## How accurate and precise is your aim ? Skilled and unskilled archers

In a previous post, The Blindfolded Archer, I described the difference between wild and mild randomness, the former exemplified by the blindfolded archer and the Cauchy probability distribution, and characterised by the “long tail”, that is, precence of extreme events, a.k.a, “outliers”.

The graph above demonstrates mild randomness, as given by the normal/gaussian probability distribution. In the graph, 4 different archers, some of them skilled, some less so, but none of them blindfolded, take a number of shots at at target, where bullseye is located at (0,0) in the plot.

Starting with the best archer, the red one, we can observe that his shots are clustered symmetrically around the bullseye, with moderate spread.

The blue and green archers also  have a moderate spread, but their shots are offset to the right and down, respectively, implying that there’s some systemic problem, perhaps their bow sights are damaged…?

All three archers, red, blue, and green can be said to have good accuracy, but while red also has good precision – many hits close to the bullseye, green and blue’s precision is not that good, as indicated by their shot center being off the bullseye by some distance.

Remains the yellow archer: this guy is spreading his shots wildly off mark. He is neither accurate nor precise, his shooting is characterised by both systemic and random errors.

For the stats nerds: all four shooters draw their results from a normal distribution, where the red shooter has a mean of 0 (‘bullseye’) and a standard deviation of 1, in both dimensions (x,y). The blue and green shooters also have a standard deviation of  1, but blue’s x-mean is 2, and green’s y-mean is -3.

Yellow has both x and y means at -4, and a standard deviation twice that of the rest, that is, 2.