough 3s to cancel out his own, efficient 6-6 on FG.  In total, while they put up their offensive numbers, they gave up enough on defense to balance out their scoring production. 
• In this game, Arenas had a big net-turnover problem.  He lost 5 and got none.  Butler managed to balance his possessions out some, while Jamison brings nothing and takes nothing away on that front.
• McGee put up one of the highest rates of FGAA/minute on the team.  It was an interesting mix of being super-active to get involved in more plays and help teammates (which is good), while also losing his responsibility enough to allow an easy attempt (which is bad).  The time he was on the floor in match-up zone really magnified both of these issues.  The McGee giveth and the McGee taketh away on defense.
• It would be interesting to see what McGuire would have done by these measures in more minutes.

Also, here's the Mavs:

Mavs notes:

• Yahoo's player of the game was Marion.  He was definitely not the 4F player of the game -- he allowed way, way too many FGAA-M, mostly by losing Butler or Butler just plain beating him.  Marion also got beat on some switches, etc.
• Nowitzki was impressive.  The 5 drawn fouls and 3 forced turnovers were legit, and his 5 shots allowed with only 1 make were largely forcing Jamison to shoot over him.
• Beaubois generated turnovers.  Interesting prospect.  He and Beaubois combined for +5 turnover margin, which seems quite impressive.
• Barea is a very irritating defender and it shows up well in the numbers.  He killed Foye in their matchup.
• Humphries got praise from the announcers and did do some visibly good things, but his defense (18 points allowed on 7 shots and 6 fouls) suggests he was a net minus for the Mavs.  That notion fits well with the fact that he was on the floor for a couple of the Wizards' runs.
• Kidd couldn't do much to slow Arenas in the third quarter.  But, he made enough 3s to balance that out.  That's right, Kidd the defensive liability makes up for it with outside shooting--for one preseason game, anyway.
• Gooden did a lot to keep the Wiz in the game.  If Haywood had made his FTs, his line would be a complete train wreck.

One note about the box scores:  for this game, I did not do a "team" line, so totalling up the FGAM-A columns won't match the official box score total.  In particular, the Mavs had some 3-pt attempts off of quick ball movement and a fast break that were not counted against a particular Wiz defender.  I expect that the "team" category will be a good measure of team-wide, systemic breakdowns.

Some more about FGAA/M

Here is some defense/explanation of this approach, in the form of Q&As:

Q1:      Isn't it arbitrary to give equal credit for every "forced" miss?  Isn't a complete rejection different in nature from just being lucky that a player has an open look rim out?

A1:       That is somewhat of a fair point.  On the other hand, this is something we live with quite happily on the offensive side of the ball.  If the defense rotates away from Shaq for a moment and allows him to receive the ball cleanly with no one between him and the basket and he drops in a bucket that 99% of the league could make 99% of the time, it counts exactly the same as if Kobe pulled off the most stunning, double-team beating, hand in face defeating move possible.  We're ok with that.  We understand the context different players score in.  I think we can do the same with defense.

Q2:      Isn't it possible that different positions will be difficult to compare?

A2:       Yes.  In particular, I'm expecting Centers to pose a challenge versus other players because they (it seems) should have larger numbers in this area than other players, due to their last-line-of-defense and help responsibilities.  That doesn't mean we shouldn't collect the information, only that, again, context matters.

Q3:      As with the Center problem, won't some players potentially look *worse* because they are good?  For example, they take over too much responsibility due to getting over to help teammates who have been beaten?

A3:       It seems there are two ways a player could end up with a lot of FGAA and a relatively low FGAM (FG against missed).  One is to be a bad defender who just gets abused.  The other is to be an active defender who is frequently able to try to recover for a teammate's mistake, only to be ultimately unable to stop the make.  I suspect that if we really track this category, it will be apparent which players are which, but that is speculation on my part and this issue *could* pose a problem.  Still, it is possible that something like "range factor" from MLB defense could emerge.  One way to do this would be to keep separate categories for what players do in their head-to-head matchup versus the "at the time of the shot" approach I've set out.  That way, if we find that a player's matchup has done little, but the player still has a problematic FGAA/M stat, we can attribute it to their "range" in helping teammates.  I think, however, that's more than I will take on for now.

Q4:      Teams defend as a whole.  Passing out individual credit could be very misleading.

A4:       I'll again point to what we already accept on the offensive end.  Players help each other get into better position to score all of the time, in a host of ways, but we only keep one flawed, limited, subjective stat to account for it:  assists.[x]  Nevertheless, we still all think FGA/M is meaningful.  This is ok on offense and I don't see why defense should be different. 

Here is another way of looking at it: consider football defense, with its tackles and sacks.  These are both understood as individual achievements, while we also accept that to some degree they are products of the system and personnel around a player.  Ray Lewis playing middle linebacker in a 4-3 alignment with good defensive lineman in front of him will get a lot of tackles.  Some will happen because the guys in front of him are occupying would-be blockers and channeling the ball carrier to Ray.  Some of it will happen because Ray is Ray.  That's ok.  We look at "tackles" and can understand that.  Again, it is a matter of having a context for the stat.  I think FGAA/M can work much the same way.  Just like tackles come in the context of the team's defensive achievements (scoring and yards), the FGAM-A can too.

[i] If you have even a passing interest in basketball stats, particularly team stats, I'd recommend it. A very nice thing about it is that much of it should be appealing to those who might be open to quantification/analysis but who (understandably) remain skeptical of the win shares/PER/perfect player evaluation worldview.

[ii] The Secret Weapon had a nice "four factors" analysis of the Wizards' first preseason game. 

[iii] Another very simple yet very interesting idea in the book is that Offensive and Defensive rebounding are two different skills/abilities.  One is a part of a team's offensive game, the other is part of a team's defensive game.  So, "rebounding" is not its own phase of the game in the way that "special teams" are in football-there isn't offense, defense, and rebounding.  Rather, there is offense, where rebounding is a way to win, and defense, where rebounding is a way to win.  I confess that while I've been interested in offensive rebounds and total rebounds, I never thought to view offensive and defensive separately.  I think if you just watch the game with that idea in mind, or think about your own experiences playing, it quickly starts to make a lot of sense.

[iv] The answer to the rhetorical question is, of course, that even if we accept as given the importance of the Four Factors for explaining the how of course you still need to know the WHY of the factors, you stat-head moron.  Yes, I completely agree.  But:  that's too much for here and now and we need to start somewhere.

[v] Something I really don't get is the recent addition of "BA" to the full box score.  I'm sorry, but I have an incredibly hard time caring who had how many of their shots blocked.  Am I alone in this?  The shots were missed, we get it, but we already have that information in another category, and does it really matter how?  (If so, shouldn't we first make "idiotic 20-ft fadeaways" their own category?)  This is somehow a bigger priority than learning just how many fouls a player drew or various other potentially useful pieces of information?

[vi] Of course it doesn't punish a player for biting on a pump fake to go for the block, only to leave his man with a gimme. 

[vii] It strikes me as quite possible that statistically-minded teams have perhaps achieved some good things along these lines without taking it public, but that obviously doesn't do fans any good.

[viii] Tracking these new "direct" stats will also open up the possibility of creating other new stats.  One possibility I'm particularly interested in is net possessions created/lost (akin to football giveaways/takeaways).

[ix] I know I can't do this for every game, or even as many as I'd like.  If, however, folks would like to join in, we can, as a community effort, try to track the whole season and give ourselves a whole new complete menu of Wiz numbers for kicking around.  If you are interested, please let me know in the comments and, if there is sufficient interest, I'll figure out how to put something together.  We still won't, of course, be able to compare across the league, but on a team as deep, diverse, and interesting as this year's Wizards squad, this could still be a very interesting exercise.

The tracking of the game was harder than I expected in one way:  it takes a lot of attention (or a different sort than I am used to paying) to tell what defensive player actually did what on a given play.  There is no way I could have done this without a dvr and slo-mo that I could control.  It took a lot of slowing and re-watching plays to pick out exactly who was the defender at the time of the shot or who actually got the deflection.  That said, my biggest surprise was actually that I did not have to make nearly as many judgment calls as I expected. 

The tracking was itself an interesting experience and forced me to watch the game in a way I never had before.

[x] Tracking defensive "assists" might be a fun option.