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Computer Simulation Details

This section will attempt to explain key simulation parameters.

Describing Pellet Patterns

Shotgun pellet patterns have a particular look about them. This is because the way the pellets are distributed on the pattern card follows a mathematical form called a bivariate normal distribution. This has been confirmed by shotshell manufacturers (see Wallack).

The following figures show examples of pellet patterns (usually just called patterns) with chokes of 60% and 75% respectively. The second figure is slightly denser than the first.

It is easy to generate, on a computer, patterns with the same form as shotgun patterns. This is what we did with the above figures. That is, we can generate patterns which could have been obtained from a real shotgun.

It important to realise that not just any pattern of dots will qualify. The figure below is not a shotgun pattern. Despite its random nature it is actually far too regular to be a real pattern. Graham Norris of the Victorian Field and Game Association, has, for example, used diagrams with pellet patterns that don't have the correct form to dispute our wounding rate estimates in SWC.

A NON pattern

Describing Shooter Skill

When a shooter fires a shotgun at a duck, the centre of the pellet pattern misses the center of the duck by varying amounts. The average of the amounts by which they miss is called their average aim error. For example if you fire 3 times at 3 ducks and miss by 5cm, 80cm and 60cm respectively, then your average aim error (for these 3 shots) is about 48cm.

We could imagine plotting aim errors on a large sheet of cardboard. Put a point in the center of the sheet representing the duck and draw dots on the cardboard at the position of the center of the pattern for each shot you fire. There isn't any device that will actually allow this to be done but if we did have such a device we would generally get a pattern of dots with the same mathematical form as a shotgun pellet pattern. The word "generally" was used in the preceding sentence because there may be some shooters whose patterns don't quite fit the form. These shooters may miss preferentially in some particular direction. They may more often miss "behind" the duck than in front, or to the top right of the duck or in some other specific direction. Our model only considers shooters without any particular directional bias in their shooting.

While average aim error is a very concrete measure of shooter skill, it is very difficult to measure in the field. On the other hand it is very easy to measure shots per bagged bird (SPBB). Simply count the shots a shooter fires and divide by the number of birds they bag.

It should be noted that there are many field studies of shells-per-bagged-bird. Sanderson and Bellrose cite 5 field studies with observed shells-per-bagged-bird values ranging from 4.2 to 9.4. The Victorian Department of Conservation and Environment has estimated shells-per-bagged-bird to be about 10 as a state wide average.

Many shooters may have some idea of their skill in terms of shots per bagged bird so when we present wounding graphs later, we will plot wounding rates primarily in terms of SPBB rather than aim error.

Bagging Criteria

Any model of shotgun lethality must first decide how many of the pellets under consideration in which parts of a duck will bag it. This is by far the most difficult parameter to estimate in the model. In the late 1960's and early 1970's thousands of birds were tied to moving platforms and shot with electrically controlled guns (see studies by

Andrews and Cochrane ). These researchers then categorised the ducks. Each was either bagged, crippled, or a survivor. It is instructive that these researchers didn't use "death on impact" as a bagging criterion but rather death within 5 minutes.

Various bagging criteria have been suggested in the literature. See for example Wallack who considers 4 #4 lead pellets in a vital region of 20 square inches will bag. There is also a chart from Tom Roster cited in Bihrle and Johnson .

Our model is a little more complex than the Lowry model in that we consider both the vital and non-vital regions of the duck. Typically we define bagging criteria by 4 numbers p(q,r)s where p, q, r, and s are numbers of pellets such that a duck is considered bagged if either:

p or more pellets hit the duck --- regardless of the position of the hits, or
q or more pellets hit the vital region and r or more pellets hit the rest of the duck, or
s or more pellets hit the vital region.

For example 5(1,2)2 indicates that a duck is considered bagged if hit by at least 5 pellets (anywhere) or by at least 1 in the vital region and 2 elsewhere or by at least 2 in the vital region.

The Lowry model ignores pellet hits outside the vital region - considering they won't contribute to bagging the bird. It seems reasonable however that if enough pellets hit the bird, even if all are outside the vital region, then the bird will be bagged.