And the winner is...

by Burkard Polster and Marty Ross

The Age, 15 February 2010

It's so exciting! The Winter Olympics began last week, and we've been watching intently, working hard to choose a winner. No, not the winner of any of the events. We're looking to award a prize to the Olympic event with the stupidest scoring system.

A few years back, this would have been easy, with figure skating winning hands down. You may in fact recall some of the odd happenings at the 2002 Winter Olympics. The most bizarre incident occurred in the women's singles figure skating. In that event the American skater Michelle Kwan was in the gold medal position with only one skater to go. The final skater was the Russian Irina Slutskaya, and she skated extremely well. As a consequence, Michelle dropped from first to ... third!

How could one final skater result in Michelle dropping from gold to bronze? Here's how. Each contestant skated twice, in a short program and a long program. In each program the skaters were scored, and the scores were used to rank the skaters. That's fine. The bizarreness comes with trying to combine the rankings for the two programs.

Common sense suggests that we simply forget the rankings, suitably weight the scores for the short and long programs, and add those weighted scores; then the best total score wins the gold. Instead, the 2002 system involved treating the rankings as numbers, and then those numbers were added, as indicated in the table below. As a consequence, a skater didn't know her ranking number for a program until the last skater had skated.

Lower ranking numbers indicate better performances, so we see Michelle Kwan was in the lead after the short program. The long program is more important, which is reflected in the doubled numbers. In the long program Sarah Hughes skated better than Michelle but it was not enough, so it seemed, to overtake her.

But then Irina skated, finishing second in the long program. As a consequence, Irina lowered Michelle's ranking number, overtook Michelle for silver and, on a tiebreak, propelled Sarah Hughes into the gold medal spot. What a performance!

Alas for absurdity fans, the International Skating Union modified their rules in 2004, and rankings are no longer added together. So, figure skating is out of the running in this year's Stupid Scoring competition. But there are still some worthy entrants.

We might consider sports such as the bobsled and the luge, but they clearly have no chance: these events amount to turning yourself into a missile, with the missile taking the least time to get to the bottom of the hill winning the gold. Many sporting events are of this nature, with some objective physical quantity determining the winner.

There are also many sports with a subjective element, such as mogul skiing and, of course, figure skating. More intriguing are sports such as the biathlon, consisting of skiing and rifle shooting; performance in each sport can be precisely evaluated, but there is unavoidable subjectivity in weighting the two performances. We can't imagine how the authorities determine the weighting.

However, it is a trifle unfair to make fun of sports with a natural subjective component. We would much rather make fun of a sport that is judged subjectively, even though an objective measure is right at hand. But who would possibly do such a thing?

Welcome to ski jumping. This magnificent event is the highlight of the Winter Olympics, where skiers shoot off the ramp at close to 100 km/h and fly more than 100 meters through the air. And of course, it's easy to determine the winner: whoever jumps the furthest gets the gold. Wrong!

In its wisdom, the International Ski Federation has decided that ski jumpers should be judged not only on distance, but on style as well. But it is simply beyond us how anyone can regard the "best" style as anything other than the one which takes you the furthest. And, we wonder how the Federation explained it to the Olympic silver medalists in 2006: both Matti Hautamaeki and Andreas Kofler would have won gold based upon distance scores alone.

With their stunning entry, the International Ski Federation has blitzed the Stupid Scoring competition. Ladies and Gentlemen, we have a winner!

Puzzle to ponder

Feel free to use the comments section to suggest solutions. Later in the week we'll post our solution in the comments section.

With the 2002 scoring system, Michelle was sitting first with one skater to go, and fell to third; but at least she still went home with a medal. Is it possible that a skater could have been coming first with one skater to go, and then fallen to fourth?

Burkard Polster teaches mathematics at Monash and is the university's resident mathemagician, mathematical juggler, origami expert, bubble-master, shoelace charmer, and Count von Count impersonator. 

Marty Ross is a mathematical nomad. His hobby is smashing calculators with a hammer.

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