Rifle & Pistol Insight - real example . . .

This is a quick example showing how groups of shots can be averaged and compares extreme spread calculations with true average spreads.

The air rifle rifle is a very old and not particularly well cared for Webley Vulcan. The trigger is so heavy I sometimes need to check that the safety catch is off! Two types of pellet are compared: Eley Wasps are a round nose general purpose "plinking" pellet; HN target wad cutters. Test distance is 10yds.

Define the individual groups . . .

Eley Wasp.

Eley wasp groups. The POA in both cases is the centre of the bulls-eye target. The gun is shooting low and to the right. The six shot first group is due to a counting shortcoming on the part of the shooter! 


 HN Target Wad Cutter.

HN wad cutter groups. The POA in both cases is the centre of the bulls-eye target. The gun is shooting low but looks good laterally. 


Add the two groups for each pellet type together and compare the two pellet types . . .

Eley Wasp. 11-shot average. 

Average radius shown as 0.337". 

Extreme spread shown as 1.600".

HN Target. 10-shot average. 

Average radius shown as 0.371". 

Extreme spread shown as 1.297".



If the traditional "extreme spread" measure is used, the HN Wad Cutters measure as the best. Using the true "Average radius" the Eley Wasps come out slightly better. This shows that the measurement method makes a difference. If the "extreme spread" measure is used, this could be misleading. This effect has also been observed when measuring test groups published in magazines. The shell declared "best" by the magazine is often not the best when the more valid "average radius" is calculated. Try it for yourself on some published pictures of bullet groups!   

There is a final "word of caution": Statistical Significance! This allows one to decide if two groups with different average radii are genuinely different or whether they are actually too close to call. In simple terms, if one ten shot group measured 8" average radius and a second group with a different gun or ammo gave a 10-shot group of 1" size, one can be pretty confident that the second combination is genuinely better. If it was a 6" group versus the 8" group, things get trickier. With only a 10-shot group one cannot be confident that the equipment combination that gave the 6" group is genuinely better than the equipment that gave the 8" group. If one had taken groups of 100 shots then one can have more confidence that there is a genuine, long term difference between the two guns or ammo. Statistical significance is described more fully here: Statistical significance.

In the Eley vs HN pellet case considered above, the average radii of 0.337" and 0.371" are too similar to declare as genuinely different. Either the average radii need to be much more different or many more pellets need to be averaged to confirm the small difference.  



(c) Dr A C Jones