Defensive Errors

There are a few ways offenses end up with unguarded shots, either in transition, off of screens and when defenses make errors. The thinking here is (deliberately) quite simple: defenders should be guarding someone. If they aren’t, they should be rotating or hedging a screen to resume guarding someone. The goal is to not give up open shots, which is always trumped by the goal to not give up open layups.

I categorize defensive errors in two ways:

  1. A blow-by
  2. A missed rotation

The first is an error in man defense, when one’s man beats them to the rim – “blows by them,” in hoops vernacular – either with the ball or off the ball. It’s a “blow-by” when the defender is no longer engaged in guarding the player. The second is an error in team defense, when players fail to logically rotate to an open defender, or even worse, don’t rotate to the rim to prevent an open layup (the majority of “missed rotations”).

In either case, two players can receive half an error each if two players were equally involved in the error. For a blow-by, this is simply when a double-team is split and left in the dust, but for a missed rotation it is equally blaming two proximal defenders who could have rotated to an open man and did not. It’s common for half missed rotations to take place when two players incorrectly rotate to the same shooter on the perimeter and fail to collectively protect the rim against an open layup. (They usually then start pointing at each other or looking around in befuddlement. The lesson: defensive communication is important!)

Defensive errors essentially create a power play — similar to the power play we saw in opportunities created — that spikes the opponent’s offensive efficiency by nearly 50%. In the simplest terms, tracking defensive errors is assigning responsibility to players who give up open shots when they otherwise shouldn’t.

As is the case with assigning credit for an assist, there is a gray area (mostly involving whether a player could have rotated and didn’t).

Some examples of defensive errors:

  • Being beaten off the dribble and no longer being within reach of the dribbler (BB)
  • Being backdoor cut on the wing without staying with the cutter (BB)
  • Being run by on the way down the court by your man (BB)
  • Failing to rotate to the basket when the screener rolls free as his defender double-teams the dribbler (MR)
  • Failing to rotate to a man to box out after a similar defensive scramble (MR)
  • Staying in the backcourt (cherry-picking) and not running back in a reasonable time to defend anyone (MR)

Through March 15 (162 team games tracked), here are the players with the  most defensive errors in the 2011 regular season (minimum 300 possessions played):

Statistics are per 100 possesions; BB = Blow By; MR = Missed Rotation

And the players with the fewest defensive errors:

Statistics are per 100 possesions; BB = Blow By; MR = Missed Rotation

*Qualifier players for leaders listed in this post play for: Atlanta, Boston, Chicago, Dallas, Denver, Indiani, LA Clippers, LA Lakers, Miami, New Orleans, New York, Oklahoma City, Orlando, Phoenix, Portland, San Antonio, Utah. Remaining teams don’t have 300+ possessions in the 2011 database.

For those wondering, the correlation coefficient between defensive errors and team defensive rating this year is about 0.35.


In 1974, the NBA started tracking steals. And apparently, they thought that was a sufficient measure of forcing turnovers on defense, because they haven’t added anything related in their box score since.

The easiest measure of forcing turnovers is to track offensive fouls drawn. Hoopdata provides charges taken, although nothing is listed for the 2011 season. In my stat-tracking, I note any offensive foul drawn, excluding the moving screen.

In last year’s playoffs, the average player drew 0.31 offensive fouls per 100 possessions. In tracking games this year, that number is 0.49/100 possessions (there was a lot of good offense in the 2010 postseason, despite the NBA Finals). Here are the leaders in “charge” rates — offensive fouls taken per 100 possessions — from last year’s playoffs:

Nick Collison was hitting the deck like a sailor in the Thunder’s six games against LA. Derek Fisher drew the most total charges, with 14. A familiar name for those who are abreast to charge-related statistics is Glen Davis, who was this year’s NBA leader at the last unofficial count I heard.


There are other ways to force turnovers on defense that don’t reach the box. There are two in particular that I track and both have to do with deflecting the ball in a manner not registered as a steal:

  1. Knocking the ball off an offensive player and out of bounds
  2. Knocking the ball away as to force a shot clock violation

The second method is inherently less valuable because it has to happen near the end of the shot clock, when the value of the possession is already reduced. Nonetheless, both are quite easy to keep track off and add to the overall picture of a player’s defensive ability to force turnovers. These kinds of forced turnovers occur at a rate of about 0.30 per 100 possessions.

Along with steals,we can combine all of these into one defensive measure for “forcing turnovers.” Below are the leaders from the 2010 playoffs (league average was 2.09/100):

Stats are per 100 possessions

Obviously, this is quite a different list than the one portrayed by looking only at steals. Here are the complete leaders from the 2010 playoffs in non-traditional turnovers and total forced turnovers.

In a post last week debunking the nuclear overreaction to Miami’s late-game failures, I alluded to the Heat’s lack of depth and size. Which led me to thinking, just how little is Miami — still 43-21 and the boasting the best schedule-adjusted differential in the league — receiving from its non-stars?

According to broadcaster Eric Reid, the Heat’s bench has accrued 22% of the team’s points this year; Dead last in the NBA. This wouldn’t be too big of an issue if the Heat’s starters were a well-oiled, balanced machine.

They aren’t.

Using the Simple Rating at 82games (a combination of on/off and production), the Heat have two superstars, a good third player, and only two players hovering around even (James Jones and Zydrunus Ilgauskas). The elite teams giving them trouble have the following distribution (total quality players in parentheses):

  • Chicago (9 quality players): 1 good player, 3 positives, 5 players around even
  • LA Lakers (7): 4 good players, 2 positives, 1 player around even
  • Boston (6): 1 elite players, 2 good players, 1 positive, 1 player around even
  • Dallas (6): 1 elite player, 1 good player, 2 positives, 2 players around even
  • Orlando (6): 1 elite player, 1 good player, 1 positive player, 3 around even
  • San Antonio (6): 1 elite player, 1 good player, 3 positive players, 1 around even
  • Oklahoma City (6): 1 good player, 2 positive, 3 around even

Miami may have the best duo in the league, but they are somewhat redundant in role (neither can guard centers, neither can shoot 3’s too well). Another quality player, especially on the interior, would do wonders for Miami. Dean Oliver thinks less dribbling from the stars might also help help create better shots and offensive balance.


In my own stat-tracking, I’ve charted 13 Heat games this year. They are 2-11 in those games, with an Offensive Rating of 99.1 and Defensive Rating of 109.4. Their combined opponent’s win percentage in those games is .614, so it’s a decent smattering of Miami losing and losing to elite teams. In those games, the team breakdown is as follows:

Pos: Possesions played, OC: Opportunities Created, FD: Fouls Drawn

Here we can see the nosedive that Miami’s role players have taken in these games. It’s hard to say which is worse for them, the point guard position or the center position. In all likelihood, Miami doesn’t have a point or a center that would play relevant minutes on any other contender in the league. Not a one. Joel Anthony and Erick Dampier have at least been around average on defense.

But the shooting in these games from the rest of the supporting cast borders on offensive: Mario Chalmers is the only other player over 50% True Shooting, and still clocking in at about 2% lower than league average. Mike Miller has been dreadful in these games. Excluding Wade and James, Miami is shooting 31% from downtown and making just 3.7 3-pointers per game in this sample (season averages 33.7% and 6.7, respectively).

Chris Bosh’s performance also drastically falls off (even if we exclude the 1-18 disaster). They have almost zero production from their bench, with no one outside of the all-stars averaging north of 10 points per 36 minutes. To put that in perspective, nearly eighty percent of the NBA scores at least 10 points per 36 minutes.

Unless Miami can get something — average outside shooting? — from the role players and a better Chris Bosh, it’s not going far in the playoffs, regardless of what Wade and James do.

I was excited to see the topic of fouls receive some attention at last week’s Sloan Conference in Boston. Although I’m not sure how I feel about the methodology (confusing) and conclusions (potentially confounded) of that paper. Nonetheless, fouls are a small part of the game that are often overlooked in analysis.

Turns out that drawing fouls is a really good thing. And committing fouls — specifically, shooting fouls — is really bad. Nothing revolutionary there.

On offense, drawing a foul has two effects:

  1. Brings a team closer to the penalty
  2. Causes foul trouble for opposing starters

When a player is in foul trouble, he loses minutes he would otherwise be on the floor (unless he plays for Don Nelson, apparently). Usually, this is on order of 5-10 minutes, as a player sits for a period before he is no longer in “foul trouble.” Occasionally, extreme cases render a player inactive for longer, like Dwight Howard in last year’s first round against Charlotte. Howard averaged around 26 minutes a game when he otherwise would have been playing closer to 40. When starters sit, they are replaced by bench players, who (theoretically) represent a downgrade.

The penalty represents a larger advantage for teams. Every foul before the penalty is 25% of the way to the automatic bonus for a team. Once in the penalty, any foul on the court produces two free throws for a team, which is the most efficient form of offense: The value of an average possession in the NBA is about 1.07 points. The value of two free throws is about 1.52 points.

On the team level, the correlation between fouls drawn per 100 possessions and ORtg is quite strong: 0.56 for last year’s playoffs. For this metric, a “foul drawn” (FD) is only counted when a player is fouled on offense. Setting screens and intentional fouls are excluded.

Here are the leaders from the 2010 playoffs in fouls drawn per 100 possessions, with free throw attempts/100 included as reference:

Clearly, there is a strong correlation between free throw attempts and fouls drawn. This allows a fairly accurate estimate of FD using FTA. However, as is the case with Opportunities Created and assists, it is the outliers who are often the most interesting. Someone like Dwight Howard shoots far less free throws than expected based on the number of fouls he draws because he’s constantly being banged around before the act of shooting, to prevent lobs or on offensive rebounding situations. Here is the full list of players ranked by FD from the 2010 playoffs who played at least 150 possessions.


On defense, committing personal fouls isn’t terribly detrimental to the team. For one, there’s a limit of six per game, and as discussed above, players will simply head to the bench if they foul too much. There is almost no correlation between personal fouls and team defensive rating.

However, there is a correlation between Shooting Free Throws (SF) and defensive rating (0.44 after 104 team games of tracking this year.) This information can be extracted from the play-by-play for comprehensive analysis by noting how many free throws a player gave to the other team by fouling. (eg 3 SF result from fouling on a 3-pointer.)

Again, free throws are the most efficient mode of scoring, so sending a player to the line is spiking the opponent’s offensive efficiency as described above. In short, shooting fouls are bad.* Using the 150 possession qualifier, here is the complete list of players from last year’s playoffs who caused the most free throws for the opposition (SF per 100 possessions).

*The obvious exception is “intentional” fouls to prevent layups or easy attempts around the goal from horribly inefficient free throw shooters.

82games just updated its numbers for the 2011 season, and of particular interest is Miami’s performance in clutch situations (5 point game or closer in the final 5 minutes). As far as I know, no one publishes team stats for these situations.

In lieu of that, we can ballpark a team’s clutch performance by looking at the team leaders in clutch minutes. Included is the percentage of clutch minutes that player has played for his team, and the player’s overall plus-minus for the season for comparison.

From 82games.com through 3/05/11

So it’s not like Miami is crumbling or lost down the stretch of these games. They are actually about 15 points better than opponents over the course of a game using this criteria. More surprisingly, Miami’s offense with James on the court (95% of its clutch minutes) boasts an Offensive Rating of over 120. By comparison, the Lakers ORtg with Bryant is just under 109. Boston’s with Pierce is 108.5. Chicago’s with Rose 108.

Hmm. Maybe Miami’s clutch problem is against elite teams only? The Heat have played 12 competitive games against the eight best teams this year (with a 2-10 record in those games). In the final two minutes of those games, Miami’s average point differential is -0.2. Basically dead even.

In the final five minutes of these games their average point differential is -2.4. That’s -29 over 60 minutes of play; Finally some evidence of close-game failures. But even 79% of that difference comes from two games against Orlando in which the Magic bombarded Miami down the stretch (in the November 24 and February 3 games). Here’s the Heat’s complete breakdown against the top-8 by section of the game:

It’s fair to say that Miami’s struggles down the stretch are overblown. With the exception of one incredibly specific, small-sampled criteria: The final 10 seconds of games when trailing by three or less. According to an ESPN graphic posted after the game, Miami is just 1-18 shooting in such scenarios.

Is it plausible that the Heat will continue to shoot 6% in these situations for the remainder of the season and the playoffs? Unlikely. Right now, they’re on the (extreme) wrong side of variance in a small sample size (18 shots).

That doesn’t mean there aren’t legitimate problems in South Beach. Only, they have a lot less to do with close games and a lot more to do with size and depth. Which, of course, were the original problems in the first place when they cleaned house in the offseason.

The Heatles aren’t losing these games in the final seconds. They are losing them in the 3rd quarter (and into parts of the 4th). And there’s no reason to believe that isn’t a direct result of playing three on five most of the time.

Miami was thin enough heading into the season before Udonis Haslem’s injury. It has now logged over 1000 minutes at center from Juwan Howard and Erick Dampier. Combined age: 73. (Yes, they still play basketball.) Mike Miller has played 500 disappointing minutes returning from injury.

Miami’s biggest problem heading into the playoffs this year isn’t the end of close games – that issue has been greatly exaggerated, and it will improve with experience and, statistically, by default. The Heat’s biggest problem is the same one they’ve had all season: size and depth.

Errors in True Shooting%

As discussed before, True Shooting percentage is an estimate of points per shot. But it’s not exact, counting a free throw attempt as 0.44 shots. Why isn’t a free throw 1/2 a shot, you ask? Because of “And One” opportunities, when someone scores and is fouled for one extra bonus free throw. In Marv Albert’s language, it’s known as “Yes, and it counts.”

These are bonus chances after a successful conversion, so to count these free throws as half an attempt would actually be penalizing players for drawing an And One and missing compared to players who never drew the foul at all. To obtain a precise measurement of points per shot (PPS), we’d have to differentiate between And One free throw attempts and the conventional trips to the line. Without doing that, the 0.44 coefficient minimizes error across the league between points per shot and True Shooting percentage.

So how much can TS% be off by measuring PPS? Mathematically speaking, we can observe the following:

  • Free Throw percentage essentially does not affect TS% accuracy.
  • The ratio of And One FTA to total FTA affects TS% accuracy. 12% is perfect accuracy. The smaller the ratio, the more TS% will overestimate PPS. The larger the ratio, the more TS% will underestimate PPS.
  • The ratio of FGA/FTA slightly compounds TS% accuracy. The more free throws taken relative to field goals, the more TS% errors are magnified (both overestimating or underestimating PPS).

The 0.44 coefficient used for FTs in the TS formula is designed to minimize these errors as much as possible. It does that well across the league, But obviously, not all players have the same frequency of 3-point play opportunities.

The way to generate a truly accurate percentage would be to comb through play-by-play data and separate And Ones from other free throw attempts. In 2005 and 2006, 82games provided some And One data we can look at for an idea of how accurate TS% is among high-volume players. PPS/2 is points per shot divided by two, which is what TS% is trying to measure:

% of And1s is the percentage of total FTA that are And1 FTA. PPS/2 is points per shot divided by 2, which is the what TS% is trying to approximate. Error is the difference between the actual player efficiency and his listed TS% using 0.44 for free throw attempts.

As we can see, TS errors are generally small. In the games I’ve tracked this year, Wade and Bryant have And One ratios of around 12% (0.1% error for both) and James is just over 8% (for an overestimation of 0.3%). It would be nice to add And Ones to box scores, or completely track them in play-by-play, but in the meantime, TS% does a great job approximating points per shot.

A poster on the realgm forums named Nonemus recently wondered how everyone’s favorite triumvirate of wings, Kobe Bryant, LeBron James and Dwyane Wade, have stacked up against elite teams in the playoffs. Some of the numbers are worth examining here, namely how these three have performed against defenses separated by quality. Are any of them bottom-feeders? Do they equally suffer against the best defensive teams? Has one played a disproportionately large amount of games against amazing defenses?

First, we need to define elite defenses. Since the rule changes in 2005, only 41 teams have posted a defensive rating of 104 or lower. Which means, on average, a 104 DRtg is about the 6th best defense in the league and roughly three points better than average. Certainly a fair cutoff point with which to work. Similarly, let’s call “solid” defensive opponents those with a DRtg between 104 and 107 (roughly better than average), and “bad” defenses having below average Defensive Ratings (lower than 107).

Using that distinction, it turns out Dwyane Wade has played the majority of his playoff games against elite defenses (68% of all games versus such teams). LeBron has played 42% against top defenses and Kobe 38%. Below are their statistics, per 36 minutes, broken down by defensive quality. (GmSc is their Game Score).

Fittingly, Bryant and James show improvement the easier the defensive foe. Wade, however, has some surprising results. His performance versus elite D and non-elite D isn’t too different. (Note, those six games against “solid” defenses are from the 2006 Finals against Dallas.) He quite clearly outperforms the other two against elite defensive teams, even ramping up his three-point % and assists.

LeBron’s history against elite defensive teams is a tale of two players. In his first 15 games against such opponents, James struggled mightily, to put it mildly. He was dreadful, posting a 45.9% TS percentage and averaging over four turnovers per 36 minutes. Hide the women and children.

Below are his splits — the first 15 games are against 2006 Detroit, 2007 San Antonio and the first four games against Boston in 2008:

So James has been a different player against top defenses since game 5 against Boston back in 08, scoring and shooting better than he has even against solid defenses and posting a monstrous Game Score that tops Wade’s or Bryant’s GmSc against even the weakest defenses. The lesson, as always, is that LeBron James has been really good for the last few years.

Here is how each player’s series looks visually, measured using Game Score. The x-axis is a team’s defensive rating and y-axis the players average GmSc for the series:

The coefficient of correlation between Game Score and Opponent Defensive rating is as follows for each player:

  1. LeBron .582
  2. Kobe .561
  3. Wade .409

Which implies that LeBron’s Game Score by series is the most heavily influenced by opposing defense and Wade’s is the least affected. That is, the more positive correlation suggests that as the defense is worse, the performance better. That bottom-feeding trend is the strongest in LeBron’s case, and can be seen above with all his data points in the upper right quadrant.

All of this begs the question: Is it better for performance to vary according to defensive strength, or better to remain consistent regardless of opponent quality? In his only two series against bad defensive teams, Wade shows no appreciable improvement. LeBron and Kobe feed off bad defenses, to a certain degree.

In the playoffs, teams can expect to encounter difficult defenses on the path to a title. Since the inception of the three-point line in 1980, only five teams with an SRS over 6 had a defensive rating over 107. And 58% of those 6+ SRS teams qualified as “elite,” with a DRtg of 104 or lower. Which means in this case, Dwyane Wade may provide a distinct advantage on the game’s biggest stage.

Here is a complete list of each players series against elite defenses in the playoffs since 2005.