Go Team USA!

[Shadow]

Sure you can, by any meaningful definition of the word "best".

That's what I just got done saying.

More people enter = more medals. Doesn't mean the biggest team has the best athletes. The only meaningful stat is medals per ______, where _____ can be people, funding, teammates, whatever you like. But you need to normalize your stats somehow before you can compare to others in any meaningful way. How you do it is up for debate.

[Rakefur]

Stop making excuses Shadow. Raw data doesn't lie. The US has the most total and most gold medals. Finis.

[Shadow]

Ugh. Critical thinking skills.

North Korea has a larger standing ground army than the US. Does that mean they have better soldiers? Probably not, because of differences in funding levels, technology, and training opportunities.

You guys won the most medals. That doesn't mean you have the best athletes. That's the point of this little lecture.

Again, I don't care about the Olympics. Offhand, I don't even know how Canada ended up performing, not did I watch any of it. I am trying to educate you guys about interpreting data in a meaningful way. But please continue to ignore the lesson based on the assumption that I am just jealous of 'Merika.

Raw data lies all the time. You have to learn how to extract truth from it. In this case, you do that by normalizing by some meaningful measure. Team size is a good one. Population is not bad, but it ignores economic factors that are probably fairly even across people who actually enter the olympics, eg, teams.

Another good one would be to normalize by team size, and then further normalize by average funding level per athlete on any given team. That would give you a medal per person per dollar measure which would be a reasonable (though not perfect) representation of actual skill of the athlete by removing both team size and available training opportunities bias. I am not sure if that data is easily available, though.

Here is a decent (if slightly out of date) article which attempts to do exactly that (medals per person per dollar), though they use GDP per capita instead of actual average funding level. You can even download their data and analysis.

In other words: comparing raw medal counts is meaningless.

[Gen. Volkov]

I don't actually care about the olympics at all (why would any county ever volunteer to host them..?), but I do care about people being ignorant of the actual meaning of statistics they are looking at. Total medal count is almost completely meaningless as a measure of anything, and it annoys the hell out of me that people are still on about it. You should know better, Volk.

You do get that was a joke, right? If you want to have an actual serious conversation about this, I can tell you why you are wrong about the medal count being meaningless, or at the very least why your ranking by team size is just as meaningless, but I don't actually care that much.

[Shadow]

Yea you were joking. I am pretty sure Rakefur is being serious, though.

Well, I'd like you to give what you think would be a meaningful translation of medal count into athletic skill index. As I said, there are many different ways to normalize. But are you actually arguing that normalizing is not necessary if you want to extract a ranking of athletic ability by country?

[Gen. Volkov]

Well, I'd like you to give what you think would be a meaningful translation of medal count into athletic skill index. As I said, there are many different ways to normalize. But are you actually arguing that normalizing is not necessary if you want to extract a ranking of athletic ability by country?

Actually I'm arguing that the Olympics are meaningless as judge of athletic ability per country. Reason being, the Olympics are a secondary consideration for athletes in most countries. The US excels because it has a lot of athletes, China excels because they are one of the few countries who actually care, past that, the top athletes in most countries don't go on the Olympic team, they go into professional sports. Because professional sports pays really well, and the Olympics mostly don't, unless you get endorsement deals, which are rare if you don't win multiple gold medals, and there are very few people who win multiple golds.

[Shadow]

That's a fair statement. It doesn't take anything away from my point, though, which is that lots of Olympic medals says nothing about athletic ability by itself, and moreover that if any information is actually sought from the medal counts, it can't be done meaningfully with the raw data.

Whether or not there is any information to be had at all, meh. Ranking amateur athletes by country is probably the best you could get.

[Gen. Volkov]

Well, there is more to my point, but I don't have time to get into it right now. Look for an edit later tonight.

[EDIT] Ok, so, basically, I think raw medal count does say something important. But not about athletic ability. Rather, I think raw medal count shows how well each country does at selecting it's Olympic athletes. There are countries with sizable populations, and moderate development, who do terrible at the games. Like India, for example. With 1.2 billion people, they should be just as capable as China of fielding really competitive Olympic teams. But they have a very poor selection process, and put very little money into their Olympic programs.

I'd say the only sport at the games that really showcases athletic ability by country is the basketball tournament, because it features professional basketball players, who at the very top of their sport. I'll grant you that basketball is still primarily an American sport, but I think we can all remember the failure of USA basketball to win gold at the 2004 games, which shows that the rest of the world has become a lot more competitive in that sport. The days of the 1992 Dream Team are long gone. (Did you know that in the gold medal game, the Croatian players were actually begging John Stockton to stop shooting? I find that hilarious.) I thought it was just retardedly funny when Kobe and Lebron said the 2012 squad could have beaten the '92 Dream Team. Really Kobe? Really? You barely squeak by Spain and Pau Gasol, and you think you can take on Magic Johnson, Larry Bird and Michael freaking JORDAN?

[Shadow]

I maintain that to measure selection accurately you need to normalize by team size. If you submit twice as many athletes there are twice as many medal opportunities, so extra medals isn't necessarily an effect of better selection in that case. Especially for olympic events like vault, diving, gymnastics, anything where you are performing rather than racing or enduring, where you only get a couple of chances, there is huge opportunity for an upset by a mediocre athlete. Even the best athletes have bad jumps on occasion, and even the worst ones get lucky sometimes (for example, that American female gymnast who was supposed to take the gold without even trying and ended up messing up her ankle and losing outright). Having more contestants greatly increases medal counts even if the athletes chosen are sub-par when there is only a small number of attempts, because luck plays a much bigger role in small sample sizes (read: in a small sample, the standard deviation is much larger).

Small attempt numbers favor mediocre athletes, in that they have the best chance of winning in a small sample of trials. If Athlete A wins 70% of the time against Athlete B who gets the other 30%, then the win rates (eg, chance of winning a majority of trials in each case) are:

1 trial: A 70%, B 30%
3 trials: A 78%, B 22%
5 trials: A 84%, B 16%
7 trials: A 87%, B 13%

etc

So no, if the number of medal attempts for each athlete is small, then flooding the podium with mediocre athletes gives more medals than picking a small number of excellent ones. Or better yet, maximal chances happen when you pick your best, and then pick a large number of athletes who can just barely qualify. The smaller than number of trials, the greater the chance of an upset. This is why hockey games are best of 7 - because it gives a much greater chance of an accurate guage of the better team.

If olympians had many chances at each event, then you would be right that team size would not matter, but in most olympic sports that is not the case.

[Rakefur]

I was being a typical American stereotype Shadow.  :P

I don't think team size is really accurate. Ranking by funding might be a little better. But really I think we need to use a weighted medal count system and divide it by sport rather than bunching every sport together. Using the very populer gold=3, silver=2, bronze=1 system, in Archery, South Korea wins with 10 points, Italy/China/Japan/Mexico get 3, US gets 2.

Athletics:
US 60
Russia 39
Jamaica 24
Kenya 19
GB 15
Ethiopia 14

Notice Kenya is now in 4th, instead of 6th. I'd actually prefer an even more weighted system, like gold=10, silver=5, bronze=1. Using this system,

US 162
Russia 110
Jamaica 64
GB 46
Kenya 45
Ethiopia 38

This way, we can't say that the US has the best athletes in the world, we can only say it has the best runners in the world. (Which by the way, isn't true. The Jamaicans are better sprinters and the Kenyans are better distance runners. lol) And this way, gold is a lot more important than bronze.

[Shadow]

See my edit above for why team size is important.

It's good to know you weren't being serious though. I facepalmed.

[Gen. Volkov]

I maintain that to measure selection accurately you need to normalize by team size. If you submit twice as many athletes there are twice as many medal opportunities, so extra medals isn't necessarily an effect of better selection in that case. Especially for olympic events like vault, diving, gymnastics, anything where you are performing rather than racing or enduring, where you only get a couple of chances, there is huge opportunity for an upset by a mediocre athlete. Even the best athletes have bad jumps on occasion, and even the worst ones get lucky sometimes (for example, that American female gymnast who was supposed to take the gold without even trying and ended up messing up her ankle and losing outright). Having more contestants greatly increases medal counts even if the athletes chosen are sub-par when there is only a small number of attempts, because luck plays a much bigger role in small sample sizes (read: in a small sample, the standard deviation is much larger).

Yes and no Shadow. The Olympics these days seem to be gravitating more and more to events with absolute requirements for winning, and away from events that are judged. I would argue that having more athletes that are already high level performers does increase medal counts, but just having more athletes overall does not. Britain, as the host country, had the largest Olympic team at the games. But because their athletes were not as good as the Chinese and American ones, they got beat handily by both countries in the medal count, even though both countries had smaller Olympic teams. You have a point about the American gymnast, but frankly that sort of thing is rare. More common in judged events, but still rare. Mediocre athletes do not generally beat top-tier athletes. The American guy who won the 10m diving competition was already one of the best divers in the world. He had a very good day, and the Chinese guy who took silver had something of an off day, but that doesn't change the fact that the American was already an extremely good diver. He had won medals in international competitions before. Ditto the British guy who took bronze.

So no, if the number of medal attempts for each athlete is small, then flooding the podium with mediocre athletes gives more medals than picking a small number of excellent ones. Or better yet, maximal chances happen when you pick your best, and then pick a large number of athletes who can just barely qualify. The smaller than number of trials, the greater the chance of an upset. This is why hockey games are best of 7 - because it gives a much greater chance of an accurate guage of the better team.

I get what you are saying, I just don't agree with the logic as applied to the games. Most of the events where your argument would be most true do have multiple attempts, and the ones that don't tend to be things like track, where multiple attempts wouldn't help, because some people are just faster than others.

[Shadow]

The American guy who won the 10m diving competition was already one of the best divers in the world. He had a very good day, and the Chinese guy who took silver had something of an off day, but that doesn't change the fact that the American was already an extremely good diver. He had won medals in international competitions before. Ditto the British guy who took bronze.

Sure, good atheletes usually beat mediocre ones. My point was that for small trial numbers (among others, vaulters and divers get only 2 jumps, right? And the soccer game were best of 1 ^_^) then the chances of an upset are maximized. Doesn't mean they are good chances, though, which is why large athlete numbers make up the difference.

This sort of thing is rare, but flooding the podium make it less so.

But yea, races and endurance events are less subject to this in general, especially long ones. However, when the time between 1st and 4th place is measured in fractions of a second, it becomes important again, because a single mis-step can cost the race. Michael Phelps also lost one of his events unexpectedly by some obscenely small fraction of a second, I forget which one. Maybe he didn't twist his arm right. It's the little things.

[Gen. Volkov]

Sure, good atheletes usually beat mediocre ones. My point was that for small trial numbers (among others, vaulters and divers get only 2 jumps, right? And the soccer game were best of 1 ^_^) then the chances of an upset are maximized. Doesn't mean they are good chances, though, which is why large athlete numbers make up the difference.


This sort of thing is rare, but flooding the podium make it less so.

Not enough to make a significant difference.

But yea, races and endurance events are less subject to this in general, especially long ones. However, when the time between 1st and 4th place is measured in fractions of a second, it becomes important again, because a single mis-step can cost the race. Michael Phelps also lost one of his events unexpectedly by some obscenely small fraction of a second, I forget which one. Maybe he didn't twist his arm right. It's the little things.

200m butterfly, he glided in instead of taking an extra stroke like the guy who won. Lost by 4 one hundreths of a second. But the guy he lost too was one of the top swimmer's in the world, from a fairly small team. Which kinda reinforces my point.

Normalizing medals by team size just doesn't make sense to me, because if a team with 4 athletes medals, they get an absurdly high ranking, but it doesn't show anything except they have one really good athlete in 1 particular sport.

[Shadow]

Normalizing medals by team size just doesn't make sense to me, because if a team with 4 athletes medals, they get an absurdly high ranking, but it doesn't show anything except they have one really good athlete in 1 particular sport.

You can't reasonably rank any team with a very small medal count anyway no matter how you cut the stats. At the end of the day, the sample size is just too small for your results to be an accurate representation of anything. I'm assuming here that the count is high enough to be useful, so I am talking about ranking the top medal count countries, say everyone over 15 medals.

Not enough to make a significant difference.

In a large number of trials, I agree. For 1-3 trial events, it's significant.