Down With the Perfect 10: Why We Should Welcome the New Gymnastics Scoring System

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July 31 2012 7:30 AM

Down With the Perfect 10!

A mathematician explains the genius of the new gymnastics scoring system.

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Nastia Liukin. Click image to expand.
Romanian gymnast Larisa Andreea Iordache during the women's qualification of gymnastics at the London Olympic Games on July 29.

Photo by BEN STANSALL/AFP/GettyImages

The 2012 Olympic Games in London will use a relatively newfangled system for scoring gymnastic routines. The revamped rules, which debuted in Beijing in 2008, make an athlete’s artistry less important than her ability to string together loads of technically difficult moves. Today’s system has also eliminated what used to be the pinnacle of gymnastics achievement: the perfect 10. Four years ago, Jordan Ellenberg argued that the new scoring was more in line with the Olympic spirit of “faster, higher, stronger,” and he advised lovers of the perfect 10 to get over it. His original piece is printed below.

Olympic gymnastics has a new scoring system, and not everyone's happy with the departure of the famous 10-point scale. "It's crazy, terrible, the stupidest thing that ever happened to the sport of gymnastics,"wailed excitable supercoach Bela Karolyi in the New York Times. "How could they take away this beautiful, this most perfect thing from us, the one thing that separated our sport from the others?"

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What exactly is Karolyi kvetching about? This year, competitors get two scores, each from its own panel of judges. The "A" score measures the difficulty of the routine. A relatively easy move like a one-handed cartwheel on the balance beam adds 0.1 to your A score, while bringing off the astonishing Arabian double front layout rakes in 0.7. (And no, you can't inflate your score by doing 10 cartwheels in a row; only the 10 most difficult elements are counted, and repeated elements don't count at all.) Performing two or more elements in close succession tacks on "connection value" of up to 0.2 points per transition. The way to max out your A score, then, is to cram the toughest possible moves into your routine and pack them as tightly together as you can manage.

The downside of all that: In the middle of your painstakingly computed, ultra-difficult, absolutely seamless routine, you might fly headfirst off the end of the beam. That's where the B panel comes in. The B score starts at the top of the scale rather than the bottom, and every mistake takes you further from a perfect 10.0. The new system imposes a kind of mandatory minimum sentencing; after years of complaints about unobjective scoring, judges on the B panel now have less discretion about how many points to deduct for a given miscue. The standard penalties are also harsher than they used to be—a fall that would have cost a half-point in Athens now means a 0.8-point deduction. That's why American gymnast Nastia Liukin's botched dismount at the end of Sunday's brutally difficult uneven bars routine—a routine specifically designed by her father to ring up a massive A score—dropped her back to fifth place, behind several less ambitious competitors.

The final tally is the sum of the A score and B score; since the difficulty of the current batch of Olympic routines tops out in the 7s, you can expect medal-winning scores to be somewhere in the 16s. And that's one thing opponents of the new system don't like. "A perfect 16.9" lacks the ring of "a perfect 10."

"It's hard to understand. I don't even understand it," Mary Lou Retton told the Times. "Back in the old days you'd know what that means," sniffed NBC commentator Tim Daggett (himself the recipient of a 10.0 on the high bar in the 1984 Games) after watching China's Yibing Chen score a 16.275 on the vault.

But would you really? Under the old system, a 10.0 didn't mean "perfection"—the score for a flawless performance was computed by adding difficulty bonuses to a fixed "start value" (8.4 for men, 8.8 for women) up to a maximum of 10, then taking deductions for mistakes. An easier routine, carried out perfectly, might get a 9.6 instead of a 10. In other words, the old system was a lot like the new system. If anything, the new scoring is easier to interpret: A B score of 10.0 is synonymous with absolute perfection while the old unified score was an impenetrable combination of pluses and minuses arrived at only after Talmudic contemplation of the FIG's Code of Points.

But let's not focus on those details. As in most emotional disputes about numbers, people aren't arguing about precisely how the number is calculated but what it symbolizes. How we measure something reflects, and eventually influences, what we value in it. And in that view, the new scoring system really does represent a profound change.

Scales with a hard upper limit, like the old gymnastics scoring or the SAT, say that what's important is the pursuit of perfection. The goal of the SAT is to blacken the right bubble for every last one of those inequalities and analogies, and you can do no better than getting every one correct. Open-ended scales, like the new gymnastics system, value innovation and the breaking of existing barriers. You can't imagine men's weightlifting, say, being scored on how close you came to clean-and-jerking 550 pounds, with every pound above that not counting toward your score. That's because the goal of weightlifting isn't to approach a predetermined ideal. The goal—primal, simple, and satisfying—is to hoist a more awe-inspiring heap of metal above your head than the other fellow. Or, better yet, to hoist more than any other fellow in history.

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 and the author of How Not to Be Wrong. He blogs at Quomodocumque.