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.