In Defense The Scheme's The Thing

Dateline: 09/18/97

Over the past few weeks, I have had a number of conversations about defense, specifically how to play it and what makes a good defender. Part of this came as a result of my research on whether defense really wins championships. Part of it came because I posted defensive rankings for the WNBA players. And part of it came because some readers had some good questions on how to coach certain defenses, including a 1-1-1-1-1, which I had never even heard of.

In most sports, including basketball, defense is very difficult to quantify. Baseball fielders have fielding percentages and range factors that don't necessarily put Ken Griffey and Ozzie Smith where their reputations have them. Football's Junior Seau doesn't get a lot of sacks or interceptions, but he's been acknowledged as one of the best linebackers ever. Basketball's Joe Dumars has been on five All-Defensive teams for no obvious statistical reason.

There are at least two good attempts at quantifying individual defensive ability in basketball. One is (shamelessly) mine and the other is a method from Doug Steele, who does an outstanding job maintaining a statistical database in addition to coming up with this useful method.

...Doug Steele's Defensive Tendex...

Defensive Tendex is actually quite a complex thing and Doug's own write-up doesn't explain it particularly well. So I'll give it a try.

Doug rates players' overall contribution (not just defense) through something he calls Tendex, which is only somewhat different from Dave Heeren's TENDEX. Tendex (I will henceforth refer only to Doug's Tendex) roughly evaluates players by adding the good things they do (like points, assists, rebounds, etc.) and subtracts

Man Defense: A defensive player who consistently diminishes his man's Tendex values is probably a pretty good defender.
the bad things (like missed shots, turnovers, etc.). If we accept this as a measure of a player's value, then a defensive player who consistently diminishes his opponents' Tendex values is probably a pretty good defender.

This is half of Doug's method, the part I call Man Defense because it relates to shutting down a man. His algorithm for doing this is to approximate match-ups in a game -- starter to starter, sub to sub -- then evaluate whether a player is below his season average Tendex rating. The difference between what a player does in a game and his average is credited (or charged if the player has a good game) to the matched-up defender. Strictly, Doug only evaluates the offensive categories -- points, assists, offensive rebounds, turnovers -- in his Tendex formula for this.

The second half of the formula accounts for the defensive statistics a player racks up, including defensive rebounds, blocks, steals, and fouls (even though we can't really distinguish between offensive and defensive fouls). I call this second half of Doug's formula the Team Defensive part because blocks, defensive rebounds, and steals often come as a result of teammate interaction.

The top twenty defenders according to Doug's method are shown below:

Rank Name Pos Team Defensive
Tendex Rating
1 Arvydas Sabonis C Por 20.8
2 Patrick Ewing C NYK 16.1
3 Karl Malone F Uta 16.0
4 Shaquille O'neal C LAL 14.6
5 Hakeem Olajuwon C Hou 13.5
6 Dikembe Mutombo C Atl 13.4
7 Chris Webber F/C Was 12.5
8 Tyrone Hill F Cle 12.3
9 Grant Hill F Det 12.2
10 Charles Barkley F Hou 12.1
11 Scottie Pippen F Chi 12.0
12 Alonzo Mourning C Mia 11.9
13 Shawn Kemp F/C Sea 11.8
14 Greg Ostertag C Uta 11.5
15 Gary Payton G Sea 11.3
16 Vlade Divac C Cha 11.2
17 Dennis Rodman F Chi 11.2
18 Shawn Bradley C Dal 11.1
19 Gary Trent F Por 11.1
20 Michael Jordan G Chi 11.0

These are Defensive Tendex Ratings per 48 minutes.
Minimum 49 games and 23 minutes per game to qualify.
...Defensive Stops...

Defensive Stops are a concept I came up with years ago to represent the number of times a defender forces his man to end a possession without a score. If Joe Dumars forces his man to miss a shot, that is part of a defensive stop. It is only part because the shot must be rebounded by his teammate for it to truly be a stop. That person who gets the rebound deserves part of the defensive stop. How much credit is given to Dumars and to the rebounder depends upon how difficult it is to stop a shot vs. how difficult it is to get a defensive rebound. Since the NBA league average field goal percentage is about 45% and the NBA league average offensive rebounding percentage

Team Defense: Defensive rebounds, blocks, and steals are considered team defense because they often come as a result of teammate interaction.
is about 30%, this means that any old defender forces a miss 55% of the time and any old defensive rebounder gets one 70% of the time. I interpret this to give Dumars 66% of the credit and the remaining 34% to the rebounder, the values coming from a simple formula and a complex theory.

As with Doug's method, my method can be thought of as having a Man Defensive component and a Team Defensive component. The full formula is shown here; of this, the steals, blocks, and defensive rebounds are the team defensive part, while the rest approximates the man defense.

I convert defensive stops into an approximate measure of points allowed per 100 possessions using the method explained here. This defensive rating is how I evaluate defensive players.

The top twenty defenders according to defensive points per 100 possession ratings are shown below:

Rank Name Pos Team Defensive
Stops Per Game
1 Patrick Ewing C NYK 9.8 91.9
2 Alonzo Mourning C MIA 8.9 92.2
3 Dikembe Mutombo C ATL 9.5 92.4
4 Arvydas Sabonis C POR 6.9 93.3
5 Dennis Rodman F CHI 9.0 93.6
6 Shaquille O'Neal C LAL 9.8 95.0
7 Shawn Kemp F/C SEA 8.2 95.5
8 P.J. Brown F/C MIA 7.2 95.5
9 Charles Oakley F NYK 8.2 95.6
10 Hakeem Olajuwon C HOU 9.2 95.8
11 Charles Barkley F HOU 9.6 95.8
12 Grant Hill F DET 9.2 96.2
13 Greg Ostertag C UTA 5.7 96.5
14 Tyrone Hill F CLV 7.2 97.0
15 Jerome Kersey F LAL 5.9 97.4
16 Chris Webber F/C WAS 9.6 97.5
17 Christian Laettner F ATL 7.9 97.7
18 Karl Malone F UTA 8.4 97.8
19 Mookie Blaylock G ATL 8.0 97.9
20 Ervin Johnson C DEN 9.0 98.4

Defensive Ratings approximate the number of points allowed per 100 possessions.
Minimum 50 games and 23 minutes per game to qualify.
...The Two Methods' Strengths and Weaknesses...

Doug's method handles the man defense pretty well. The basis of it -- rating a defender on how far below a season average he holds his man -- is a good concept. It accounts for the fact that the best defenders guard the best offensive players and gives them credit for it. So even though Joe Dumars' man scores a lot of points on him every night, if that is less than average, Joe still looks good. I don't think his Tendex is perfectly appropriate for the task, but that is minor.

What Doug's method doesn't do as well is handling team defense. At least it does not handle the combination of it and man defense in a sound fashion. The Tendex method assumes that one possession is one point, an assumption I strongly argue against making. Ignoring that argument for the time being, Doug's theory then is that applying Tendex to a player's defensive statistics and adding that to the number of points a player prevents through man defense gives

Defensive Tendex shows Sabonis "saving" Portland 20 points per 48 minutes. Does that make sense?
a defensive rating. It hints that the rating is the number of points per game saved by a defender. I would say that "saved" here means no more than when a store says you can save 30% on something already marked up. Just look at the values for his best players. Sabonis "saved" Portland 20 points per 48 minutes??? Saved relative to what? I cannot think of a single case where one player's loss meant that much. David Robinson's loss to the Spurs was tremendous, but I can't find a single measure making it more than about 10 points per 48 minutes.

Basically, Doug's method adds the number of points a player prevents through man defense, but I cannot tell what the team part is. If you add up all the individual Defensive Tendex ratings for a team, you come up with a number that means absolutely nothing. That is not Doug's fault because he knows that and doesn't purport to imply that this is anything more than a rating. The absolute numbers don't mean anything, but the relative ranking does hold some weight.

Now that I have picked on Doug, it's time to pick on my stuff. My method's main strength, I think, is that it is put together to mean something. Whereas Doug's doesn't sum up to anything for a bunch of teammates, my individual defensive stops sum up to the number of team defensive stops, which

Defensive stops are measurable, but are not currently estimated well.
is measurable. I think my method accounts for the true value of steals, blocks, and defensive rebounds better than Doug's, though not by much.

My method's main weakness is that it does a lousy job of accounting for man defense. As it stands, my method looks at the man defense of every player on a team the same way. Joe Dumars has the same man defense as Aaron McKie, even though Dumars probably shuts his man down better. Even if I fix this, it still won't reward Dumars for guarding the toughest cover every night.

Ideally, I would really like to do something like Doug does, to look at individual games, matching up players in some way, then evaluating the man defense using scoring possessions

Ultimately a combination of the two methods may be the next step towards evaluating defensive players.
and total possessions . For instance, if I calculate that Dumars' man scores on 8 of 17 possessions, that is 9 stops that can go into my overall formula. Right now, I can only estimate that 9 stops based on team performance and it is very heavily weighted by how his teammates do.

A weakness of both methods is accounting for who a player really matches up against in games. Doug does it very approximately, but it is what I would do in his place. By matching starter to starter, it gets some bit of reality, but it doesn't show that Michael Jordan scored 20 of his 30 during an 8 minute stretch when Aaron McKie took Dumars' spot guarding him. I only hope that this is a fairly small problem, but I honestly do not know.

...NBA vs. WNBA vs. ABL...

In both Doug's list and my list of the top twenty NBA defenders, notice that there are only one or two guards. This is not a fluke nor a flaw. What I have consistently found is that big men are the most important aspect of a good NBA defense. As a simple example, one can look at the effect that Dikembe Mutombo had on Denver and Atlanta by changing from one team to the other last season. Atlanta was 15th defensively in '96 and third in '97. Denver was tied with Atlanta for 15th in '96, but fell to 24th in '97 because Ervin Johnson was not his match in the middle.

Centers are the most important defenders in the NBA, but there is no clear dominant position in other leagues.

This general trend is not true in different leagues, however. Specifically, I generated my numbers for the two women's leagues and both lists show eight guards on the list. (The WNBA list is here and the ABL list is printed here for the first time:

Rank Name Pos Team Defensive
Stops Per Game
1 Debbie Black G COL 9.9 85.2
2 Natalie Williams C POR 9.1 86.6
3 Val Whiting C/F SJL 7.7 90.1
4 Crystal Robinson G/F COL 7.4 90.3
5 Cindy Brown F? SEA 8.8 91.1
6 Tonya Edwards G COU 6.0 92.0
7 Edna Campbell G COL 6.8 92.4
8 Taj McWilliams C RIC 8.8 92.4
9 Shannon Johnson G COU 6.5 92.7
10 Nikki McCray G/F COU 6.7 92.9
11 Tari Phillips F/C SEA 6.8 93.4
12 Sylvia Crawley F/C COL 6.0 93.5
13 Stacey Ford F POR 6.3 94.7
14 Katie Smith F COU 6.0 95.0
15 Charlotte Smith F COL 6.1 95.1
16 Sonja Henning G SJL 7.9 95.2
17 Maria Sobral C RIC 6.5 95.3
18 Sheri Sam G/F SJL 6.7 95.4
19 Lisa Harrison G/F POR 6.2 95.5
20 Shanda Berry F/C NEB 7.2 96.0

Defensive Ratings approximate the number of points allowed per 100 possessions.
Minimum 30 games and 25 minutes per game to qualify.

This difference between the dominant players in men's and women's leagues should come as no surprise. Height and leaping ability are not as important in the women's game as they are in the men's. Also -- I could get in trouble for this -- in lesser leagues like recreational leagues, high school leagues, or below, turnovers are much more important than shot blocks. A defensive player who can step up pressure is more likely to end a possession by forcing a turnover from a weak ballhandler than is a shot blocker who changes a shot from an already out of control shooter. In the NBA, where ballhandling skills are excellent, it takes Pitino-like pressure to make turnovers important and, thus, guards more important defenders.

...The Effect of the System...

Ultimately, I cannot truly hope to evaluate individual defenders as well as we evaluate individual offensive players. A big part of the reason for this is coaches like Pitino. Pitino is one of several coaches who makes bad defenders good. In Pitino's case, it is because he has a gimmick defense, a term he probably resents, but I don't mean it in a negative sense. In Pat Riley's case, it is because he asks his players to be goons, a term he probably resents and I do mean it in a negative sense.

If at least several wins per year can be credited to a coach's system, a GM must recognize this in trading for a player who plays in that system.

Unfortunately for those of us trying to keep track, this coaching effect is probably the biggest influence on a large number of players, particularly non-centers in the NBA. (With a good center, coaches build their defense around them anyway.) When Larry Brown took over at Indiana, it was remarkable to see Reggie Miller turn into a good defender. The three years prior to Riley's arrival in New York, the Knicks allowed 105.2, 105.8, and 105.6 points per 100 possessions; in Riley's years there, the Knicks never allowed more than 102.3 and both Patrick Ewing and Charles Oakley were constants throughout that entire span.

That is at least 3 or 4 points per game that can be attributed to Pat Riley's defensive scheme. Those points show up as being credited to the players somehow, but it's not right. When those players leave to play for a coach who doesn't preach defense, they probably won't be as effective. Neither Doug's nor mine can account for that.


I would like to thank Coach Clay Kallam for some valuable conversation on this topic.