The ultimate test of a target archer's performance is the scores made in tournament rounds. You have the 1200 or 1300 FITA shooter etc. When it comes to getting the high scores the practical "measure" used to assess the archer's form, equipment used, bow setup/tuning etc. is the size of the arrow "groups". Group size is generally estimated on a visual subjective basis by the archer. What ArrowMaster does is attempt to define groups on a quantative basis using a statistical approach.
There are many different groups of arrows that may be relevant. For example if you consider the arrows shot in a round then possible groups include:
What is a "group" and what are the properties of a group.
The above diagrams represent three arrow groups. Each group has a "size" and a "centre". The usual question is what is the size of the group e.g you are trying to tune the setup to give you the smallest group size. Visually it's easy to say that group "A" is the smallest but usually the comparison is being made between patterns like "B" and "C". This is much more difficult visually. The problem in general is how you assess the effect of clusters of hits as opposed to single hits well away from other hits. Different archers may come to different conclusions when comparing the same two patterns. It depends on how much subjective weight is given to different arrow hits or arrow hit patterns.
ArrowMaster attempts to eliminate the guesswork in assessing groups by using a statistical approach. The distribution of arrow hits in terms of the radial distance of the arrow hits from the group "centre" is assumed to follow a normal distribution.
The above figure represents the shape of a couple of normal distributions.The vertical axis is the number of arrows and the horizontal axis the arrow hit position. The basic principle is that the probability of an arrow hitting at a certain distance from the centre (the peak of the curve) decreases as you move away from the centre. (Or in archery terms the worse the shot the less likely it is to happen). The narrow steep curve represents a smaller group then the wider/flatter curve. The area under the curve represents the number of arrows shot.
ArrowMaster first estimates the position of the centre of the distribution (the Group Centre) and based on this value the "size" of the group is represented using the Standard Deviation of the arrow hits from this centre. The Standard Deviation is a statistical function which relates the distance from the centre to what proportion of arrows will hit within this distance. e.g. statistically 95% of the arrows will hit within about two standard deviations from the centre - we have a quantitive measure of group size based on the arrow hit information. The position of the group center is calculated on a "centre of mass" basis. If you imagine having a weightless paper plate and putting an identical weight at each arrow hit position then the position of the group centre is the position where the plate would balance on your finger. This is not the exact position of the true centre of the hit distribution but with relatively sparse information (you're unlikely to have hundreds of hits to analyse) the centre of mass concept seems a reasonable approximation.
Having a quantitive measure of group size and group centre we can now put this information to use. The original purpose of ArrowMaster is for arrow selection. E.g. having just purchased a bunch of arrows which set of six should be the competion set and of that set which should be used for bareshaft tuning? As ArrowMaster can calculate arrow group information in a variety of ways it can in principle be usefully used for just about anything. Is stabiliser setup A better than setup B? How does level and direction of lighting affect group size and sight pin position - or does it? What use you can put ArrowMaster to comes down to the ingenuity of the archer.