The Clearest Of All Laws

Posted by Ian Levy on March 24, 2011 under Commentary | 15 Comments to Read

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Ian Levy is the author of Hickory High, a contributor to Indy Cornrows, and a part of The Two Man Game family. He’ll be bringing his intelligent brand of — mostly quantitative — analysis here on a weekly basis. You can follow Ian on Twitter at @HickoryHigh.

It’s been just over three weeks since Corey Brewer signed with the Dallas Mavericks. Brewer is young, athletic and by all accounts, an extremely hard worker. However, the chief attraction for the Mavericks was his reputation as an excellent wing defender. So far he’s had trouble carving out a place for himself in Rick Carlisle’s rotation, averaging just 8.9 minutes per game over seven games. It’s difficult to draw conclusions with such a small sample size, but he hasn’t yet done anything to stand out at the defensive end.

What exactly is his defensive reputation based on? Watching him play we see a long and bouncy sliver of a forward. He competes on every defensive possession; he battles through screens, moves his feet on the perimeter, and displays a knack for using his length to contest shots. Defensive impact is notoriously hard to measure statistically, but is there any numeric evidence that his excellent tools and motor translate to an effect on an opposing team’s offense?

There are plenty of defensive statistics available. The issue is that none are accepted as a completely accurate metric, with opinions varying wildly on the value of each. Today we’re going to take a tour through some of these available statistics, examining Corey Brewer along the way and trying to pin down the quantity and quality of his defensive contributions. Since he’s spent such a short time with the Mavericks, most of the stats we look at will cover his entire season or just his games with the Minnesota Timberwolves.

Box Score Statistics

These are the basics that everyone is familiar with: steals, blocks and rebounds. When we look at these stats per 40 minutes we find Brewer averaging 2.6 steals, 0.4 blocks and 4.5 rebounds. Compared to the league average for swingmen, Brewer is sub-par with regards to rebounds and blocks. However, he steals the ball at a rate nearly twice the league average.

Another way to look at these basic statistics is as a percentage of their opportunities. Steal Percentage, Block Percentage and Rebound Percentage (Ed. note: These measures have also been referred to as “rebounding rate,” etc. on this blog. The terms are completely synonymous.) are all statistics available from a variety of sources, including and Stl% is calculated as the percentage of the opposing team’s offensive possessions on which a player records a steal. Blk% is calculated as the percentage of the opposing team’s shot attempts which are blocked by the player. Reb% is calculated as the percentage of available rebounds which a player grabs. Reb% is available as a total number, but can also be split into Offensive and Defensive Reb%.

Brewer’s total Reb% of 6.2% and his Blk% of 0.8% are both below average. Again, where he really shines is stealing the basketball. This season, Brewer ranks 4th in the league in Stl%, at 3.2%. He trails only Tony Allen, Rajon Rondo and Chris Paul. Over the past four seasons, Brewer has the 17th best Stl% in the league, at 2.5%. Forcing turnovers is something the Mavericks have struggled with all season. They are currently 24th in the league, with an Opponent’s TOV% of 12.4%, well below the league average of 13.5%. Having Brewer on the floor to wreak havoc in the passing lanes could be a real asset in the playoffs.

On Court/Off Court Statistics

The premise with On Court/Off Court statistics is simple: look at how a team’s defense performs when a player is on the floor and compare that with how it performs when they’re off the floor. Theoretically, the player should be responsible for much of that difference. The problem is that these statistics have a lot of inherent “noise” in them. Since this model is essentially about comparison, trading minutes with a horrible defender can make someone look much better than they are. By the same token, a back-up may look much better than they are because they’re matched up against the opponent’s back-ups.

These statistics are available in a lot of different formats. tracks several categories for On Court/Off Court, including Defensive Rating, eFG% allowed, Blk%, Reb%, Turnovers and Free Throw Attempts allowed. allows you to look at the On Court/Off Court Defensive Rating for a player overall, and broken down by the different five-man units the player was a part of.

Looking at these stats for Corey Brewer incorporates a lot of the “noise” we mentioned above. Brewer’s place in the Timberwolves’ rotation varied quite a bit. He started just under half of the 56 games he played with them. In 11 of those games he played fewer than 20 minutes. He played over 30 minutes 9 times. The Timberwolves are also ranked 26th this season in Defensive Rating, meaning Brewer played alongside some less than ideal defensive teammates, in a less than ideal defensive system.

To try and limit the influence of some of those factors in the statistics I isolated some five-man units Brewer was a part of to look at the On Court/Off Court Defensive Ratings. I started with the 6 units Brewer spent the most minutes playing with. For comparison, I pulled out any units that had the same four teammates but a replacement for Brewer. The table below shows the Defensive Ratings for each of those units.

Brewer Lineup Graph

In three of those lineups the team’s Defensive Rating was better with Brewer on the floor, in the other three it was worse. Inconclusive to say the least. I went over these lineups several times and couldn’t identify any common patterns, such as Wesley Johnson replacing Brewer making the defense significantly better. For the purposes of our discussion, it’s convenient that this case is a perfect illustration of some of the problems with On Court/Off Court statistics.

Play-by-Play Statistics

These metrics come directly from analysis of play-by-play data. The three I see utilize the most often are Individual Defensive Rating from, counterpart statistics from, and possession category data from Synergy Sports Technology.

Individual Defensive Rating is a metric that was introduced by Dean Oliver in his book, Basketball on Paper. It’s based on the same principle as team Defensive Rating: how many points are allowed per 100 possessions. It’s calculated by using play-by-play data to figure out how many points the opposing player creates while the defensive player is on the floor.

Extensions of this data can be unreliable because it often assumes match-ups based on listed position, which is not always the case. Teams like the Mavs have a lot of positional interplay on both offense and defense, so some of the metrics derived from play-by-play data can be a bit problematic.

Brewer’s Individual Defensive Rating has only been below 110 once in his career: this season, where his time in Minnesota and Dallas have worked out too a rating of 109. The league average this season is 107.1. Granted, he’s played on some bad defensive teams in Minnesota, but this statistic theoretically captures just the points created by the opponent he’s guarding. Even when accounting for the defensive deficiencies of his teammates, Brewer does not look impressive by this metric.

Counterpart statisics are just an extension of Individual Defensive Rating. They’re also culled from play-by-play data, and show the eFG%, FTA/48, Reb/48, Ast/48, Pts/48 and PER for the opposing player while the defensive player is on the floor. Being calculated in the same way as Individual Defensive Rating, they can be unreliable for some of the same reasons. 82games displays these statistics broken down by the position that the defender was playing. The table below shows the counterpart statistics for Brewer’s time in Minnesota this season.


Keeping in mind the shortcomings of these stats, we still don’t see much evidence of defensive impact. Brewer seems to be more potent defending shooting guards but still allows fairly healthy production. I would guess that shooting guards are a better matchup for him because his height creates an advantage and his lack of strength is less likely to be exploited. These numbers also reinforce his strength in creating turnovers. However, Brewer sends opposing players to the free throw line at a fairly high rate, which indicates that his aggressiveness may be hurting nearly as much as it helps.

The possession statistics from Synergy Sports Technology are a little different in that they come from video analysis. Each play from each game is reviewed on video and than categorized by the type of possession (post-up, transition, etc.). The fact that the data comes from video analysis solves some of the defensive cross-matching problems that the other play-by-play statistics have. The table below shows Brewer’s defensive possession statistics from his time in Minnesota.

Possession% of PossessionsPoints per PossessionRankFG%SF%TO%
Pick-and-Roll Ball Handler20.5%0.8814339.7%10.9%15.8%
Pick-and-Roll Screener1%1.80-75.0%20.0%0%
Hand Off6.5%1.097047.8%12.5%12.5%

Shoddy team defense certainly affects Brewer’s numbers here, but again there is very little to indicate we’re looking at an elite wing defender. He’s solid against the pick-and-roll, does a good job closing out on spot-up shooters, and creates a lot of turnovers. But he’s not in the top 50 in any category, and on several possession types, particularly isolations, is nearly as likely to commit a shooting foul as to force a turnover.

After all looking at all these numbers we end up right about where we started. Our eyes tell us that Brewer’s physical tools and motor make him a terrific defender. The statistics say he generates a lot of steals, but plenty of fouls as well, and for all his tools doesn’t seem to make a huge impact defensively, either individually or at the team level.

Both sides of this equation could change over the next three seasons in Dallas. Perhaps playing alongside better defensive teammates and in a more cohesive system will allow the statistics to catch up with what we see when we watch Brewer play. Or perhaps playing alongside more effective defenders will expose him as spastic in the Hansbroughnian style, not always able to control and channel his effort and energy into positive outcomes. The good news for Mavs fans is that, barring injury, I can’t envision any reasonable scenario where his defense would get worse.

Brewer is a perfect microcosm of the debate between old-school and new-school methods of player evaluation. Fans who gravitate towards observation for player evaluation will likely find some reasons why the numbers don’t fully capture his performance. Fans who gravitate towards statistics for player evaluation will likely find some reasons why our eyes can’t discern his true defensive impact. The truth probably lies somewhere in between, illustrating there’s still a wide gap between what we think we see and what we think we’ve measured.

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  • Johnnie

    I've always thought he was a highly overrated defender who lived off his college reputation. His problems on the defensive end start with his lack of physical tools, surprisingly enough. He might look long but his wingspan is only 6.825, which is below average for a “defensive stopper” in a league where 7 foot wingspans are a dime a dozen for top wing scorers. Not only is his wingspan substandard but he also packs far less weight than his counterparts. The weight issue comes into play because he's easily bumped off on drives and also looks to be hesitant sticking his chest in front of drivers lest his chest caved in. Now it's possible to be scrawny and a fine defender, like Tayshaun Prince. But Prince has the benefit of a 7'3 or so wingspan. Brewer is both scrawny and short armed.

    Brewer's best defensive tool is his speed and it makes him a fine defender chasing guards who run around screens and shoot off the catch. Defensive stoppers need to have more than one strength however. They have to be versatile enough to guard all types of perimeter players and he isn't.

  • Jay

    Isn't the common pattern in the lineup chart that Brewer is better at defending SGs versus SFs? That lends further credence to Johnnie's idea that Brewer is a little too slight to handle SFs and some of the larger SGs. His rebounding numbers seem to show the same thing although we'd need to know how much time he spent at each position to really tell – I don't think lumping the positions together as swing men for Brewer's and the league average provides an accurate view.

    • Ian Levy

      Well in the lineup chart two of the lineups in which the DRtg. was better with him on the floor have him playing small forward. The issue with those lineups is the somewhat arbitrary assigning of positions. I use them a lot for Pacers' stuff at IndyCornrows and I always have to readjust the way they have them assigned. I haven't seen enough Timberwolves games to say definitively who is the shooting guard and who is the small forward when he's out there with Wesley Johnson or Martell Webster, etc. Although Rob would probably say that those traditional position designations are largely irrelevant and might have little bearing on which player he is actually defending in any particular game or on any particular possession.

  • Greyberger

    I think Defensive Rating for players is built with box-scores, not play-by-play data; if it required play-by-play then Basketball reference would only have it available for the last few years.

    I think Oliver's DRTG for players is created by adjusted the team's defensive rating up or down based on box-score inputs; steals, blocks, and defensive rebounds.

    Here's the relevant quotes from basketball on paper:

    “Current individual defensive statistics are limited… I will describe some of the many ways to augment the basic estimates of individual DRTG with other statistics… All of those ways involve taking statistics from game-by game box scores.”

    “Unfortunately, making these adjustments is neither automatic nor easy, so most of the individual DRTGs in this book will be the 'base' version, unadjusted and approximate.”

    Now that he doesn't work for the Nuggets though, Oliver definitely should make a version of DRTG for the play-by-play data age. Show the kids how it's done!

    • Ian

      Thanks for the comment Berger. I have to admit I found that chapter in Oliver's book extremely confusing. I re-read most of it this morning to try and formulate an accurate response.

      The confusing part for me is that in the book he introduces and lays out the formula for Defensive Rating in the context of The Defensive Score Sheet Project he was conducting with the WNBA's Seattle Storm. This project involved interns watching each game and keeping track of things like:

      - Forced field goal misses, when a defender forces an offensive player to miss a shot from the field

      - Allowed field goals, when a defender allows an offensive player to score a field goal over them

      - Allowed free throws, when a defender commits a fouls that leads to made free throws

      He then explains that this information isn't available for most NBA games and so you need a way to summarize defensive contributions. He then lays out the formula which includes:

      -%TeamDPossessions, the percentage of a team's defensive possessions faced by a player
      -DPtsPerScPoss, Points allowed per scoring possession by a defender
      -Stop%, the percentage of possessions on which the defender stops their opponent from scoring

      Basketball-Reference doesn't explicitly lay out the source data they use to calculate, instead just referring you to Oliver's book. Even after re-reading the chapter I'm still not entirely sure where Oliver's data comes from either. It seems to me though that several of those categories used in the formula couldn't reasonably come from any source but play-by-play data. You would need PbP to calculate how many of a team's defensive possessions a player was on the floor for. I also believe you would need PbP data to calculate DPtsPerScPoss and Stop%.

      The quotes you included are at the beginning of a follow-up section in which he talks about making adjustments to already calculated DRtg. He talks about using a team's allowed FG% by position, and games played to make adjustments and weights. However my reading of it was that these were ways to refine the Drtg. that was already calculated using the formula he layed out before. In addition although he calls these box score statistics, I didn't find any mention at all of the box score statistics we usually think of like blocks, steals and rebounds. I have no idea if Basketball-Reference makes any of these adjustments or if they provide just the base DRtg.

      I will try to take this question over to the APBRmetrics forum this afternoon and see if I can get some clarification. Maybe Oliver himself will be on to set me straight. It's entirely possible that my functional literacy failed me and I'm completely misunderstanding this chapter in his book. I'll be up front that I'm not 100% confident that I'm interpreting everything correctly here. I hope this at least explains why I classified it as being a play by play data based metric. I really appreciate you asking the question and giving me a reason to go back, re-focus and clarify my thinking. Thanks Berger!

      • Ian

        I put the question up on the APBRmetrics forum. Here's the link to the thread:

        Hopefully, someone will get on and clarify a little bit.

      • Greyberger

        You're welcome, I'm sure it's a lot easier for me to read articles like this and say “wait that doesn't sound right” than it is to write them. I don't fully understand how Drtg is calculated – Ortg either, while we're being honest – even after re-reading Appendix three.

        The main point of your post still stands; it's hard to find any way to tease out whether Brewer is a good defender, whether you're using box-score based estimates developed in 2004 (Drtg) or more recent metrics developed with new techniques and data sources. So it's kind of hard to say how good he is on defense at all…

        • Battaile

          Was also going to post that the way you're explaining DRTG is off. Basically ORTG and DRTG are great at the team level, ORTG is good at the individual level and DRTG is shaky at the individual level. In the book, there is a more robust form of DRTG available if you are tracking stops, which is why he gets into the WNBA examples, but NBA box scores don't track those so he has to try to divide stops up amongst whoever was on the floor (determined by looking at aggregate minutes, not pbp data).

  • finzent

    I wouldn't write him off as a good to very good defender yet. I'm not a huge advanced stats sceptic, but my unscientific intuition would be that the degree in which team defense influences all these defensive measures would indeed be pretty high. So I#d like to see what he can do on a team that doesn't consistently suck on defense.

    Not that I'm hugely optimistic, though. He hasn't shown anything for Dallas yet.

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  • Ignarus

    Um, looking at the defensive ratings, there WAS a clear better/worse factor: whether Brewer was SG or SF. Each and every time if was *higher* than the other lineup, Brewer was being plugged in SG. Lower D Rating? Brewer's at SF.

    • Ian

      But DRtg. is better when it's lower. Two of the three (better) lineups have him at SF, one has him at SG. All three of the (worse) lineups have him at SG. Or am I blind?

      • Ian

        Although, to reiterate, this is how Basketball Value viewed the positions. That's not to say he's actually operating as the small forward when Wesley Johnson is out there with him.

  • Ignarus

    Yeah, someone else noticed my point about the positions in d-ratings already. It's probably best to keep in mind that at SF, he's getting compared to different teammates than when he's at SG.

    Basically, the only time he looks particularly good on D is when he's being compared to fellow SF Martell Webster (stunning, I'm sure…)