"If you're born in Samoa, you have a 1:20 chance of getting in the NFL." Bullshit statistics?

The other day someone told me what he thought was an amusing factoid, phrased exactly as I quoted in the hed.

I looked up what I could. The fact that Samoa, with such a small population, has produced many pro football players is surprising and interesting. It apparently has been widely noted (Google and Wiki).

But that’s historical record. It differs, as far as I can sort it out, where the “If [insert circumstances]…then the chance is …” in responsible medical statistical statements when the causative effect is more or less unambiguous.

True, the causative effect of being from a Samoan culture, which the Wiki and other cites claims is so conducive to football, may have an impact, but cultural dynamics comprise enormous factors. If you’re from farm country you’re odds of being a stoopball wiz (do you all know what stoopball is :)) are slim. But that statement is a “that” one: the odds are that you are is not predictive.

So, in general, here’s a question that has bothered me whenever I see this kind of statement, which is often. It is constant, for one example, in the medical literature I’ve read (ie, for laymen), but is used with abandon in all sorts of situations.

I think that statisticians must have identified the kind of fallacy that I think is going on in the hed.

If not, I’m interested in sorting out the science, as best as I can. It’s really bugged me, and is used so commonly in rhetorical arguments where I think it is a snow screen.

Sorry, read it three times and still can’t figure out what the question is.

I’m not really sure what you’re getting at. Are you just pointing out that 19 Samoans had a 0% chance of getting into the NFL while 1 had a 100% chance? It is mathematically valid to turn that into a 5% statement about what a random Samoan. You shouldn’t read it as you (Leo Bloom), but as you (random Samoan). I think that’s just a given - the writer doesn’t generally know who you are.

If the complaint is more about the historical nature of the data… I think it’s a given that this is historical data and that we all know historical data is not necessarily predictive of future performance. If that’s your concern, then you just need to read every prediction and statistic as if it had that caveat appended. (If you have a way of gathering future data, let me know. :slight_smile: )

Statistical status of past influences “chance” of similar statistical pattern in future. In all cases. Bullshit? Statistical pattern of past may be just a happenstance.

The phrase you’ll most often see in finance is “Past performance is no guarantee of future results.” Pretty much every mutual fund includes it in their prospectus.

But, for Samoa, it’s probably a matter of the fact that outliers are more likely to be found when examining a small sample.

So that quote in the hed is a complete and utter bullshit statement? (And others of its ilk? I don’t give a damn about Samoans or the NFL.)

Just to start, there’s the fallacy of bad statistics. The population of Samoa is 194,320. If one Samoan out of every twenty was playing in the NFL, there’s by 9716 Samoans NFL players. That’s well above the total NFL roster of 1696.

There are, by one count, thirty-six Samoans playing in the NFL. (I also found counts of sixteen and thirty but I’ll go with the high one.) That makes the odds of a Samoan being a football players is about one out of 5400.

It is a good old application of the Ecological Fallacy where inferences about individuals are made based on characteristics of the group - the same fallacy committed by stereotyping and hopefully covered by every first-year statistics course.

It should be more widely known, because it’s very important to be aware that it is a fallacy. kudos to you, Leo Bloom, for noticing this.

The exact odds odds may in fact be different. But making the NFL is not due to random chance. There are many non-random factors involved. For Samoa, one of the most important is the cultural influence that leads kids to emphasize American football. Another may be the type of physique that is common among Samoan males.

The caveat is that the odds may apply only to kids who would be eligible this and the next few years. They would not apply to a baby born this year, since the same cultural influences may not be in effect when he is growing up, nor may the same kinds of skills be important in the NFL in 2033.

Of course as stated the percentage is wrong. However, one would have to take it as applying to males of the appropriate age class. It would also apply only to American Samoa, whose population is more like 55,000 (although a significant part of the population may be living in the US itself).

This isn’t the right analysis though. We don’t want to compare the current population of Samoa to the current number of Samoans in the NFL. If we give the author the benefit of the doubt and assume he’s addressing males, then the relevant population is only half of your 194,320.

But we also can’t count any males that are too young to have yet had a chance. One valid comparison would be the number of Samoans ever to play in the NFL to the number of Samoan males over 22. About 30% of the population is under 21 and about half of the rest are female so 194,320 drops to 68,012. The numerator is at least your 36; I don’t know how many retired NFLers are Samoan. But 36 gives us 5.3% of “eligible” Samoans play in the NFL. This is about 1 in 20.

I can easily see a 1 in 20 chance getting mis-reported as 20% somewhere along the way.

The actual number of players born in Samoa in the NFL seems to be overstated as well.

This table indicates that 29 NFL players who were born in American Samoa played in the NFL, but only 5 were active in 2012. There have also been 7 from Western Samoa, but none active since 2003.

That must include all players of Samoan descent, including those born in the US rather than born in Samoa itself. But I find it hard to believe there are 31 Samoan Americans (American Samoan Americans?) in the NFL. I suspect that the figure of 36 must be a combination of all players from either American or Western Samoa who have ever played in the NFL, not a current figure.

There are apparently 180,000 people of Samoan descent living in the US, including those of partial ancestry, which is about equal to the population of Western Samoa.

I’m also not sure what the OP is getting at, but I can come up with a few statistical fallacies that might fit what he is looking for.

  1. Correlation doesn’t imply causation: There might be a higher percentage of Samoans in the NFL but if I’m 99 pound weakling, moving to Samoa isn’t going to improve my chances of getting into the NFL

  2. Multiple comparisons: With so many little states and towns to look at, one of them is going to have an unusually high percentage of NFL players

  3. Law of small numbers: In a small population you are more likely to get abnormally high percentages.

  4. The world changes so old models may no longer be valid. Whatever caused so many Samoans to be in the NFL may no longer be occurring.

The OP provided an exact quote - “If you’re born in Samoa, you have a 1:20 chance of getting in the NFL.” - so I used that. The quoted statistic didn’t say “If you’re born in Samoa and are a male” or “If you’re born in American Samoa” or “If you’re born in Samoa and have the skills to play professional football”.

I did, admittedly, base my figures on the current population of Samoa and the current number of Samoans in the NFL. I think that’s reasonable because I’m comparing two equivalent figures. It’s not like I compared all of the people who have ever been born in Samoa with the current NFL roster.

And 5.3% of 68012 is 3607 not 36.

You’re correct. I checked back on that source and the guy was listing retired as well as active players.

Those figures all seem to be misstated in various sources.

Let’s establish the basic figures for population and NFL players.

Western Samoa: 194,000 (2012 estimate), of which 92% are ethnic Samoans.
American Samoan: 55,000 (2010 census)
People of Samoan ancestry living in US: 180,000, including those born in the US and those of partial Samoan ancestry.

There are significant numbers of Samoans living in NZ and probably other places outside the islands, but let’s ignore these.

Total: Around 430,000 ethnic Samoans, maybe a bit more.

The figure of 30 current players in the NFL is almost certainly wrong. There were 5 players born in Samoa in 2012, and 7 in 2010. Even if we assume that double those numbers of American born Samoans were playing also, that still gives us only 15-20 ethnic Samoans in the NFL.

Wiki says:

However, their cite for that is a tourism site, and what it actually says is:

Considering American Samoans only, and ignoring those residing in the US:

Based on the US census, males 20-34 years old (which will include the bulk of NFL players) make up very roughly 10% of the population. The percentage is probably a bit higher in American Samoa for demographic reasons, but lets ignore that. So the pool of available males would be around 5,500. Since there are currently 5 Samoan born NFL players, this works out to a percentage of 0.1% (about .001 of this population). So the figure of 1:20 probably overstates the actual one by at least 50 times.

Considering all ethnic Samoans, we have a population of males in the right age range of 43,000; or including just American Samoans and Samoan Americans, 23,500. Even if we accept the figure of 30 ethnic Samoans in the NFL the percentages will be 0.07%, or else 0.13%.

Whatever the case, the figure in the OP has obviously been garbled pretty wildly.

In Western Samoa the most popular sport is Rugby Union and for the size of the country, their Rugby Union team is extremely good (not good enough to be a serious contender for the Rugby World Cup, but good enough that they can cause any team problems. They’ve also produced some top quality Rugby Union players and there are plenty of Samoans also playing professional Rugby League.

I remember something like this a few years ago but it was more like if you are a Soman and playing division I football you were 20 times more likely to be drafted by the NFL than a non Somoan. Sorry don’t remember the specifics but that seems more likely the the 1:20 of the original post.

I was thinking something similar, that one out of 20 Samoans playing college ball get drafted.

71% of all statistics are made up on the spot. The remaining 38% are mis-stated.

I’ve read this a couple of times, and it seems like you’re saying 36 is 5.3% of 68,012. I’m not good at the new math, but that’s off by a factor of about 100. So even with all the caveats, limitations, and “benefit of the doubts” we can throw in, it’s still not true.