1 year, 11 months ago
A question for soccer-loving statisticians... (details inside)...
This question needs some knowledge of probability and statistics and soccer. If that's you... read on!
Background:
I am interested in insights on how big of an advantage (other things being equal) a large country would be expected to have over a small country. In particular, I am interested in this....
Is there some country size (population-wise) beyond which being a lot larger would not be expected to make all that much difference to the national team's average skill level?
e.g. If skill level is rated on a level 0-100, is it the case for example that we'd expect the average skill level of country of population 1m to be 77, one of 10m to be 87, but one with a population of 100m to only be 89?
What I'd like:
By any means you can think of, shed light on the question I'm interested in.
Your methods may be purely theoretical, or they could be purely empirical, or some mix of both.
For example, you might approach the question by thinking about things like this...
- What is the most likely distribution of soccer skill in a population of humans?
- If the population size is n, what is the expected average skill level, s, of the best m players. (Where m might be let's say 11 for the national team, of 20 for the whole squad, or whatever you think is good.)
- What is that variance of the average skill level?
- How does s change with n, and at what point do large increases in n make only small differences in s?
- How do the chances of having an exceptional player (skill level > 95 or whatever) vary with n
You DON'T have to approach the question in the way I suggested though!
Any approach you can think of that gives interesting insights about the topic is fine. :)
Background:
I am interested in insights on how big of an advantage (other things being equal) a large country would be expected to have over a small country. In particular, I am interested in this....
Is there some country size (population-wise) beyond which being a lot larger would not be expected to make all that much difference to the national team's average skill level?
e.g. If skill level is rated on a level 0-100, is it the case for example that we'd expect the average skill level of country of population 1m to be 77, one of 10m to be 87, but one with a population of 100m to only be 89?
What I'd like:
By any means you can think of, shed light on the question I'm interested in.
Your methods may be purely theoretical, or they could be purely empirical, or some mix of both.
For example, you might approach the question by thinking about things like this...
- What is the most likely distribution of soccer skill in a population of humans?
- If the population size is n, what is the expected average skill level, s, of the best m players. (Where m might be let's say 11 for the national team, of 20 for the whole squad, or whatever you think is good.)
- What is that variance of the average skill level?
- How does s change with n, and at what point do large increases in n make only small differences in s?
- How do the chances of having an exceptional player (skill level > 95 or whatever) vary with n
You DON'T have to approach the question in the way I suggested though!
Any approach you can think of that gives interesting insights about the topic is fine. :)
Separate topics with commas, or by pressing return. Use the delete or backspace key to edit or remove existing topics.
You can leave an optional "tip" with Mahalo's virtual currency, Mahalo Dollars. If you are asking a difficult question that might require some research, or if you'd like a wide variety of feedback, a higher tip often leads to more answers to your question.
M$3 Answers
I agree that an increased population (p) will always yield an increased skill level (s). There is no limit of s based on p. With an ever larger p you will always be able to improve upon your s of the national team (m).
I think that analyzing the m's s by p is the incorrect way of going about it. Sorry for the abbreviations.
For instance, look at Uruguay. Uruguay has a population of roughly 3.5 million people. Throughout the history of the World Cup, Uruguay has won two 1st place titles.
Now look at the population of the United States of America - roughly 309.5 million
How many championships? None.
At this point averaging a teams skill based on national population becomes ridiculous, it is based more on the culture of the nation at hand.
Interestingly, when you look at Brazil, which lets say has a similar culture to that of Uruguay, and a population of 192 million you find that they have won five 1st place titles in the World Cup.
So I guess the best way to "analyze" a teams average skill level is first by region and culture (South America and Europe with advantages) and then within that region analyze by population.
I think that analyzing the m's s by p is the incorrect way of going about it. Sorry for the abbreviations.
For instance, look at Uruguay. Uruguay has a population of roughly 3.5 million people. Throughout the history of the World Cup, Uruguay has won two 1st place titles.
Now look at the population of the United States of America - roughly 309.5 million
How many championships? None.
At this point averaging a teams skill based on national population becomes ridiculous, it is based more on the culture of the nation at hand.
Interestingly, when you look at Brazil, which lets say has a similar culture to that of Uruguay, and a population of 192 million you find that they have won five 1st place titles in the World Cup.
So I guess the best way to "analyze" a teams average skill level is first by region and culture (South America and Europe with advantages) and then within that region analyze by population.
You can leave an optional "tip" with Mahalo's virtual currency, Mahalo Dollars. If you are asking a difficult question that might require some research, or if you'd like a wide variety of feedback, a higher tip often leads to more answers to your question.
M$
I'm not sure country size has a whole lot to do with a country's skill level. I feel that a country's economic capabilities has the greatest effect on developing a skillful team.
I think you would be hard pressed to find a country that DOESN'T have great talent and skill. The difficulty is harnessing that skill, training your athletes, providing them with high quality equipment, fields, clothing, excercise equipment etc.
The next greatest factor in soccer, is the culture around the sport. I think it would be difficult to find a country in the world that could outplay the United States in professional football, baseball and even basketball. We have developed a culture around these sports. Children play them in the street, we watch them on television, we go to the games and hear about the Hall of Fame and Heisman Trophy winners.
However, statistically speaking, the larger populated countries theoretically should be developing the most skilled players. I mean, with a population of over 1 billion people in both China and India, each country should produce over 1,000,000 superstars, if only 0.10% of their population reach that level. In turn, if the United States, with a population over 300,000,000 had 0.10% reaching the level of superstar, that would only be 300,000 superstars. But for some reason, the U.S. develops many more highly skilled athletes. I believe this is a cultural phenomenon, not a statistical/mathematical one.
I think you would be hard pressed to find a country that DOESN'T have great talent and skill. The difficulty is harnessing that skill, training your athletes, providing them with high quality equipment, fields, clothing, excercise equipment etc.
The next greatest factor in soccer, is the culture around the sport. I think it would be difficult to find a country in the world that could outplay the United States in professional football, baseball and even basketball. We have developed a culture around these sports. Children play them in the street, we watch them on television, we go to the games and hear about the Hall of Fame and Heisman Trophy winners.
However, statistically speaking, the larger populated countries theoretically should be developing the most skilled players. I mean, with a population of over 1 billion people in both China and India, each country should produce over 1,000,000 superstars, if only 0.10% of their population reach that level. In turn, if the United States, with a population over 300,000,000 had 0.10% reaching the level of superstar, that would only be 300,000 superstars. But for some reason, the U.S. develops many more highly skilled athletes. I believe this is a cultural phenomenon, not a statistical/mathematical one.
You can leave an optional "tip" with Mahalo's virtual currency, Mahalo Dollars. If you are asking a difficult question that might require some research, or if you'd like a wide variety of feedback, a higher tip often leads to more answers to your question.
M$
As stated above, population does not necessarily correlate to an extremely successful international soccer team. If that was the case, than the United States, China, and India would always be the favorites, but that is simply not the case. It is more important to look at what countries can be labeled as soccer countries, where soccer is the most popular sport (or one of the most popular) and also which countries have professional soccer leagues.
Places where soccer is one of the most popular sports can be successful even if they have to form a team from a small pool of players. Look at Slovenia; the least populated country in the tournament is on the verge of advancing to the round of 16. Although smaller countries do not have as many people to choose from, if it is a soccer country, odds are that the best athletes are going to be pushed towards playing soccer (the money is there, that is what they were raised with). In a country such as the United States where we have a huge population, are best athletes are spread through a number of different sports: basketball, football, baseball, etc... because that is where the money is in the U.S. and because of our culture; what we see on t.v. directly influences what sports we start and continue to play as we get older.
The other fact we should look at is countries with professional soccer leagues. Think about the most prominent and prestigious professional club leagues. The English Premiere League (England), La Liga (Spain), Serie A (Italy), Bundesliga (Germany) are the four most well known leagues around the world. Every single one of these countries has also happened to win at least one World Cup which is no coincidence. Think about it. Any country that has a league where players in the country can play against the best and also gain valuable game experience are going to improve at a faster rate than those that are playing in second rate leagues or none at all. The improvement of United States soccer can be linked to the MLS, which was created in 1996.
Why hasn't an African nation been able to be extremely competitive in the World Cup? It is not because of population. It is not because of small populations. It is because of their lack of professional leagues.
Places where soccer is one of the most popular sports can be successful even if they have to form a team from a small pool of players. Look at Slovenia; the least populated country in the tournament is on the verge of advancing to the round of 16. Although smaller countries do not have as many people to choose from, if it is a soccer country, odds are that the best athletes are going to be pushed towards playing soccer (the money is there, that is what they were raised with). In a country such as the United States where we have a huge population, are best athletes are spread through a number of different sports: basketball, football, baseball, etc... because that is where the money is in the U.S. and because of our culture; what we see on t.v. directly influences what sports we start and continue to play as we get older.
The other fact we should look at is countries with professional soccer leagues. Think about the most prominent and prestigious professional club leagues. The English Premiere League (England), La Liga (Spain), Serie A (Italy), Bundesliga (Germany) are the four most well known leagues around the world. Every single one of these countries has also happened to win at least one World Cup which is no coincidence. Think about it. Any country that has a league where players in the country can play against the best and also gain valuable game experience are going to improve at a faster rate than those that are playing in second rate leagues or none at all. The improvement of United States soccer can be linked to the MLS, which was created in 1996.
Why hasn't an African nation been able to be extremely competitive in the World Cup? It is not because of population. It is not because of small populations. It is because of their lack of professional leagues.
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M$
No need to be curt.
Q: Is there some country size (population-wise) beyond which being a lot larger would not be expected to make all that much difference to the national team's average skill level?
A: Yes there is. What is it exactly? No idea, considering you would need an amazing amount of data through sampling and surveys to even scratch the surface of this question.
(Though when competing and the professional level, you need every little advantage you can get. So obviously its worth it to have the larger population to choose your players from.)
Q: What is the most likely distribution of soccer skill in a population of humans?
A: I know that you are assuming that all other variables (culture for one) are void. I'm not sure I understand what you are asking for in this question.
Q:How do the chances of having an exceptional player (skill level > 95 or whatever) vary with n?
A: They obviously go up. I'm not able to go into more specific numbers just based on a lack of data.
Q: How does s change with n, and at what point do large increases in n make only small differences in s?
A: s is directly related to n. When n rises so does s. When it comes to small differences - you are asking for a very large survey project. (I charge more than $2 tip for those)
I wouldn't offer an M$2 tip just to be told which countries traditionally do well at the World Cup. :)
I brought up a valid point about how population can matter when it comes to specific regions. Brazil which we can assume has a similar culture to Uruguay (in other-words, the culture variable is disregarded) has done better in the World Cup due to, what we can only assume to be, their larger population size.
I am not interested (for this question) in why some countries deviate from what would be expected.
I'm interested in first understanding what would be expected if there were no differences between countries other than population size.
-- Quote
...how big of an advantage (other things being equal) a large country would be expected to have over a small country...
-- /Quote
Note the part where it says: "other things being equal"!
Once we have an understanding of how big or small an effect would be expected just from differences in population size, then we can start to think more clearly about what other factors come into play.
This question is a *math* challenge, for people that like math challenges... I'm expecting people to make intelligent simplifications for the purpose of model-building and getting some insight.
In the real world for a start we wouldn't be interested in the raw population of a country but in how many people actually play football etc, which varies a great deal.
This question is not about the real world per se, it is about the math of probability distributions and population sizes.
Real world data can be used to tune the model, but what I want is the model.
I wouldn't offer an M$2 tip just to be told which countries traditionally do well at the World Cup. :)
In fact, we already had a good discussion of all the things you mentioned, and much more in a previous question... (and this is partly what motivated my question in the first place)...
http://www.soccer-answers.com/do-you-think-the-world-cup-winner-can-be-predicted-based-on-economic-measurements