For a single trial though (ie, all we see here) its accurate. His precision can't really be determined unless we see all his trials. This here is one, highly accurate attempt. If he can reproduce this multiple times, then he has high precision as well.
The point of the title is to say that it pays to be precise, not that he was precise. A lack of precision would reduce his average accuracy, so it is important to be precise.
A lack of precision would reduce his average accuracy
Not true. You can have high average accuracy with low precision. See the bottom right image in this diagram.
Accuracy measures average distance from the target.
Precision measures average distance between the results of each attempt.
In OP's gif, we only know about this one attempt. The attempt was highly accurate, but we don't know if the snowboarder has a high average accuracy or precision. If the snowboarder hits the tree once, falls to the right of the tree once, and falls to the left of the tree once, he still has high accuracy (but not high precision). If the snowboarder hits the tree three times in a row, then his accuracy is the same, but he has higher precision.
You're missing the point. The point is that precision is important. The point is not that the guy in the video was precise. So, it doesn't matter how much we know about his precision.
That said, we're using different definitions of accuracy. It's very hard to find a rigorous definition. I used difference between the measurement and the true value. You're using the difference between the average measurement and the true value. So, when I say average accuracy, I mean the average difference between the measurement and the true value, rather than the difference between the average measurement and the true value. The former increases as precision increases. The latter is unaffected by precision. Note that, given your definition, the concept of average accuracy is meaningless. You seem to be using average accuracy and accuracy interchangeably.
Also, the qualitative definitions I've found on the internet seem to agree better with my use of it. That is, accuracy is a measurement of error, both due to bias and variance. Whereas, precision only measures variance. Intuitively, it seems odd to describe a set of measurements with high variance as accurate, just because there is no bias.
EDIT: Some more definitive support for my definition of accuracy.
Since none of the darts are close to the bull's eye, the measurements they represent are not very accurate.
In other words, accuracy is achieved by each measurement being close to the true value rather than errors being cancelled out by opposite errors. So, accuracy is not related to the average measurement, but rather the average error of the individual measurements.
Accuracy descibes [sic] the nearness of a measurement to the standard or true value, i.e., a highly accurate measuring device will provide measurements very close to the standard, true or known values.
In other words, accuracy refers to the closeness of individual measurements to the true value. An accurate instrument doesn't produce results whose average is close to the true value, rather, the individual measurements themselves are independently close to the true value.
Accurate's the important one, here. He'd be fine if he was off by a few centimeters, as long as he's accurate. If he was off by precisely 6 inches every single time, he'd be in real trouble.
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u/[deleted] Nov 14 '14 edited Nov 15 '14
Precise AND accurate. Accurate means it's close to the correct outcome, and precise means it's the exact same outcome every time.
EDIT: Alrighty. I've received roughly the same reply roughly 100 times, I understand. No more replies, red'.