In the 6.0 system, one tiny mistake could keep a skater off the medal podium, Chan said, and the judging seemed based more on failure than success. In the current system, to encourage risk taking, skaters are still rewarded at least 70 percent of the value of a jump on which they under-rotate.

Frank Carroll, who coaches Ten in Southern California, said his skater “could not have been happier” in finishing second. Ten’s success had seemed improbable for a young man who learned to skate on outdoor rinks in Kazakhstan — a former Soviet republic that had won a medal at the world championships — bundled in so many layers of clothing that he said he “looked like a cabbage.”

But Carroll took issue with what many see as a vulnerability in the judging system — the program component score, or P.C.S., a rough equivalent of the artistic score given in the 6.0 system. In the previous system, a skater received one score for artistry or presentation. Under the current system, the component score is actually five scores given for skating skills, linking footwork and movement, performance, choreography and musical interpretation.

The subjectivity of the component score, skating officials concede, still allows judges to manipulate their marks, taking a skater’s reputation into account when he or she has a subpar day. This is sometimes known as awarding “hero points.”

“I think Patrick is fabulous, but when you fall a couple of times or make three or four mistakes, why are you the best in choreography, the best in artistry, the best in skating skills?” Carroll said. “That’s the problem with the new scoring system.”

After Chan narrowly defeated Ten, Todd Eldredge, the 1996 world champion from the United States, said on Twitter, “No disrespect to Patrick but a skater shouldn’t be able to fall twice & get such high PCS.”

In a broader sense, the 2013 world championships also validated for Carroll and some other experts that skating had become what he called a form of bean counting.