I don’t know about you, but I find it hard to watch certain events at the Winter Olympics without wondering about the relative importance of some of the more marginal sports. Well into my second hour of watching curling, I started thinking to myself that even if their physical weights are the same, not all gold medals are equally impressive.

I mean no disrespect. I’m sure that curling is difficult and stressful. And I’m aware that sliding down the mountain in a 4-man bobsled is dangerous. I’m also convinced that the third-line defenseman for the winning hockey team has played a valuable role in the team’s success and deserves to stand on the podium and have that glittering disc hung around his or her neck. It just seems to me that it’s much, much harder to win a gold medal in, say, individual giant slalom.

And if you want to compare the Winter Games to the Summer Games, isn’t it a heck of a lot more difficult to win the 5000m run than to win the 5000m speed skating title?

Imagine you are at a party, and someone points out a person across the room and says, “you see so-and-so over there? You wouldn’t believe it but twenty years ago, s/he won an Olympic gold medal!” Keeping in mind the relative likelihood of such a thing, what is your first guess about their sport? And how does the sport influence how impressed you are?

As I thought about this, it occurred to me that we should have a rigorous way of comparing the relative impressiveness of gold medals in certain sports. I don’t mean the commercial value (how much someone benefits financially from winning gold, since that varies too much based on the personal attributes of the winner); I mean how impressed we should be and how much esteem that medal carries.

In this sense the esteem with which we hold the winner of a gold medal — which we can designate as “e(Go)” — is a function of several factors:

• “Popularity” (P) — a measure of how many people compete in that sport (this seems to be a more relative factor than how many people watch the sport). Values of P range from 1 to 5, roughly corresponding to a log scale where

1 x 10^6 (1 million) or less = 1
1 x 10^7 (10 million) = 2
1 x 10^8 (100 million) = 3
1 x 10^9 (1 billion) = 4

• “Risk” (R) — i,e., the risk of bodily injury, in other words the danger factor. Values of R range from 1 (safe) to 4 (high risk of serious injury)

• “team dilution” (t) — the number of teammates with whom credit must be shared.

Using these factors, I’d like to suggest the following formula for calculating the e(Go) number:

e(Go) = P^2 * R / t      (eq. 1)

Our reference number is an individual medal in speed skating, where e(Go) = 1 * 1 / 1 = 1. In other words, if you own an individual gold medal in the 1000m speed skate, your e(Go) number is 1. Congratulations. You should be very proud.

Compare that with curling, with approximately the same number of competitors worldwide, but where competition is between teams of four. The e(Go) number for a curling gold medal is 1 * 1 / 4 = 0.25. In other words, a speed skating gold is worth four curling golds.

(As an aside, if curling is in the Winter Olympics, why isn’t Billiards in the Summer Olympics?)

How about Nordic skiing? Well, there are a heck of a lot more people who participate in the sport, probably well over 10 million. Without going to the trouble of looking it up (when I get more readers, I’ll go to the trouble to look these things up), we’ll say P = 2.2, so for Nordic skiing:

Individual gold medal:  e(Go) = 2.2^2 x 1 / 1 = ~4.8 (~five times more esteemed than a speed skating medal)  

Relay gold medal: e(Go) = 2.2^2 x 1 / 4 = ~1.2 (slightly more more esteemed than a speed skating individual medal).

How about hockey? Well, lots of people play the sport, the risk of injury is higher, but you have to share the esteem with 20 teammates, so e(Go) = 2.5^2 * 2.5 / 20 = ~0.78, or about three-fourths as impressive as a speed skating individual gold medal.

I could go on, but you get the idea. Note that this equation can also be used to compare gold medals from the Winter Olympics and Summer Olympics. Winning the Olympic Marathon 5000m, an event where you must be better than every other person on the planet who runs or jogs, is 16 times more impressive than a speed skating gold medal, but being on the Jamaican 4×100 relay team is only 4 times more impressive.

Perhaps if I have the time, I’ll rank all the sports by their e(Go) numbers. In the mean time, I’m going back to catch the next round of  Ski Ballet.