Put a Hat on It

In statistics, there is a symbol known simply as a “hat.” It looks like this: ^. According to Wikipedia (the grad student’s seedy dealer, from whom you can never academically admit getting your stuff), the hat operator “is used to denote an estimator or an estimated value.”

Seriously, we call “p” just “p” (like the actual letter), and “hat_p” is called “p hat.” It doesn’t get much lazier than that.

Despite its ridiculously simplistic nomenclature, putting a hat on a parameter and discerning an estimate is a perfectly acceptable method. Estimation is necessary in statistical models that seek to make inferences about a population from a sample. Your estimate is accepted by professional types if your methodology is solid, your model proves statistically significant and of adequate magnitude, and you are able to convincingly argue your conclusions.

Of course, people will know when your estimates are bad.


Basically, putting a hat on something means to get as close as you can get to the real thing given your limitations.

It dawned on me after some time that the “hat” concept is not entirely isolated to the world of statistics. While deployed, I often used the phrase “Afghan good enough” (for better or worse). It meant completing a task to a satisfactory level, but not to the maximally desired level. Perhaps there wasn’t enough time, enough resources, or enough cooperation from our ANSF partners.

For example, one of my tasks down range was to advance the implementation of the Afghan Human Resources Information Management System (AHRIMS). I would have loved to see my Afghan Uniformed Police partners stand up a robust section dedicated to enthusiastically embracing and implementing this revolutionary system that would surely help every uniformed police officer in their region with records management and pay streamlining.

They instead hired one civilian part-time and gave him an old, slow scanner for digitizing paper records.

They didn’t do nothing. They did an approximation of the larger, more ambitious goal that was “Afghan good enough.”

They put a hat on it.

Another phrase I’ve heard used in the Army is “I’d rather have 75% now than 100% in two weeks,” or some variation thereof. You may have seen a simpler version of this if your boss ever told you “just give me what you’ve got.” The idea is that urgency is important, and you can’t have all the time in the world to make your product perfect. Do your best, get as close to 100% as you can, but give me what you got. Time now.

What results are decisions made with a level of risk assumed by leaders.

Leaders put a hat on their decisions.

But just like in statistics, a hat might not be a bad thing. And if done well, that estimated hat is practically the same thing as a 100% product. Your risk is accepted by higher if your methodology is solid, your reasoning is significant and of adequate importance, and you are able to convincingly argue your conclusions.

Combat is an amorphous and urgent thing that relies on the disciplined initiative of leaders on the ground. Decisions must be made on the fly and with whatever existing information and estimates that are available at that time.

In the Army, there’s no escaping it.

Very often you have to put a hat on it.

In conclusion, sorry about nerding out on statistics.


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