Some Statistics on Paintballs
by Gary Dyrkacz and Neal Dyrkacz

In order to do the calculations in the physics and trajectory documents, it was necessary to have data on some of the properties of paintballs.  At the time, we had three samples available: Brass Eagle paintballs, bought at Kmart approximately four months before the measurements, RP Scherer Premium paintballs, purchased three weeks before the measurements, and Zap Pro Series paintballs purchased three months before the measurements.

The Brass Eagle balls had been stored in the original 200 count plastic bottle. The Scherer paint was stored in loaders, while the Zap was in the original bag. Scherer and Zap paintballs were from full cases, and were purchased as field paint.  All the balls were stored between 60 and 75 F in a basement environment.  All the measurements were made in February, 1999.

Weight Measurements
Weight measurements were done using an electonic pan balance and a five place electronic analytical balance.  On the analytical balance, we found it was not practical to use weights beyond three places due to films on the balls and handling.  The room temperature was 71.9 F and the relative humidity was measured at the balance and found to be 16%  The balls were allowed to equilibrate under these conditions for about an hour. This may not have been long enough, but no drift in weights due to moisture loss or gain were noted during weighings.

Two separate weighings were done.  In the first case, appoximately 100 balls of each type were counted, placed in a tared beaker and weighed. Next, 20 paintballs from each manufacturer were individually weighed and recorded.

The weight data on the bulk measurements for the paintballs can be seen in the following Table:

Average Weight of Paintballs
  Brass RP Scherer Zap
  Eagle Premium Pro Series
number of balls 73 95 96
wt (g) per ball 3.221 3.185 3.196
       
average wt. (g) 3.201    

The Brass Eagle ball are the heaviest, followed by the Zap and last the RP Scherer.  The next Table describes the statistical variation in the individual paintballs:

Weight Statistics for Paintballs
  Brass RP Scherer Zap 
Statistic Eagle  Premium Pro Series
Mean (grams) 3.217 3.187 3.195
Standard Error 0.0088 0.0015 0.0021
Median 3.222 3.189 3.195
Mode #N/A 3.190 3.196
Standard Deviation 0.0394 0.0067 0.0093
Range 0.125 0.022 0.032
Minimum 3.15 3.174 3.181
Maximum 3.275 3.196 3.213
Count 20 20 20
Confidence Level(95.0%) 0.0184 0.0031 0.0044

The mean information is consistent with the bulk weight measurements. Brass Eagle balls are the heaviest, and Scherer ball the lightest. Brass Eagle paintballs, from this lot at least, appear to have a serious quality control problem.  The standard deviation of the mass is over five times that of the Scherer or Zap balls. Standard deviation is a measure of the variability in the measurements, in this case the masses. The Scherer paintballs appear to have the least mass variation, but the differences compared to the Zap are not very large. The last entry, the 95% confidence interval tells us that statistically 95 % of the values would fall in the range +/- the number shown.  Thus, for Scherer paintballs, 95 % of the weights would fall between 3.184 g and 3.190 g.  A visual representation of the mass distributions is shown in the histogram below:

Weight Distribution The Figure quite dramatically shows the weight distributions.  The Brass Eagle balls have an enormous range compared to the other two paints. Comparing the Zap and Scherer paintballs, the Scherer is indeed very narrow and has a more symmetrical distribution. Note that the Zap distribution is skewed toward higher weights.







Size Measurements
A few days after the weight measurements were done, the size of the paintballs were determined.  A micrometer was used to determine the sizes. This is not the perfect gauge for this.  Paintballs are not hard, and therefore even a light force will deform them.  We were very careful to try and avoid compression. Repetitive measurements showed variations of +/- .001 inches. We first began taking single measurements of the diameter and then realized that most of the balls where not completely symmetrical. The largest variation in most cases was between the equator or seam, and the "poles". We therefore decided to record both the diameter at the seam, and the diameter from pole to pole from each paintball. For each manufacturer we measured 22 balls. The table below shows the overall diameter statistics of the three different type of paintballs:
 

Statistical variation of seams and poles of Paintballs
  Brass Eagle RP Scherer   Zap Pro  
      Premium   Series  
Statistic seam pole seam pole seam pole
Mean (inches) 0.685 0.672 0.681 0.677 0.680 0.677
Standard Error 0.0018 0.0018 0.0007 0.0009 0.0006 0.0009
Median 0.686 0.671 0.681 0.677 0.680 0.676
Mode 0.688 0.671 0.677 0.678 0.681 0.673
Standard Deviation 0.0085 0.0082 0.0033 0.0043 0.0030 0.0042
Range 0.032 0.041 0.011 0.019 0.013 0.016
Minimum 0.669 0.656 0.676 0.671 0.673 0.67
Maximum 0.701 0.697 0.687 0.69 0.686 0.686
Confidence Level(95.0%) 0.0038 0.0036 0.0015 0.0019 0.0013 0.0019
Data from 22 paintballs from each manufacturer; measured with micrometer
Temperature 78; rel. humidity 28%

The Brass Eagle balls exhibited the largest seam diameter, and the smallest pole diameters. In both diameters, it had the largest variation of any manufacturer, and shows the largest standard deviation by a big margin. The Zap and Scherer balls are nearly identical in both their characteristics. To show a little more clearly the difference in ball shape, we took the ratio of the pole/seam diameters:
 

Statistical variation of pole/seam ratio 
  B. Eagle RP Scherer Zap
Statistic   Premium Pro Series
Mean  0.980 0.993 0.995
Standard Error 0.0036 0.0015 0.0019
Median 0.975 0.993 0.993
Mode 0.971 1.001 0.988
Standard Deviation 0.0167 0.0070 0.0091
Range 0.0680 0.0306 0.0353
Minimum 0.953 0.977 0.981
Maximum 1.021 1.007 1.016
Confidence Level(95.0%) 0.0074 0.0031 0.0040

These data emphasize the difference between pole diameter and seam diameters. All the ratioes are less than one. Thus, on the average the seam diameter is larger than the pole. In addition, the maximum size recorded in each of the three lots is closer to to 1.0 than the minumum value. This means that it is quite rare to have a ball where the seam is smaller than the pole. As already indicated, the Brass Eagle balls have the smallest ratio, that is, these balls are the most oval. The means show that the Brass Eagle paintballs have about a 2% difference between the seams and the poles. Both the Zap and Scherer are quite a bit better with roughly a 0.6% variation.From this data it is apparent that the Zap and the RP Scherer paintballs are quite similar in nature.

It is clear that very few balls from any manufacturer are really spherical. However, the Brass Eagle paintballs stands in a class by themselves. To be fair this is only one set of measurements, on one lot of paintballs. It would be useful to see if these number hold up over several lots of balls. From the many compliants I have heard about Brass Eagle paintballs on the rec.sport.paintball group, I suspect the data presented here are not extraordinary.

Of course, despite these differences there are other problems we did not mention. Specifically, we did not measure any other imperfections in the ball, and there were some noted, such as dimples. It also is not clear just what any of these variations mean in terms of paintball accuracy. What will a 0.6% difference in sphericity mean in terms of the path a paintball will follow? Are the effects below detectabiility in terms of other subtle factors such as barrell smoothness or scratches that might affect the trajectory of a ball?

The large variations noted in Brass Eagle balls are certainly in line with the general impression many paintball players have about the balls. They do appear to be more erratic in flight, so from this weak non statistical evidence, it would appear that the magnitude of distortions measured for them here, may indeed be overriding other factors affecting range and accuracy.

 


Send comments and suggestions to: dyrgcmn@comcast.net

Last Updated: December 19, 2004