My latest article at RealGM takes a look at the persistent mainstream media claim that the 2007-08 Washington Wizards were a significantly improved defensive team. A closer look at the numbers tells a very different story.

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My latest column at RealGM. This one uses advanced stats and my homemade MVP Calculator to determine which player meant the most to his team. Hint: It's not the guy pictured here.

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Everyone following the Wizards know Antawn Jamison is the team's most valuable player this season.  I like to put numbers to these kinds of things, so I ran each of the Wizards through my MVP Calculator.  The Calculator combines on/off stats from 82games.com with minutes played and a summary measure of individual statistical production.  Then I set the MVP's score to 100 and scale everyone else below.  Here are the results for the Wizards so far this season:

So, Jamison is the MPV and Butler has had about 59% as much value to the Wiz.  A lot of that is due to Caron's injury time.  Adjust Butler's minutes to match Jamison's (who has played 80% of the team's minutes) and Butler's MVP Score rises to 82.

Of interest is that Haywood has overtaken Stevenson for the #3 slot -- he'd been trailing Deshawn for most of the season.  Also worth noting is Songaila's leap from hanging out with Pecherov and McGuire to seventh.  His play has improved significantly.

I'll be publishing more about this in the coming days over at RealGM -- talking about who comes out as the league's MVP.

PS -- Don't ask me why the table looks like that. It's formatted perfectly in the writing page.

By way of Henry Abbott's True Hoop blog at ESPN, Sports Illustrated's Chris Ballard tells the story of how Michael Jordan lost a game of one on one.  Wrote Ballard:

The game begins, fittingly, with Jordan still ribbing a previous victim. "Don't be mad at me, I'm just too good," he booms. "What, you think I had this camp just so you all could beat me?" Taking the ball first, Rogers drives right and lofts in a runner. Then he goes left to hit a leaner. The crowd of 150 or so -- campers but also coaches like John Thompson and Mike Krzyzewski -- begins to murmur. Predictably, Jordan evens it, and the end appears imminent until... Michael misses a jumper. Then he clangs another!

So Rogers again hurtles left and, nearing the hoop, jumps off both feet. Jordan, clearly into it now, times his leap to swallow up the shot. Only Rogers, in a move he's practiced a thousand times but that still appears impossibly awkward, leans away from MJ as if eluding the curl of a crashing wave. He spins the ball up, up, up and over Jordan's fingertips, off the glass and in. On the video the first thing you hear is Jordan ("Oh, no!"), followed by comedian and camper Damon Wayans, who jumps at the chance to mock MJ. (Lest you think Jordan had lost his edge, he ­immediately brought Wayans onto the court and ­humiliated him 3-0.)

Naturally, Jordan demanded a rematch with Rogers, right? Actually, he didn't. ­Instead he hugged Rogers -- the two go back a ways from Jordan's days in Chicago -- and said, not so huggably, "Next time we're on the court together, I'll show you what it's like to play in the NBA." But that has yet to happen. Rogers ­hasn't been back to Flight School, and MJ stopped playing campers a few years ago. As for Rogers, he had DVDs made from the tape and dispensed them to friends and employees, because, well, wouldn't you?

The description is a great lesson about fluky results due to sample size. It's why underdogs in basketball have typically slowed the pace of games -- fewer possessions increases the chance of a random result. And, when a weaker team (or player) faces a much better opponent, randomness favors the dog.

So, in a game of one-on-one, you'd rather play Jordan to three rather than 30. In a boxing match, you'd rather fight Mike Tyson (I seriously can't name a single heavyweight fighting today -- is Evander Holyfield still boxing?) for one minute than three. Going to three against Jordan, you might hit a few lucky shots and Mike might miss a few, and you might actually win. Going to 30? There just ain't that much luck.

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Without clicking over and checking, which is the NBA's tallest team?

If you said the Washington Wizards, give yourself a cookie. Well, sorta. The Wiz are the league's tallest going by straight average, but they fall to eighth when weighting the list by minutes played. Frigging small ball.

supersub15, who started the thread over at APBRmetrics -- the best site for discussion about advanced statistical analysis of basketball -- also included a list of teams by experience. He used data from Justin Kubatko's Basketball-Reference, which (especially after the recent reboot) is the pre-eminent resource for NBA box score derived stats.

The height lists don't appear to be meaningful. That's not particularly surprising because the variation in heights is pretty small. Using straight averages, the difference between the league's tallest and shortest teams is just under three inches. The difference shrinks to 1.76 inches when looking at the minutes-weighted list. Having tall guys around doesn't necessarily help a whole lot -- the key is having GOOD tall guys.

Just eyeballing the list, experience appears to be a much more important factor. Even experience, though, doesn't seem to be all that great a predictor. The top few teams are good, but then there are teams like the Clippers and the Kings, which are both "experienced" and...umm...not good.

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I've been threatening to start publishing at RealGM again, and now I've finally gone and done it.  This one addresses the question in the headline.

From the article:

The dominant basketball story in Washington the past several years has been the ascendancy of Gilbert Arenas. His legend should be familiar by now. Underestimated and undervalued throughout his career, Arenas
blossomed with the Wizards into a bona fide All-Star and one of the game's most lethal offensive players.

The Wizards were dreck before Arenas arrived via free agency, but have gone to the playoffs each of the past three years. And there's no question that Arenas was the alpha player on each of those teams.

This season, Arenas played decently on a creaky knee still not recovered from surgery, then re-injured the knee and has been forced to sit. The Wizards lost their first five games, won three in a row with Arenas in the lineup, and have gone 17-12 without Arenas.

And so begins the murmuring — The Wizards are better without Arenas. They share the ball more. They take better shots. Arenas was a ball hog. They play more of a team game. Caron Butler was sublimating his
game — now that Arenas is out, we see what Butler can really do.

Each of these sounds logical and plausible. But none of them address
the real reasons why the Wizards have survived the loss of Arenas.

Read the rest here.

Last week, Bullets Forever proclaimed Haywood the second best center in the Eastern Conference, and referenced a blog entry I made about Haywood's consistency.  I wanted to take a look at whether Haywood has actually become more consistent this season, so I took five minutes this morning to plug Haywood's game log from this season into my consistency calculator.

Last season, his overall performance (as measured by a simple PER-like stat formula) had a consistency rating of 55 (zero would mean perfectly consistent -- no variation in performance), which rated 29th among NBA centers who got significant playing time last season. Average for an NBA center last year was a 49, so it was safe to say that he was a bit less consistent than average last season.

This season, Haywood's consistency score is a 41, which would have tied him for 10th (with Shaq, Amare and Dwight Howard) among NBA centers last season.  So, his per minute performance has been more consistent than it was last season.

One of the more interesting questions to come from my study of consistency is which comes first -- consistent minutes or consistent performance.  While in general the relationship between minutes and performance is fairly weak, players who perform more consistently on a per minute basis tend to average more minutes per game.  The same information could be restated as players who receive consistent playing time game to game tend to perform more consistently on a per minute basis.

As for Haywood, his minutes are more consistent this season.  His per game minutes have a consistency score of 21 vs. a 34 last season, a 28 in 05-06, and a 24 in 04-05.  The best season of his career (before this one) was 04-05.

Interestingly, while Haywood's overall performance consistency has improved, the correlation between his minutes and his performance has declined.  This suggests that Haywood's playing time this season has less to do with his performance, and more to do with the lack of options the Wizards have at center.  Which may be a slight indicator that minutes beget consistency -- at least in Haywood's case.

Lots more to discuss here, but not much more time.

Blog Note: I will update a bit more regularly over the next few months, as my work schedule permits.  I'm also making a return to RealGM -- I'll have an article up this week, then weekly columns at RealGM throughout the rest of the season.

 A few years ago, I came up with a simple system to use per minute stats as a method for identifying potential breakout players.  I dubbed it the "Diamond Rating" (finding diamond's in the rough), and have used it as a method to generate lists of players worthy of further research and watching for the future.

My old colleague from Hoopsworld, Kevin Pelton, who is now writing articles for the Seattle SuperSonics and Basketball Prospectus (he really needs to go ahead and write a book) tests how the Diamond Rating actually performs in identifying potential breakout players.

I'm pleased with the results, in part because of how I envision the rating being used.  It is not, and was not intended to be, something that would generate a definitive list of guys who would become "breakout" players in the future.  The idea was to identify players who might be getting fewer minutes than their production and ability suggests they deserve.  The formula would spit out some names, which would then serve as a list for further research and scouting.

Anyway, Pelton's article is a good read.

NOTE: I haven't been updating a lot lately, primarily because work demands are high at this time of year.  I expect to update on a more regular basis beginning in December.

In a column by the Washington Post's Mike Wise, there was this quote from Washington Redskins defensive coordinator Gregg Williams, "It was a glaring stat for us to see that Jon Kitna's quarterback rating versus pressure defense was 102 going into this game," Williams said. "You just gotta take a look at what's the lesser of two evils."

And it struck me how different the NFL is from the NBA.  NFL coaches not only make use of advanced statistical data, they embrace it, they study it, they use it to make their game plans.  Here's a prime example -- the Skins' defensive coordinator knows the opposing QB's rating against a specific type of defense.  Do you think your typical NBA head coach could tell you the opposing PG's offensive rating against a zone trap?

Wise's column does not emphasize the statistical angle, but it's interesting how Williams analyzed the various bits of data available.  Williams is renowned as a blitz-happy, pressure-the-QB coordinator, but when he saw how Detroit and Jon Kitna handled pressure defenses, he decided not to blitz.

Contrast it with the NBA, where I've had several different coaches (both head and assistant) tell me, "I'm not a stat guy..." or the equivalent.

Stats -- especially for professional basketball -- are imperfect.  Stuff happens that simply doesn't get captured, but the numbers are better than ever and still improving.  There's an array of good statistical information available that can be used to help make teams better.  And, where there are information gaps (like on the defensive end), methods exist (or can be created) to collect that data.

Bottom line -- many NBA teams could be helped by examining existing stats, and/or collecting and analyzing new stats tailored to their needs.  Not doing so is leaving possibly important information on the table.  The NFL is miles ahead of pro basketball when it comes to stats.  A few NBA teams are implementing stat programs.  Now would be a good time for the rest of the league to enter the information age.

Last week, Pradamaster at Bullets Forever posted some very good thoughts about how to fix the Wizards defense.  I responded in his comments, and decided to bring those comments over to my own blog and expand on them a bit.

I've done some pretty extensive tracking of the Wizards defense over the past 3 seasons, and the results readily reveal holes in the Wizards' defense.  The team's only quality defender is center Brendan Haywood, who actually forces opponents to miss shots.  Not at the level he did in 2004-2005, but still better than anyone else on the roster.

The guy who replaced Haywood in the starting lineup (Etan Thomas) shows up as a serious defensive issue.  Thomas struggles in post defense against bigger players, and is awful in screen-roll defense.  He contributes with blocked shots and defensive rebounds, but continues not to challenge shots he doesn't think he can block.

Antawn Jamison is a terrible defender in most respects, though he does help some on the defensive glass.  Gilbert Arenas is another problem (especially on containing dribble penetration and losing track of his man on the weak side), but he contributes by getting steals, forcing turnovers, and getting back to defend fast breaks.  Arenas, despite his deficiencies is not the team's worst perimeter defender.  Daniels, who arrived in DC with a good defensive reputation (and who is sometimes praised for his defensive contributions), tracks as a worse defender overall than Gilbert, particularly when it comes to containing dribble penetration. 

While it would be possible to dissect in considerable detail the flaws of each player on the roster, there is a significant and more fundamental issue -- the scheme.  Yes, the defense could be better if the players performed better on the defensive end.  But, it's also possible that the players could perform better if they were in a more sensible system.

Year after year after year the numbers show that NBA defense is first and foremost about making the other guy miss his shots.  The second most important part of defensive in the NBA is then rebounding those opponent misses.  Last season, the Wizards were third worst in defensive effective field goal percentage, and seventh worst in defensive rebounding percentage. 

Last year, the Wizards made a fetish of protecting the rim. They did this by collapsing to the paint when the ball went inside, and by sagging to the paint on weakside defense. The result? Inside FG% dropped a very small amount, but perimeter shooters got open looks because their defenders had either left them in help D or had sagged too far and couldn't recover.

The Wizards struggled mightily with containing dribble penetration.  Undirected penetration forced rotations, which inevitably left shooters open.  So, let's define what "containing dribble penetration" means. For good defenses, it does NOT mean preventing penetration. The best defense of the past decade (the Spurs) don't try to stop all dribble penetration -- in fact, they encourage it. Their defense is designed to force ball handlers to the sideline, then to the baseline -- into help defense. The perimeter defender's job is to contest three-point attempts and keep their man from penetrating to the middle.

The Spurs force rules are the same now as they were when Popovich took over the team a decade ago. Same defense year after year, game after game, possession after possession. The Wizards have had as many defensive sets as offensive. Responsibilities change with the variety of defenses, and the force rules change as well. They attempted to simplify the system last season with Bill Berry, but they still had a much larger array of defensive sets than the NBA's better defensive teams.

There's a wisdom to the Spurs' system. Tracking shows that taller players force more misses than smaller players (duh). The Spurs' system, which runs shooters off the 3pt line and forces penetration to prescribed areas, means that a greater proportion of shots will be challenged by a tall guy. The predictability of their system means that the big can anticipate where he needs to be, and that he'll have less ground to cover to be in proper help position. And, perhaps most importantly, their system emphasizes challenging shots, NOT forcing turnovers. The numbers clearly show that defense in the NBA is about forcing misses. Not steals, not forcing turnovers, not creating "disruption," not "playing with force."

I can hear the naysayers now -- "But the Spurs have great defensive personnel.  The Wizards don't have Duncan or Bowen, so what the Spurs do couldn't work for the Wizards."

Okay, what about Cleveland?  Can anyone name a great defender on the Cavaliers' roster?  Last season, no Cleveland players was named to the All-Defense team, and only one player (LeBron James) even received votes for the All-Defense team.  Yet the Cavaliers improved from 14th in defensive rating in 2005-2006 to fourth in 2006-2007.  How'd they do it?  By using a defensive system that copies what the Spurs do.  They even hired Hank Egan -- the long-time defensive assistant to Popovich -- to implement that system.

Bottom line, the Wizards are doing a lot wrong when it comes to scheme. Improving the team's defense should involve creating a better scheme, insisting that the players execute, and getting the right personnel on the floor. Yes, that means more minutes for Brendan Haywood and less minutes for Etan Thomas.  The coaches, the players, and the win-loss column would all also be helped by creating an objective way to evaluate players.  Stop talking in generalities about "force" and "protecting the rim" and define what those things mean and how they look on the court.  Then track them to see who's actually performing.

 

Recent stories about NBA referee Tim Donaghy consorting with gamblers and rigging the outcomes of games is scary news for the NBA and its fans.  The fundamental agreement between a sport and its fans is that the fans can trust outcomes of the games.  A ref monkeying with results strikes at the league’s integrity.

NBA fans and brass can only hope that Donaghy is one bad individual, and not the tip of an iceberg.  The prospect of more refs being involved in this sort of activity is likely driving up David Stern’s antacid bill.

Media has largely focused on whether or not Donaghy influenced the winners and losers of games, in particular the controversial game three of last year’s Suns-Spurs series.  While that’s interesting, gambling experts are beginning to identify ways that Donaghy affected outcomes relevant to bettors.  At very least, Donaghy was involved in rigging over/under results.

For gambling neophytes (like myself), over/under refers to a wager based on total scoring in the game.  For example, the casino might set an over/under for a specific game at 200 points.  If a bettor thought the teams would score more than 200 points combined, he’d bet the “over.”  If he thought they’d score fewer than 200 points, he’d bet the “under.”

How would a ref cause teams to score more points?  Simple — by calling more fouls.  And, according to the league’s foul-calling data, Donaghy not only called more fouls than any other ref, but also handed out more technical fouls.  More fouls called means more free throws, and more free throws means more scoring.

Did it happen?  Well, according to gambling expert R.J. Bell, in games Donaghy has reffed over the past two seasons, the “over” has won 57% of the time.  In other words, the two teams playing in Donaghy-reffed games scored more points than the Vegas over/under line.  It should be 50%, but is 57% significant?

Bell has calculated that there’s only a 5% chance that it’s a random result.

Then add in the fact that it’s a marked change from Donaghy’s previous record — in the preceding two seasons, the “over” won just 44% of the time when Donaghy was reffing.  According to Darren Rovell of CNBC, there’s a 1-in-1,000 chance that the “over” just randomly won 44% of the time for a two-year period, and then just randomly won 57% for the next two year period.  It just doesn’t happen by luck.

So, this is at least one way that Donaghy rigged outcomes for profit.  And, the numbers suggest that he may have been doing it for more than the past two seasons — which is the period the FBI is investigating.

Causing teams to score more (or fewer) points can change a betting outcome without changing who wins the game.  I don’t believe for a second that a crooked ref would stop at engineering over/unders and leave out profitable point spread wagering.  And if he futzed with point spreads, at some point he probably did change the outcome of games along the way.

And, according to Bell, there’s some evidence to suggest Donaghy did futz with point spreads.  Bell found that in games where the spread moved at least 1.5 points, the team receiving the heavy betting covered 10 consecutive times in games reffed by Donaghy from January through April of this year. The odds of that happening were 1,024 to 1.

Meanwhile, there’s intriguing research from Jonathan Gibbs, who examined the issue of point shaving in the NBA for his economics honors thesis at Stanford.  His paper has not yet been published, but should be on Stanford’s economics website later this month.

Completed and submitted in May of 2007 — two months before the Donaghy story made the news media — Gibbs paints a scarily plausible picture for players to engage in point shaving.

My thought has always been that players make too much money to get involved in this kind of thing.  But Gibbs points out something that I hadn’t considered — a player who shaves points would likely be able to see that he’d get the benefits of affecting the final margin of a game while not having to suffer the serious penalties.  Point shaving would offer a player two ways of winning — he could win the game, and win his wager.  And, the likelihood of detection is very low, in no small part because a well-timed stupid turnover looks a lot like a stupid turnover, not a guy shaving points.

Gibbs points out that betting markets are designed by the bookmakers to be efficient marketplaces.  The bookmaker sets a number to encourage half the bets to be on each side.  The closer he gets to 50% wagering on each side, the more he’s guaranteed a profit because bookmakers keep 100% of losing wagers and pay out only 90% of winning wagers.

Gibbs then goes through 14 years of point spread data and finds some market inefficiencies in point spreads.  If I’m reading his data properly, it looks like a bettor who knows nothing about the NBA could have an advantage by betting against the favorite in games where the point spread is larger.  Eyeballing the data, it looks like the advantage starts when the spread is about eight points.  It’s largest at around 10 points, and then again over 12.5 points.

I’ve been a fan of the NBA since the late 1970s.  In that time, I’ve never bought the conspiracy theories.  Instead, I’ve always thought that a bad play, bad call, bad performance was just part of the game.  But now there’s evidence that at least in the case of Donaghy, it was something else.  And in Gibbs’ paper, there’s indication of someone, possibly players, involved in fixing games.

I hope Donaghy is alone in this.  I hope that Gibbs’ analysis is wrong.  Anything else is very bad for the league and its fans.

Friend of the blog Chocolate City Jordanaire (a regular at RealGM), has built a reputation through the years as something of a draft guru.  He's showcased time and again an almost uncanny ability to identify college players who will go on to have successful professional careers.  When others were downgrading players like Carlos Boozer, Paul Millsap, Marquis Daniels and others for perceived shortcomings, CCJ steadfastly proclaimed they'd be good pros.

CCJ never had extensive scouting resources.  He didn't spend an inordinate amount of time parked in front of the TV scouting college players.  He did it in the most simple way possible -- by looking at the stats and finding guys he liked.  And most of the time, he was right.

The rest of the world may finally be catching on to CCJ's "secret" method.  The Portland Trailblazers are using a statistical model developed by Jeff Ma to help in their draft preparations.  At least two other teams are making extensive use of stats in their evaluation of draft prospects.  And advanced statistical analysis is filtering into online draft analysis as well.

This year, DraftExpress has included an array of statistical tools, including per 40 minute numbers, NBA Efficiency, Dave Berri's Win Score, and John Hollinger's PER.  While it's nice to have such measures available, there's not much analysis of the numbers -- there's nothing to tell us what the numbers say about the player's prospects as a professional.

Enter Ed Weiland of HoopsAnalyst and ESPN's John Hollinger.  Both Weiland and Hollinger have taken an intriguing approach.  They've looked at the college numbers for players in previous drafts, then compared those numbers to the players' performances as professionals.  They use this analysis to determine which stats are the best predictors of professional success, then apply it to the current draft pool.

In Hollinger's case, he translates an array of statistical inputs, as well as other variables such age and height, into a single number.  The higher the number, the better the professional prospect.

Weiland uses a similar approach, looking for the best statistical predictors for each position.  He leaves some more room for subjective analysis in the final ratings, which allows him to incorporate factors that could be missed in a purely statistical evaluation such as defense and injuries.

It's hard to say how successful a team would be if they relied entirely on one of these methods.  Weiland doesn't show how his system did in previous drafts, though there is a persuasive logic to his approach.  His basic evaluations are similar to Hollinger's, and Hollinger does show his system's predictions since 2002.

How are the results?  His system would have had the forgettable Curtis Borchardt 4th in 2002, and he had Mike Dunleavy, Jared Jeffries and Vincent Yarborough rated ahead of Caron Butler and Tayshaun Prince. In 2003, he would have recommended picking Mike Sweetney ahead of Chris Bosh and Dwyane Wade, and TJ Ford ahead of Hinrich and Josh Howard.  In 2004, he'd have picked Luke Jackson ahead of Josh Childress and Andre Iguodala.  In 2005, Sean May, Rashad McCants, Chris Taft, Danny Granger and Nate Robinson rated as better prospects than Deron Williams.  In 2006, Patrick O'Bryant, Paul Davis and Ronnie Brewer rated as "better" than LaMarcus Aldridge. So his system ain't perfect.

On the other hand -- NBA GMs let Tayshaun Prince slide to 23rd in 2002, while Hollinger rated him 11th. In 03, Josh Howard went 29th, Hollinger rated him 7th -- five spots better than Jarvis Hayes, whom the Wiz picked 10th. That same year, Hollinger also correctly identified Kyle Korver and David West as good pro prospects.  In 2004, he ranked Kevin Martin 10th. Martin went late in the first and is becoming a good pro. Hollinger's system also rated Carlos Boozer as the number one prospect in 2002 -- NBA GMs let him slide to the second round.  Boozer has turned out to be a terrific pro.

On the APBRmetrics message board, Hollinger points out that several of the notable "busts" in his system had injury problems -- Borchardt, Taft and Luke Jackson.  Sweetney appears intent on eating his way out of the NBA.  And, Hollinger readily acknowledges that his system blew it by rating Vincent Yarborough, Andre Emmet and Troy Bell so highly.  The point here, however, is that Hollinger's system successfully identified the guys who'd become quality NBA players -- including guys like Prince, Josh Howard, David West, Kyle Korver, and Kevin Martin each of whom GMs had much lower rated.

The system isn't perfect, but then again there's probably no such thing.  What Hollinger (and perhaps Weiland) are showing is that good statistical evaluation can go a long way toward improving the draft choices made by NBA general managers.  And, with millions of dollars on the line for all involved, that seems to me a smart thing to do.  Even if it ends up stealing some of CCJ's thunder.

A few weeks ago, I examined the statistical record to see whether there was any validity to Brendan Haywood's reported claim that he's treated unfairly by head coach Eddie Jordan.  Today, I'm looking at the counter-argument -- that Haywood is inconsistent, and therefore unreliable.

For a first check, I used my consistency measure on the Wizards roster.  In that measure, a low score means there's less variation in a player's performance.  Zero would mean perfectly consistent -- no variation.  A player's consistency is a self-referencing measure.  In other words, the variation in that player's performance is compared to his own average performance.

The issue of whether consistency -- more precisely, small variation in a player's performance -- is a good or bad thing is a separate issue.  Consistent excellence is good, but for a mediocre player, extreme performance variation may be preferable.  But that's an issue for another day -- back to the topic at hand.

In my consistency measure, Haywood scored a 55, which ranked fifth among Wizards regulars last season.  Caron Butler and Etan Thomas scored as most consistent (both with a 38), followed by Antawn Jamison (47), Gilbert Arenas (51), and Haywood.  DeShawn Stevenson (68), Antonio Daniels (70), Darius Songaila (73), and Jarvis Hayes (94) each had lower consistency scores than Haywood, but played a similar number of minutes per game.  Except for Stevenson, who played a lot more.

I shared these numbers with a Wizards official, noting that Thomas rated as more consistent than Haywood.  His response, "This is a case where the numbers lie."  He went on to say that Etan's defensive deficiencies are serious, and do much to reduce his postive effects in other areas.  I readily agree that this is a weakness in measuring consistency -- because of the lack of defensive data (I didn't track enough games this season to feel comfortable using those numbers in this sort of measure) I'm forced to rely on box score data.

But, most basketball stats are imperfect measures, and what I'm really looking for are indicators moreso than a definitive statement.  If defensive data becomes available, the method can easily be adjusted to include that information.  Anyway, back to the topic at hand.

After comparing Haywood to his teammates, the next obvious step was to compare him to his counterparts around the league.  I ran the numbers on 38 centers, and Haywood showed up as less consistent than the average center in that group.

The top 10:

1. Tim Duncan -- 26
2. Chris Bosh -- 29
3. Pau Gasol -- 33
4. Marcus Camby -- 34
5. Yao Ming -- 35
6. Emeka Okafor -- 35
7. Al Jefferson -- 36
8. Tyson Chandler -- 38
9. Etan Thomas -- 38
10. Shaquille O'Neal -- 41

The average consistency score for the group of centers I studied was 49 and the median was 47 (remember that Haywood scored a 55).  Overall, Haywood ranked 29th out of 38 in my consistency metric.

One important issue to consider is minutes played.  The correlation between minutes per game and consistency of performance was 0.7, which is reasonably strong, but not considered statistically significant.  (1.0 is perfect correlation.)  In other words, guys who got more minutes were likely to be more consistent.  Or, to put it another way, guys who were more consistent were likely to get more minutes.

It's impossible to say which direction causality flows in this case.  On the other hand, only three players (Etan Thomas, Rasho Nesterovic and Jamal Magloire) scored as more consistent than Haywood and played fewer minutes.  Five of the nine players who ranked "less consistent" than Haywood played as many minutes or more than Haywood.  That group includes Mikki Moore, Nick Collison, Andrew Bynum, Alonzo Mourning, and LaMarcus Aldridge.

What does all this say about Eddie Jordan's frustration with Haywood's performance?  For one thing, it says to me that Eddie had at least some justification to be frustrated with Haywood's consistency.  To put this in perspective, Kwame Brown scored as more consistent than Haywood this past season.  However, it's also worth considering that the group of consistent players also tended to have less variation in their playing time (another chicken/egg issue).

So, who's right, the coach or the player?  Maybe they're both right.  Eddie may be correct that Haywood's inconsistent.  Haywood may be correct that Eddie treats him differently.  Here's a possible solution: Eddie can commit to playing Haywood a certain number of minutes per night, while Haywood commits to becoming more consistent.

Note: many thanks to the guys at Wizznutzz.com for the photo of Haywood at the top.

The idea here was to see if there is a way to use box score stats to ascertain what coaches value when they make playing time decisions.  Of course, none of the correlations show up at a level statisticians consider to be statistically significant (.95 is usually that cut-off).  Honestly, I would have been surprised if any result did rise to that level -- the closest is Phoenix's 0.9 for eFG.  This analysis was about looking for tendencies (not certainties), and I think it does a decent job of that.

One thing to consider, is the causality direction.  That's to say, does Eddie Jordan give playing time to scorers because he favors scorers, or does he give playing time to scorers because they happen to be his best players?  Does D'Antoni prefer playing good shooters, or are his better shooters also his best players?  I don't know the answer to the causality direction question, which is one reason why I'm trying not to overstate the results.