Although the Serena Williams episode provoked my interest in the puzzle of temporal variance, I’ll start not with tennis, but with other sports in which a practice of temporal variance might seem more secure – sports like football, hockey, and basketball. In each, whistles for minor physical contact toward the end of tight contests predictably elicit a cry from the stands: “Let ‘em play!” or “Swallow the whistle!”
Though the plea is familiar, its rationale is obscure. To be sure, the tighter the rules are enforced, the less physical contact there will be. And observers may reasonably disagree about the level of physicality that makes a sport the best it can be.
But however a league might answer that question, it is not self-evident why the optimal degree of laxity should differ in crunch time during an NBA game relative to ordinary time, or throughout the NHL playoffs relative to the regular season. It is not obvious what can be said for “letting them play” at this particular time different in character or force from what can be said generally for “letting them play.”
Still, basketball remains a good place to start. I doubt that many tennis fans are justifiably confident that tennis officials do (or don’t) allow players a little more foot faulting toward the end of close matches than earlier. Maybe they do (or don’t), but foot faults just aren’t called enough to permit those without intimate knowledge of the sport to be sure what the enforcement patterns are.
Basketball is different. That basketball referees respect some measure of temporal variance seems clear to many hoops fans. Maybe that’s because the case for temporal variance in basketball is unusually clear. (Or maybe not.) If we can explain and justify slack in the calling of basketball fouls, we might be better able to assess whether temporal variance makes sense elsewhere too.
One rationale for temporal variance invokes essentially aesthetic considerations: the referee’s whistle disrupts play, thereby reducing spectators’ enjoyment of the action. And while disruption of play almost always incurs an aesthetic cost, disruption during crunch time is especially costly (aesthetically speaking) given heightened dramatic tension.
There is something to this justification for temporal variance. It would seem to apply, though, only when play would continue uninterrupted but for the calling of a foul. However in some sports that arguably respect temporal variance play stops either way.
For example, it appears to me (and not only to me) that football officials are often more reluctant to call defensive pass interference during crunch time even though an incompletion stops play just like a penalty flag. Because an aesthetic or dramatic preference that play continue unabated wouldn’t seem to explain or justify temporal variance everywhere it appears, it might not provide the whole story even in basketball. So without denying that appreciation for dramatic excitement can help explain why officials should give the competitors somewhat greater slack during moments of high drama, we have reason to look for an alternative account too.
A second answer, recently advanced by Chicago economist Tobias Moskowitz and SI columnist L. Jon Wertheim in their book Scorecasting, depends entirely on the omission bias. By relying entirely on a cognitive bias, however, the authors all but ensure that, even insofar as their account might help explain temporal variance, it is unlikely to justify it.
The alternative account I offer runs as follows:
(1) In the main, a sanction imposed for an infraction has a greater expected impact on contest outcome (against the rule-violator) than does the infraction itself (in the violator’s favor). This must be so for the sanction to serve a deterrent function in addition to a restitutionary one.
(2) The expected impact of all outcome-affecting contest events – e.g., scores, base hits, yardage gains, infractions, penalties, etc. – are not constant, but context-variant. To start: the closer the contest, the greater the impact. The variance that matters for my purposes, however, is temporal: when the contest is close (and holding the closeness of the contest constant), the expected impact of outcome-affecting events varies in inverse proportion to the distance remaining to contest’s completion.
For example, touchdowns and baskets, 15-yard penalties and free throw opportunities, all have greater impact on the expected outcome when occurring 2 minutes before the end of a then-tied game than when they occur 2 minutes from the start. (I expect pushback here, and look forward to debates in the comments.)
(3) From (1) and (2) it follows that the absolute magnitude of the gap between the competitive impact of the infraction (say, a non-shooting foul) and the competitive impact of the penalty imposed for the infraction (say, the award of free throws) is significantly greater in crunch time during close games than earlier in the same contest. The penalty becomes more overcompensatory in absolute terms.
(It does not become more overcompensatory in relative terms, which is why some of yesterday’s posters rightly observed that if the stakes become higher for the competitor who would wish to invoke temporal variance, they become higher for their opponents too.)
(4) It is a general principle of competitive sport that athletic contests go better insofar as their outcomes reflect the competitors’ relative excellence in executing the particular athletic virtues that the sport is centrally designed to showcase and reward. (This is a first cut; no doubt my proposed principle could be profitably refined further.) This is why we prefer to reduce the impact of luck on outcomes (e.g., we generally want playing surfaces to be regular thus reducing unpredictable bounces).
It is also why almost everybody agreed, in Casey Martin’s lawsuit against the PGA, that if (as the Supreme Court majority essentially concluded, but as the dissent denied) the central athletic challenge the PGA Tour presented was the ability to hole a ball by means of striking it with a club, in the fewest number of strokes, while battling fatigue, then golf is less good – it exemplifies a core value of sport less well – if it requires competitive golfers to walk the course even when it is extraordinarily difficult for them to do so and when they are greatly fatigued without walking.
(5) From (3) and (4) we have a reason (not a conclusive reason) to enforce restrictions on minor or incidental contact less strictly toward the end of close contests if – as is contestable but surely plausible – the ability to refrain from minor bodily contact with opponents is a peripheral athletic virtue in basketball as we know it. If this is so, then a penalty of nominally constant magnitude that it is optimal to impose early in a contest may become suboptimal later in that same contest.
To be clear: I do not claim that the excellence of avoiding minor contact is something that no sport could wish most to valorize. My argument for temporal variance in basketball is explicitly contingent on its being the case that this particular excellence does not rank so highly among the excellences that basketball wishes to feature and encourage. Whether this is so is an interpretive question.
That’s my proposed pro tanto argument for temporally variant enforcement of non-shooting fouls in basketball. The argument extends to similar fouls in sports like football and hockey. At bottom, it’s based on an aversion to the awarding of windfall remedies disproportionate to the harm suffered. That’s a principle the law frequently endorses – from the harmless error rule to contract law’s material breach doctrine.