Warning: Graphs Ahead

Maybe because of the acute conference imbalance or the utter lack of pre-ordained hierarchy, the ‘06-‘07 season seems to have witnessed a wholesale departure from traditional, standings-based evaluation and the headlong embrace of Power Rankings. After decades of unchallenged service as the legitimate arbiter of league pecking-order, win-loss records have been discharged like any other quaint convention, replaced by a battery of secret and not-so-secret formulas, each with their own measure of greatness and wretch. Yet as Matthew Yglesias recently observed, the criteria behind the formulas are often hard to discern. This is even true of Hollinger’s rankings: although his predictors are, strictly speaking, “objective” (i.e. point differential, strength of schedule), the weights he assigns them are essentially arbitrary. On the most crucial question of all, then – of who is saved and who is dammed – we find ourselves lost in uncertainty and darkness.

As acting chairman of FreeDarko’s Subcommittee on Weights and Measures, I have studied this matter closely and arrived at the following conclusions. First, that arbitrariness itself is nothing to fear; it is simply our irrevocable condition, and should be embraced by all as such. Second, that the real problem with today’s Power Rankings isn’t so much that they’re wrong, but that they’re boring. Thus, what we need is a ranking system that is both:

a) more overtly arbitrary and subjective; and

b) funny to look at

It is with these goals in mind that I am pleased to present Installment #1 of FreeDarko’s power ranking system, known hereafter as the PLAZAS OF DREADED PREDESTINATION.

When we attribute foreknowledge to God, we mean that all things have ever been, and perpetually remain, before His eyes, so that to His knowledge nothing is future or past, but all things are present. Predestination we call the eternal decree of God, by which He hath determined in Himself what He would have to become of every individual of mankind. For they are not all created with a similar destiny; but eternal life is foreordained for some, and eternal damnation for others. – John Calvin, 1537

Much as medieval Catholicism determined salvation at the end of each life through an simple audit of good works and bad, so too today’s power rankings consider point differentials at the end of each game, and from them derive measures of strength and weakness. And just as Puritanism replaced the Church’s ad hoc accounting with concern for the totality of one’s ethical surefootedness, so too the Plazas of Dreaded Predestination aim to grasp each lump of wins and losses in their actual unfolding through time.

In the graphs below, game time (in minutes) lines the x-axis, while the +/- differential is on the y; the resulting curves trace the mean point differential for each team at each interval. These curves are given (as moving averages) for the sum of games won, games lost, and total games in the 06-07 season. The current analysis is limited to Dallas, San Antonio and Phoenix - currently the league’s three best teams, in terms of winning %.

#3. The Dallas Mavericks

When the Mavs win, they win in fits and waves; an early lead of +7, followed by two quarters of calm, then a final surge to +13 in the closing minutes of the game. Their 40 wins is a league best. I rank them #3, however, because their losses, while infrequent, are as decisive as their wins. In these games, the Mavs' average deficit grows steadily from the very first minutes of the game all the way to the fourth quater, when it bottoms out at –12.

#2. The San Antonio Spurs

The Spurs 16 losses this season far outnumber the Mavs 9. Yet unlike the latter's perpetual decline, the Spurs actually lead for the first 24 minutes of an average loss, and only in the last 6 or 8 minutes does their opponent win decisive advantage. As for their 33 wins, San Antonio’s trajectory is slow, constant and almost perfectly linear. Very Popovich. Very Spurs.

#1. The Phoenix Suns

There are three remarkable features of the Suns trajectories which make them the obvious #1. First, consider their losses. Those who have witnessed a Phoenix defeat this season probably sensed that it was less a matter of beating the Suns than just hanging with them until the end. Even more than the Spurs, an average Suns loss doesn’t actually involve loosing until the very last minutes of the game: for the first 40+ minutes, Phoenix is basically in control. The second feature concerns Phoenix’s margin of victory. Whereas Dallas and San Antonio reach their highest lead (+13) in the final minutes of a win, Phoenix hits this same ceiling with almost an entire quarter of play remaining. Over the last 10 minutes of an average win, the Suns' advantage actually begins to decline, a result of either great exhaustion or modesty. I prefer to believe the later cause, and that were it not for decorum, Nash and Co. would claim victory margins averaging 25 points or more.

This leads to the third unique feature of the Suns’ PDP, and that is the rate of increase itself. As we observed with Mavs and Spurs, most winning teams follow a typical pattern: establish a quick and early lead, protect it through quarters 2 & 3, then end with a final surge. The Suns follow just the opposite pattern: they start slow and finish slow, but in the middle of the game they increase their lead with a remarkable urgency. This difference is best expressed in terms of the acceleration of the Suns’ point differential - the rate by which it grows over time. The following graph shows changes in this rate for the '07 Spurs, Mavs and Suns, using averages for total games (wins+losses).

From the preceding discussion, it should be clear that the Plazas of Dreaded Predestination meet our standards of arbitrariness and aestheticism better than most any other power ranking system. Most would agree that graphs are more fun to look at than numbers. And even more than Hollinger’s mysterious weights and coefficients, the privileging of one geometric feature over another is almost completely unjustifiable.

Nevertheless, the regularity of these trajectories and of their correspondence to team outcomes suggests that the Plazas of Dreaded Predestination may yet possess some objective, strategic value. For example: by knowing that a slim lead in the closing minutes almost inevitably foretells defeat, perhaps Steve Nash would be able to intervene so as to better protect his team’s fragile margin. From this universe of lines and shapes, might a team learn enough of itself to help itself win/be saved?

I had once entertained an affirmative response to this question, but now reject it as both unsound and unsafe. For one thing, it is unlikely that the mere knowledge of the Plazas would cause Nash to deviate from his normal course; to believe otherwise would assume that, in situations like the one described, Nash isn’t normally trying to protect the Suns’ margin. More importantly, knowledge that either outcome (winning or loosing) is preordained by one’s current trajectory risks plunging both player and league into the darkest and loneliest kind of stupor. The contrast here with Protestant predestination, could not be more stark. The Calvinist works hard to succeed in order to prove to himself that success is his destiny; yet he remain motivated only so long as God’s will is inscrutable and the outcome of his struggles uncertain. What we have here is the exact opposite case, where at any point in a given trajectory, the predestined outcome is both fully certain and fully knowable. The strategic employment of the Plazas, then, would collapse league psychology to a position akin to fatalism. Predestination in the absence of inscrutability is a recipe for Disaster.


At 2/09/2007 4:47 AM, Anonymous Kaifa said...


P.S.: Would love to know what the Lakers' curves look like.

P.S.S.: What would be very interesting to me: based on this analysis, taking a closer look at the Suns for example and seeing who of the players does what during these destinct phases. Maybe Nash is looking more for his own shot during the final minutes when the Suns lose leads or Amare doesn't get touches at all. And when you find out something like this, then your concept would not only have analytical but maybe also strategical value.

At 2/09/2007 5:19 AM, Blogger Max said...

Brilliant. Absolutely brilliant. It's refreshing to see an idea for power rankings that tell you something more substantial than which team John Hollinger or Marc Stein thinks is better than which.

At 2/09/2007 5:42 AM, Anonymous Larry Joyle said...

Maybe it's the gin talking, but this feels downright revolutionary. Each team's style is reflected in its trajectory: even disadvantaged fans like me, who don't have cable (and so rely on this stuff to get their NBA dish), even we know that the Mavs are a 1st and 4th quarter team, the Suns run hardest once they're warm—but before they're tired—and the Spurs win by attrition. You watch a game or two at the bar on Friday night, you'll know which team's "controlling the tempo," as the commentators say. If this were quantifiable, like say with time of possession in football, it'd be a top indicator…And also: we've all heard the old saw about how basketball is a "game of runs," and we hit the mute button because we know it's true, and the clock is arbitrary, and the Suns would win every game if they had a few more minutes…And while I'm at it: I'd like to see the graphs when these teams play each other.

At 2/09/2007 9:29 AM, Anonymous JTS said...

Power Rankings, as a tool for measuring a team's worth, are a crutch of the over-paid and unthinking mass of "analysts" employed by the big sports conglomerates. Other than Hollinger (and perhaps a few other that I don't have the patience to read), who at least feigns interest in statistics and observable facts, most are just arbitrary orderings by writers who are too lazy to do any actual reporting or thinking.

As usual, FD has bucked that trend and flipped a casual and highly amusing bird. Arbitrary and subjective, sort of. Funny to look at, very nicely done.

At 2/09/2007 9:36 AM, Anonymous lightninghank said...

I like it, and I would say with a lot of certainty that it is modesty that is responsible for the Suns' late-game decline. Seems to me they ride 6 guys to close the 3rd with a big lead and then the 4th quarter is Marcus Banks time.

At 2/09/2007 9:46 AM, Anonymous paper tiger said...

wonderful! let me suggest, though, to add to the fun without compromising arbitrariness, that each line should have at it's leading end an icon, like the yodeling mountain climber game on the price is right. for the suns winning line, an amare dunk. for their losing line, a raja bell punch. for the spurs, a duncan bank shot and a duncan missed free throw. for the mavericks, hasselhoff, always.

At 2/09/2007 10:30 AM, Blogger stopmikelupica said...

Brilliant. Freedarko does it again.

I would add that the Suns 2nd & 3rd quarter surges are also probably related to having one of the best benches (Barbosa) in the league. As weird as it sounds, I would bet the Knicks have a similar graph - start off very poorly (big holes early), then work their way back into the game thanks to their bench.

At 2/09/2007 11:22 AM, Anonymous RuDX said...


At 2/09/2007 11:28 AM, Anonymous Anonymous said...

I would love to see more analysis of more teams. Just remember "losing" and "loosing" aren't the same thing.

At 2/09/2007 12:06 PM, Anonymous Anonymous said...

completly retarded. wins are wins regardless of how they come about. and the same goes for a loss. so it's better to run out of steam in the fourth quarter of a tight game? thats you're penultimate acheivement? that's why the suns are great? penis.

At 2/09/2007 12:16 PM, Anonymous G-Fo said...

stopmike - I agree about the Knicks. And I think, at least in recent games, their line would turn exactly at the moment Jerome James is lifted for David Lee. Witness that Clippers game, where Big Snacks came out at 3:16 and the Knicks promptly went on a 9-0 run.

It'd be interesting to see this for losing teams, too. Where do they run out of gas/give up? How many take it to the closing seconds? Etc.

At 2/09/2007 1:24 PM, Anonymous Anonymous said...

Darkofan: DF proves itself again the most cerebral of the NBA blogs, even if Shaq and Wade make all the great analytic work irrelevant once again, by showing up for the playoffs with whatever margins the competition requires.

At 2/09/2007 1:38 PM, Blogger stopmikelupica said...

I want to second Paper Tiger's suggestion, if for no other reason than because I'm sure whatever little flourishes freedarko adds to the end of the graphics would be awesome... I can only imagine what sort of graphic ya'll would do for the Wizs (Swag!).

Also, doing this type of analysis for lesser teams would be more useful than the power rankings; it would allow for analysis that might be helpful for gamblers. Take the Nets - they are 7-11 in games decided by 5 or less points; they must also be among the top teams in the league in number of "close" games played. The Knicks, who I would have thought to have played alot of close games, are 8-5 (only 13 "close" games). Denver, another team with a similar overall record, is only 3-11 in "close" games.

From this info, I guess we can draw a few conclusions: One, Denver is either better than their record (and just unlucky), or they need to learn how to finish games. Two, the Nets are among the most likely team in the league to play a close game, so don't bet a huge spread in a Nets game. Even against the Bobcats (only 7 "close" games this year), both the Knicks and Nets played "close" games (accounting for 2 of Charlotte's 7 on the season)....

At 2/09/2007 1:52 PM, Blogger Stumbleweed said...

Someone needs to do this for the Nuggets. They are completely dumbfounding me right now with their suck. They always have leads in hand and blow it, but I have trouble figuring out the real reasons... I'm sure everyone wants their team evaluated, but damn, these guys are boggling my mind.

At 2/09/2007 3:06 PM, Blogger stopmikelupica said...

Hmm, the Nuggets. Why are they 3-11 in close games? Perhaps it's because their offense (whether 'Melo, Iverson, or Melo + Iverson) is dependent on jump shooting and driving to the basket; so 4th quarter = less fresh legs, which makes it harder to drive hard, draw fouls, and elevate on your jumper. To prove this we would need to evaluate the Nuggets 4th quarter shooting% versus the rest of the game, and the Nuggets FTA in the 4th versus other quarters.

I took at look at the logs of their last three close games: loses vs NOOCH, PHO, and CHAR. First thing I noticed: JR Smith is the offense for most of the first half of the 4th quarter. Worth noting.

Stat breakdown (really rushed, so might be errors, and clearly not a great sample size)...

vs. Charlotte:
1-3rd Q: 26-60 FG 43.3%; 20-24 FT
4th Q: 9-20 FG, 45%. 3-5 FT
Last 5 minutes: 1-7 FG, 3-5 FT.

vs. Pho:
1-3rd Q: 31-68 FG 45.6%, 11-16 FT
4th Q: 12-23 FG 52.2%, 4-5 FT
Last 5 minutes: 6-12 FG, 2-3 FT

vs. NOOCH:
1-3rd Q: 35-76 FG 46.1%, 14-21 FT
4th Q: 9-22 FG 40.9%, 5-6 FT
Last 5 minutes: 2-10 FG, 2-2 FT

Um, my spotty conclusions from such minimal effort (maybe I'll work on this some more over the weekend) is that the Nuggets don't get to the line as well in the 4th. And that in the last 5 minutes of the 4th, when JR isn't the key offensive player, but Iverson and Melo are, they don't shoot well.

Of course I haven't watch too many Nugget games this year, so I can't speak as to whether this even sounds right or not...

At 2/09/2007 3:14 PM, Anonymous Anonymous said...

I think you're dumping on Hollinger a little too hard. He's not weighting his predictors arbitrarily, but rather based on historical precedent. By researching previous seasons, he can tell the degree to which, say, a good defensive field goal percentage corellates with playoff success. Based on those correlations, he can weight the predictors pretty accurately.

At 2/09/2007 3:16 PM, Blogger The Electric Zarko said...

Anon 12:06 - If a win is a win and a loss is a loss and anything else doesn't matter, why even watch the game? Or even read the box score? Knowing the result then would then be the only meaningful act.

A is A!

(I know, don't feed the trolls, etc.)

At 2/09/2007 3:25 PM, Blogger Brigadier Pudding said...

I think you're dumping on Hollinger a little too hard.

not possible.

At 2/09/2007 3:39 PM, Anonymous bernard snowy said...

Completely unrelated to anything here, but I had a dream last night that J.R. Smith dropped 76 in a game, prompting Shoals to label him "thoroughly unfuckwithable".

WV: lzkznxd = lesbian cousin went straight-edge

At 2/09/2007 3:49 PM, Anonymous D-Wil said...

Unfortunately, this is just another regular season set of stats. The more accurate set of statistics come from this: what happened to the Suns during the playoffs last season when they played a quality opponent - Dallas. what happens to the suns when all of their regular season statistical advantages are muted. what happens when their number of possessions, field goal attempts, field goals made assists-field goal ratio shrink due to slower-paced games?

This, I feel, is truer indicator of the Suns' potential success.

In other words, what happens to Phoenix when their advantages are nullified while opponents continue to play their normal style. Additionally, because of the Suns inherent defensive weaknesses, opponents' offensive strengths become enhanced while the Suns strengths are lessened.


And to stopmikelupica... I just so happened to have written a post last night about the nuggs' explaining their problems & why they won't make the playoffs this season.... Their deficiencies and resultant poor record have more to do with injuries, a suspension, and new bringing in new players - all leading to a lack of continuity, plus a lack of commitment on the defensive end than with luck & knowing how to finish games...

At 2/09/2007 3:54 PM, Blogger Bethlehem Shoals said...

wait, i haven't called j.r. "unfuckwithable?"

and anon12:06, anyone who doesn't know how to use "penultimate" in a sentence might as well make himself a "pompous ass in a fire" jersey.

At 2/09/2007 4:04 PM, Blogger The Electric Zarko said...

D-Wil - Actually, wouldn't the playoff results be predicted by these graphs? The fact that the Suns tend to lose the games they lose at the end of the game is a clear indicator of their inability to close out a game, which is the defining phase of play in the playoffs, since the fact that all the teams are pretty good means more close games.

This may just be hindsight, though.

Also: the Warrior's graph would be hilarious, a distillation of the ineptitude and angst that has become the hallmark of the organization.

At 2/09/2007 4:09 PM, Blogger stopmikelupica said...

"unfuckwithable"? Like Sandra Bernhard?

Ah, thanks for the headsup D-Wil... I make a note to check out your blog every day or two, and must have just missed the new posts yesterday. I like your technique, and agree with alot of your takes (Bonds, for example). Will take a look at it....

At 2/09/2007 4:13 PM, Blogger Mr. Six said...

This might end up as a double post, but ...

I'm going to third paper tiger's suggestion and up the ante with a proposal that the graphs be integrated with the icons from the Competitive Style Guide.

wv: govgcd--.gov gives corporate discount

At 2/09/2007 4:26 PM, Anonymous D-Wil said...

electric z-
I'd need to go back to the play-by-play of the Suns playoff games last season. Just from thinking about them, though, they usually have one run in them, but upper-tier coaches and teams limit that run. Other than the inevitable, albeit limited Phoenix run, they generally get steadily ground down in the 4th....

sml - cool...

At 2/09/2007 4:40 PM, Anonymous Anonymous said...

Thats a very interesting analysis you came up with. I must note that you need "normalize" the scoring involved. The fact that scores are greater and that opponents scores are greater, creating a greater gap for phoenix must be normalized against the spurs and mavs. This is something that is done in music production on volumes and I think it relates well here. If you dont normalize the statistics, you are just comparing apples and oranges.
These analysis are fun though! And they are very good looking at individual teams, just not comparing them. Also, point differential does not seem to be a sound indicator of games won. While this may work between the suns and celtics, its not so good at comparing the suns and the mavs. You, and hollinger have created a factor that gives benefit to uptempo teams, without any reason to back this up, while detracting from better defensive teams, and teams that consistently win close games. Games won under 4 point differential should be a plus factor that contributes as well.

At 2/09/2007 11:16 PM, Anonymous Anonymous said...

They're interested in shapes, not numbers. Normalization shouldn't matter. We FEEL our way through basketball at FD.

At 2/10/2007 2:00 AM, Blogger Daniel said...

I find this analysis incomplete and unconvincing. Dallas has a better overall record, a better record against teams that would make the playoffs if they started today, and they won both head to head matchups against Phoenix. They've also done it against a much tougher schedule than Phoenix. I don't much care that the Suns can run laps around the Bobcats and Grizzliesin January. When it comes to nutcutting time, they are clearly one notch below the Mavericks.

As for the assertion that San Antonio is better than Dallas, I again have to heartily disagree. After the nucleus of Duncan, Longoria and Manu, they have absolutely nothing. Their supporting cast is older than the Golden Girls. There's no way they're overtaking Dallas in a seven game series given the Mavs superior depth and firepower.

At 2/10/2007 12:30 PM, Anonymous Anonymous said...

brilliant post, i give ESPN three weeks to trot out a similar feature

q though: where did you get the data from?

At 2/10/2007 4:37 PM, Anonymous cw said...

Excellent work.

About Calvin, I think Calvinist bigwigs believed that their elevated status in this world meant that they were of the Elect. Which makes sense, if God has predestined you to salvation, that means he likes you, and if he likes you he's not going set you up in some crappy little apartment in the suburns of Rockford, he's going to give you the nice mansion on Long Island. Its' the equivilent of superstar calls. When the powers that be decide you are a superstar, then you get the calls. It has nothing to do with what actually happens out on the court. On the court there are the Elect and the Preterit (the rest of us). The preterite are there to be dunked apon, to blow by, to commit fouls, to lose.

At 2/10/2007 5:54 PM, Blogger Eli said...

Awesome work, guys.

At 2/10/2007 5:55 PM, Anonymous Anonymous said...

Is this a new Espn feature (the "Game Flow") i've never noticed it before but it seems just like the plazas


At 2/10/2007 7:14 PM, Blogger SilverBird5000 said...

great comments.

a few quick things:

anon: game flows show total points on the y axis (always positive, always increasing), whereas the plazas show point differential, which is a far more meaningful indicator of games are won. also, game flows aren't aggregated or split up by W/L.

Daniel: yes, as an actual ranking system, it is both incomplete and unconvincing. that's sort of what i meant by "completely unjustifiable". but i do think it tells us something about how different teams do their thing.

cw: yeah, you're right about JC. despite his own party line, he was probably the most certain that he would be saved. phenomenal swag.

At 2/11/2007 1:49 PM, Blogger PeteJayhawk said...

I dunno about that, cw; there are some pretty nice apartments going up in the Roscoe/Rockton and western Boone County areas these days.

At 2/11/2007 11:57 PM, Blogger Daniel said...

Beautiful work.

This post and posts like the Comprehensive Style Guide make you guys the best hoopsters in all of tubeville.

I would also like to throw my vote in for analysis of more teams, even spasmodic monstrosities like my beloved OK City Sonics. If the graphs and stats are a pain to compile, I'll understand you not doing it. But if it's just a matter of clicking and dragging, maybe you guys could create a link to all the teams in the A.


At 2/12/2007 12:26 AM, Anonymous paper tiger said...

okay, it's slow, so now seems as good a time as any to flaunt ignorance: can someone please explain word verification to me?

At 2/12/2007 12:47 AM, Anonymous paper tiger said...

100% nevermind.
must the joy of a light bulb be undercut by the slow-witted shame of darkness?
i say yeah.

wv:qmpyq= whatever i'm knew at this.

At 2/12/2007 2:57 AM, Blogger Ben said...

"After the nucleus of Duncan, Longoria and Manu, they have absolutely nothing."
Longoria :)

I agree, the Spurs are so unremarkable other than Manu. Duncan is pretty overrated lately. You can't say he's just a great quiet player if he hasn't been loud enough to get his team all that powerful this season. He does his job, but he's not a leader like Nowitzki or Nash.

These are enlightening graphs, but I still don't give much credence to power rankings as opposed to a decisively superior record. I don't worry about the Mavs being able to take down the Suns in the conference finals with the strong defense the Mavs have, because if the Suns can't get good looks for 3-pointers, all that they have left is getting Nash to pass it into the paint and Diop and Dampier have both proven to be able to stop them from finishing those moves.
I'm more worried about the Bulls making it to the Championship and stepping up to the big team like they always seem to do.

At 2/12/2007 3:41 PM, Anonymous Anonymous said...

"he's not a leader like Nowitzki "

Don't say that in front of D-Fraud.


Post a Comment

<< Home