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:
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