# More Than Coincidence

In yesterday’s post we saw that 6 cadets were involved in the Florida cocaine/fentanyl event.

This got us wondering. How likely was it that the football players “just happened to be involved” in the issue? In other words, how what was the probability that this was an event with randomly selected cadets?

### Method

To this we had to go back to our statistics courses and recall our trials doing things such as calculating probability of drawing N red marbles out of a jar containing X red and Y blue marbles.

We know that the Corps is about 4400 cadets with a football team size of approximately 180. We employ the probability calculator at dcode (which we confirmed calculations of*) to find the probability that of the 6 cadets in the incident, all 6 were football players, and as a second case checking the probability if only 4 were football players.

### Findings

Here’s what we found.

If the group of cadets in the incident was randomly selected, for 6 football players to be present would represent a probability of .0000004%. Or about a 1 in 231,294,523 chance.

Well, that’s a little tough, not very likely at all. Maybe there were some non-football players present. So if the group of 6 cadets in the incident was randomly selected, for 4 football players to be present would represent a probability of .0037%, or 1 in 26,675 chance.

So that’s not very likely as a random event.

What about other recent issues at West Point?

Let’s look at the 2021 cheating scandal. Of 73 cadets involved in the cheating, 55 were athletes, and of the 55, 24 were football players.

So we run a similar analysis on the tool with 4400 cadets, 73 cheaters, and 55 athletes. From our previous data files we find that the average number of athletes per year is somewhere around 650 (being all-inclusive on sport categories and keeping in mind limitations of the dataset):

We find that the probability of this occurring randomly was… infinitesimal. 1.08E-29%. Too small to display. We try again with just the football pool – so, 4400 cadets, 180 football players, 73 cheaters, and 24 football cheaters.

Answer: not very probable. That’s 2E-14 %.

While we are not statisticians and the Statistics PhDs out there may offer methodological improvements to the above (such as continuous distributions, for or summing all the probabilities for N < 24, or as a commenter notes understanding the drug-using population at west point and overlap with football players, confidence intervals and so on), this is a very small number. (Of course if we are directionally wrong, please comment and let us know. Updated 3/26)

We will go out on a limb and guess that assessing more historical adverse events will tend to show the same thing.

### Conclusion

All this is to say that having football players consistently involved in these incidents is not random. It’s not even close to random. It is in fact highly unlikely unless something else is affecting the results.

Maybe West Point is causing the football players to have problems. Or perhaps–and we’re just guessing here–it is because USMA allows lowered admissions standards for certain groups, which results in admitting candidates with less capability to handle USMA’s academic and behavioral requirements. This may be why football players (and most heavily recruited sports) tend to separate at much higher rates for conduct, honor, and academic reasons than the general cadet corps.

USMA could avoid these issues by maintaining merit-based admission standards. But it chooses not to.

As always, factual corrections and thoughtful methodological criticism are welcome.

**We confirmed the calculator’s results below.

### 5 thoughts on “More Than Coincidence”

1. Of course it is not “random” in the sense that if one football player is doing something with a group of cadets, it is highly likely the other members of the group are also football players. If a group of cadets is doing something, it is highly likely that the members of the group have some connection: same company, same sport same club.

It seems like the athletes seem to get one or two bad eggs that the rest follow off the cliff.

but to your larger point of lower standards for athletes, yes, that is a problem

• “athletes seem to get…”
precisely our point. Why do the corps squad athletes tend to be disproportionately represented in these events?

2. In order to apply these methods, data must be iid (independent and identically distributed). They’re definitely not independent. Also, your sample is of those who have been caught/tested positive for cocaine usage. The sample isn’t large enough to apply generalizations to the population. We can’t assume that those caught represent the population of those using drugs.

• Thanks for the comment.

to recap the hypotheticals: given an adverse publicity event (not just a drug event) with 6 randomly chosen cadets, what is the probability that 4 or 6 of them are football players. of an event of 73 randomly chosen cadets, what is the probability that 24 were football players. this calculation does in fact assume (as you say) iid.

Then we contrast it with what happened. We didn’t stipulate that they were randomly selected in real life, the point is that this was not random. We note that the disproportionate representation of fb/recruited athletes in these adverse events clearly demonstrates that it’s something about that program and its participants that situates football players to have problems at west point.

alternate conclusion demonstrations are welcome.
cheers,