Down With the Perfect 10!
A mathematician explains the genius of the new gymnastics scoring system.
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There are some Olympic sports in which an upper limit might be more appropriate than in gymnastics—in sprinting, for instance, where today's fastest runners may actually be very close to the absolute physical limits of human ability. There is some mark in the 100-meter dash that's the equivalent of getting all the questions right on the SAT—you just can't do any better. I asked Peter Weyand, a professor of kinesiology at Rice and an expert on human locomotion, how far away that ultimate limit was from the current world record. Like a good scientist, Weyand declined to make a precise prediction. But the scenario he presented for serious improvement in sprinting verged on the science-fictional, involving a drastic enhancement of the density of type IIX muscle fibers, achieved via cloning or extremely fortunate mutation. It doesn't seem a bad guess to say that the sprinters in Beijing, not the gymnasts, are the ones for whom "perfection" is an appropriate metric.
The same goes for other track-and-field events highly dependent on sprint speed. This write-up from the American Institute of Physics explains how to use the conservation of energy to estimate your maximal possible pole vault from your top running speed. If we plug the current 100-meter world record into the formula, a vaulter who's 2 meters tall (about 6-foot-7) would have a maximal clearance of 6.5 meters—not so far above Sergei Bubka's world record of 6.14 meters. You want to grade pole vaults by their nearness to 6.5 meters, with deductions for inappropriate music or a bounce on the landing? No objection here.
Gymnastics, by contrast, isn't constrained by simple applications of Newtonian mechanics. Gymnasts can perform moves that no one's carried out before—that no one ever thought of carrying out before. Now, the sport has a scoring system that's built to reward that. In theory, yes, there's still an upper limit. There are only so many different possible elements in a routine and only so many possible connections between them, and each one, at least for now, is worth at most 0.7 points. But this new upper boundary is less like a perfect SAT score than a 1.000 batting average: a limit so far out of reach it might as well be no limit at all.
"The new 'open-ended' scoring system was designed in part to prevent us from outgrowing the rules," international gymnastics judge Judy Schalk told me via e-mail. Before the new system, just about all elite competitors performed routines difficult enough to bring the start value up to a 10.0; sailing over that threshold earned you no more points than barely clearing it. With the new system, gymnasts have the incentive to keep making their routines tougher and more complex. In every other sport, the competitors in Beijing are superior to their predecessors and get better scores to prove it. Why should gymnastics be the only sport without world records?
With the new system, gymnastics comes into compliance with the Olympic motto. That's "faster, higher, stronger," not "more graceful, more beautiful, closer to perfect." It's no coincidence that the Olympic sports that have historically chased the latter ideal are the same ones in which the women's game overshadows the men's: gymnastics and figure skating.
Figure skating ditched the perfect 6.0 after crooked judging in the 2002 Salt Lake City Olympics embarrassed the sport. The old scoring system already had many discontents, most famously great French champion Surya Bonaly, who showed her disdain for the judges at the 1998 Olympics by landing a backflip on one skate. It was illegal, it carried a mandatory deduction, and she was the only woman in the world who could do it.
If the judging controversy in figure skating is any guide, don't expect gymnastics to enjoy a smooth transition into the new era. Some people think skating's new system has bastardized the sport, forcing all competitors to adopt the same intricate and high-scoring combinations of moves, tougher without being better. "A triple Axel with two fingers into the skater's nose would definitely be more difficult than the usual triple Axel, but could we consider that an improvement?" asked former Olympic judge Sofia Banchetti Garbato in an open letter to the International Skating Union president. (Note: The triple nasal axel is not currently an ISU-sanctioned element.) On the other hand, the second-place finisher in this year's men's world championship complained that the new system didn't offer enough points for difficult jumps, thus encouraging skaters to turn in perfect but less demanding programs.
The new gymnastics system is substantially simpler than the one figure skating adopted, and the effect is likely to be clearer: more difficult routines, more athleticism, less focus on beauty and presentation. Dance elements count for much less, spectacular flips and dismounts for much more. "The artistic value is further repressed in the quest for more difficulty," says Schalk.
And that's for the best. Right now, gymnastics fans look back to the flawless performances of Nadia Comaneci and Mary Lou Retton and say, "How can gymnastics survive without the perfect 10?" But the next generation of fans, watching their heroes smash one another's records with ever more spectacular physical feats, are more likely to ask a different question: "How did gymnastics survive without the golden 17?"
Jordan Ellenberg is a professor of mathematics at the University of Wisconsin. His book How Not To Be Wrong is forthcoming. He blogs at Quomodocumque.
Photograph of Nastia Liukin by Kazuhiro Nogi/AFP/Getty Images. Photograph of Mayu Kuroda on the Slate home page by Franck Fife/AFP/Getty Images.