Matching Ammo To The Rifle

Jeroen Hogema

The reason why it may be a good idea to match your ammunition to your rifle is shown in Figure 1. If you pick a random can of pellets, you may end up in a situation where you lose points simply because of an unlucky combination of ammo and rifle.

This article discusses the effects on the result (i.e. shooting score) of error introduced by non-perfect ammo in combination with a non-perfect shooter. The discipline regarded is ISSF air rifle shooting, but qualitatively, the results will be the same for other disciplines. The results were obtained by a Monte-Carlo type of analysis. For many combinations of shooter quality and ammo&rifle quality, thousands of virtual shots were fired in a computer programme to find out the effects on the score.

Two ways of counting the score are distinguished:

• the normal score, i.e. with an integer score of 10, 9, 8, etc
• the finale score, i.e. counting with a resolution of 0.1 points and a maximum of 10.9 for each shot

The following assumptions were used.

• The location of the X-co-ordinates of the shots (Left-Right) vary according to a normal distribution.
• The location of the Y-co-ordinates of the shots (High-Low) vary according to a normal distribution.
• The x- and y-distributions are independent (i.e. no stringing of the shot group).
• The standard deviations (SDs) of Left-Right and High-Low deviations are equal (i.e. a circular shot group, not an elliptical one).
• The rifle is accurately zeroed, i.e. the means of the X and Y distributions are zero. Thus, the centre of a shot group will, on average, be in the ‘10’.
• The error introduced by the shooter and the error introduced by the ammo are independent from each other.

Figure 1 Two five-shot air rifle groups, fired from a rest: good ammo, bad ammo and a detail of the ISSF air rifle target shown on the same scale.

Thus, the statistical characteristics of the shot group dispersion is decribed by a single parameter, the SD (standard deviation). The first question is how this SD relates to the shot group diameter, i.e. the largest distance between the outer edges of a shot that can be found in a shot group of a given number of shots. Figure 2 shows this relationship for a 3-shot group and for a 10-shot group. There is a linear relationship between the shot group diameter and the SD. If the SD equals zero, the shot group diameter equals the diameter of a single pellet, i.e. 4.5 mm. Of course, a non-zero SD, the average shot group diameter increases with the number of shots fired.

Figure 2 Average shot group diameter as a function of the standard deviation.

The next question is how the SD relates to the shooting result, i.e. the score. This is shown in Figure 3 for a 60-shot match.

Figure 3 Mean score as a function of the SD.

Again, there is a linear relationship: for each mm increase of the SD, the mean score drops by 30 points. However, for a SD below 1 mm, there is no effect of the SD on the normal score. This can easily be understood: considering that (1) just touching the ‘10’ is enough to get a ’10’ on your scoring card, (2) the ‘10’ has a 0.5 mm diameter and (3) the pellet has a 4.5 mm diameter, you can see that starting from a 10.9 there is some margin for error before the ‘10’ becomes a ‘9’. When the SD increases, starting at 0, at first you are still within the margin that gives you a ‘10’ even for a non-perfect shot. Once you are out of this margin (above SD=1 mm), the score drops with increasing SD.

Now, distinguish 2 independent sources of dispersion:

• the shooter
• the ammunition

These sources contribute independently to the total shot group dispersion. The question is how the total dispersion relates to these two sources of dispersion. As statistical textbooks will tell you, the total variance is the sum of the two variances. Since the standard deviation is the square root of the variance, this means:

[1]

• Three quality levels of pellets are distinguished. Arbitrarily, three shot group diameters were chosen as shown in Table 1; the corresponding SDs can then be found from Figure 1.
• Next, the performance level of the shooter is varied from ‘perfect’ down to non-that-perfect.
• Given the SDs of the ammo and of the shooter, the total (shooter+ammo) dispersion can be calculated according to [1].
• Next, the relation between the total SD and the score from Figure 3 is used to obtain the effects on the score.

Table 1 SD for three pellet qualities

Pellet quality shot group size shot group diameter (mm) SD (mm)
Perfect inf. shots 4.5 0.00
Bad 3 shots 9.0 1.87
Fair 3 shots 6.75 0.94
Good 10 shots 5.0 0.13

Normal score

For non-perfect pellets, the total SD depends on the SD of the ammo and the SD of the shooter according to [1]. Figure 4 shows the effect of the SD of the shooter and the ammo quality on the normal score. For perfect ammunition, SD AMMO =0 and according to [1], the SD TOT equals the SD SHOOTER. Thus, in this situation, the relation between the SD of the shooter and the score is the same as in Figure 3.

The same data are shown in Figure 5, now using the score the shooter would obtain with perfect ammunition along the horizontal axis.

Figure 4 Effect of SD of the shooter and the ammo quality on the average normal shooting score.

Figure 5 Loss of points due to non-perfect ammo as a function of ammo quality and shooter’s ability (normal score)

The figures shows that:

• The score you lose by using non-perfect ammo depends on your performance level.
• Good ammo can hardly be distinguished from perfect ammo in this graph; the maximum deviation is 0.2 points. (Therefore, this condition was omitted from Figure 4)
• Using fair ammo costs a maximum of 9.1 points wits respect to perfect ammo. This is the situation for a shooter who, with perfect ammo, would score 595.
• Using bad ammo costs a maximum of 31.1 points wits respect to perfect ammo. This is the situation for a shooter who, with perfect ammo, would score 597.
• In contrast, if a shooter’s performance is around 500 points, he/she loses merely 3 to 12 points by using fair or bad ammo, respectively.
• When the shooter’s ability improves beyond 595 (assuming perfect ammo), the loss of points due to non-perfect ammo decreases.

Finale score

The same approach was used for the situation with the finale scoring. Here, the maximum score over a series of 60 shots is 60*10.9 = 654. The results are shown in Figure 6 and Figure 7.

Figure 6 Effect of SD of the shooter and the ammo quality on the average finale shooting score.

Figure 7 Loss of points due to non-perfect ammo as a function of ammo quality and shooter’s ability (finale score)

The figures show that:

• The maximum loss due to good ammo instead of perfect ammo is merely 1.8 points (at a score of 653.7, i.e. a mean of 10.895 per shot).
• For fair ammo, the loss of points with respect to the situation with perfect ammo increases with the shooter’s ability, up to a maximum of 25 points for a perfect shooter.
• For bad ammo, the loss of points with respect to the situation with perfect ammo increases with the shooter’s ability, up to a maximum of 53 points for a perfect shooter.

• The loss of points due to non-perfect ammo depends on the level of performance of the shooter. The better the shooter, the higher the loss of points due to non-perfect ammunition.
• Using 'good' pellets for your rifle will practically elliminate the loss of points due to the ammo-rifle match, irrespective of your level of performance. If it's not a 10.9, it is your own fault...