This panel provides a simple graphical presentation of the statistical model applied by FlyingSticks to calculate scores and to simulated shooting. The curves are generated numerically using the simulator's random shot generator and then smoothed for presentation. The curves reflect the current conditions of range, wind gust, archer's form, etc.
The accuracy of arrows striking a target is dependent on may factors, with most of them having a random component. The default distribution is a Circular Bivariate Gaussian distribution as selected in Preferences. FlyingSticks assumes the randomness in the horizontal and vertical directions are independent. Available research indicates this is probably a fair assumption. However if the observed grouping oval is consistently leaning to one side, then your form has introduced a correlation between the horizontal and vertical probabilities, and the model will not accurately represent your form - although errors should be minimal.
Five plot options are provided. Each plot also shows the relevant group size as vertical lines with slight shading in between. The drop down menu allows the selection of a probability density function to display:
The one dimensional probability density of an arrow strike at a horizontal distance from the target center.
For reference the two vertical lines make the group width for the two dimensional distribution.
The one dimensional probability density of an arrow strike at a vertical distance from the target center.
For reference the two vertical lines make the group height for the two dimensional distribution.
This is the product of the above two orthogonal probability density distributions with the result treated in a similar way. Simply imagine the radial vector of each shot being rotated, in the shortest direction, to the x-axis. This remains a one dimensional distribution despite the fact it is constructed from two orthogonal distributions.
It is the probability density of an arrow striking at a distance in any direction from the group center. The result is a mirrored Rayleigh distribution with symmetric peaks one standard deviation on either side of center.
This plot has little direct practical application as it ignores the fact that target area progressively increases with radius, but is presented as a stepping stone to the following distribution that accounts for target area:
Plot of the two dimensional circular density probability function, or more correctly a circular bivariate Gaussian probability density function. This is determined by dividing the Vector Probability Density by the strike radius (vector length). It reflects the true probability of an arrow strike an area from target center. Importantly it shows the target center has the highest probability per unit of target area!
Shows all of the above in a single plot for easy comparison, with the Circular Probability Density highlighted.
All plots share the same axis' of distance (x) and probability density (y), although the definition of each of these differs a little between the plots.
The distance units of the horizontal axis in the above plots is the current units of the Group Width field (i.e. the first of the "Group (w x h)" fields) beneath the panel's Target Image.
For the one dimension plots, the distance is simply in the direction of orientation from the target center.
For the circular probability plots, it is the radial distance. When the group skew is unity (i.e. no skew as with most experienced archers), the interpretation is simple. However when there is skew, the circular probability density oval is also skewed which is not obvious in the 2D plots.
The vertical axis units are a little arbitrary for these plots as we are
attempting to illustrate how the statistics work. The scaling in the
vertical axis of each trace is adjusted such that the area under each
curve is unity when the horizontal axis units are in standard deviations
rather than the shown length units.This makes for an easy visual
comparison , particularly in the combined plot.
With the Groups>Theory panel showing, the Show Plot Windows button at the bottom right is enabled.
This allows the spawning of a plot window containing a resizable version of the plot discussed above.