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#1 rntlee

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Posted 12 May 2012 - 06:30 AM

I have a large data set of recorded shots (103 shot @ 75') that I broke down a bit. Nothing really new but it does confirm consistency must be quite poor to affect accuracy much at medium range.
Here's the original group and underneath it just the shots within +-2fps
Here's just the shot >= +-5fps

#2 Molybdenum

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Posted 12 May 2012 - 09:22 AM

That's very interesting. I would suggest you try to shoot a group at deteriorating inconsistencies, but consistency is a rather difficult variable to control without changing paint.

#3 Troy

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Posted 12 May 2012 - 10:55 PM

I took the liberty of graphing shot velocity verses height:

Posted Image

Within the given dataset, the trendline that maps this data has a coefficient of determination (r^2) of .0004 (where 1 is a perfect line) Just to give you an idea as to what a GOOD r^2 value is, I frequently threw out data that was worse than .96 when I worked in a lab. I can say with a VERY high level of confidence, within this dataset, there is no correlation between shot velocity and impact height.

Where's that damn nail? I've got a coffin to shut...
\m/

#4 cockerpunk

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Posted 12 May 2012 - 10:59 PM

great data set lee!
The ultimate truth in paintball is that the interaction between the gun and the player is far and away the largest factor in accuracy, consistency, and reliability.

And yes, Gordon is the sexiest manifestation of "to the front."


#5 drg

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Posted 12 May 2012 - 11:17 PM

That's very interesting. I would suggest you try to shoot a group at deteriorating inconsistencies, but consistency is a rather difficult variable to control without changing paint.


You could possibly mix paints of different diameters.
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#6 The_Economist

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Posted 13 May 2012 - 12:41 AM

Nice job. More data to show that consistency and accuracy are very tenuously linked in paintball.


#7 cockerpunk

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Posted 13 May 2012 - 08:58 AM


That's very interesting. I would suggest you try to shoot a group at deteriorating inconsistencies, but consistency is a rather difficult variable to control without changing paint.


You could possibly mix paints of different diameters.


dirty regulator might work too. then clean it, and shoot a sample again.
The ultimate truth in paintball is that the interaction between the gun and the player is far and away the largest factor in accuracy, consistency, and reliability.

And yes, Gordon is the sexiest manifestation of "to the front."


#8 drg

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Posted 13 May 2012 - 02:03 PM

Or simulate by using a clean stable reg and turning it up or down?

Edited by drg, 13 May 2012 - 02:04 PM.

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#9 Troy

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Posted 13 May 2012 - 03:32 PM

Or simulate by using a clean stable reg and turning it up or down?


This is what I was thinking. Use the same paint, same marker, just adjust the reg... thus keeping the amount of air actually delivered to the paintball variable, and as many other variables as constant as possible.

In other news, I just picked up an F1 Alpha Shooting Chrony... mainly because I have an older Timmy that I needed to tune, but it gave me the proper excuse to get a nice chrono, so I could do some tests myself.

Edited by Troy, 13 May 2012 - 03:35 PM.

\m/

#10 Snipez4664

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Posted 14 May 2012 - 11:26 AM

Forum malfunction, ignore post.

Edited by Snipez4664, 14 May 2012 - 11:31 AM.

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#11 Egomaniacal

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Posted 14 May 2012 - 11:44 AM

What was the paint/barrel like that you were using?

I only ask because as "scientists" we must be careful to consider the conditions of our tests, as that will affect their applicability. Unfortunately, although this is a very extensive dataset, we cannot draw a strong conclusion because of a lack of information on conditions.

All I feel comfortable saying is that with paint of unknown roundness and size, a barrel of unknown quality and dimension, an unknown paint to bore relationship, there is no correlation between accuracy and consistency over the range of 275-285 fps.

I'm not one to believe there is a correlation that won't be washed out by other effects, but unfortunately that's all we can say with the data provided. There's no doubt you would begin to see a correlation if you increased the standard deviation to +-50. Who knows, maybe if you were to use highly round paint and a properly under-bored barrel you might see an effect show through, even at +- 5.

Is there any chance you have a pair of calipers you could throw about 20 balls at, get a measure of seam and pole diameters? Measure your bore? Either way it would help just knowing the make and model of the paint and make and model of the barrel.

Edited by Egomaniacal, 14 May 2012 - 12:00 PM.

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#12 UV Halo

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Posted 14 May 2012 - 11:46 AM

Great Data!!

Questions:
Was the barrel level?
How was the zero established?
Was the paint weighed and sized?
I'm not saying these influence the results but, I'm looking to do a real-world comparison to my model.

In any case, I've long felt that inherent inaccuracy largely overshadows most velocity influenced deviations.

#13 cockerpunk

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Posted 14 May 2012 - 11:53 AM

What was the paint/barrel like that you were using?

I only ask because as "scientists" we must be careful to consider the conditions of our tests, as that will affect their applicability. Unfortunately, although this is a very extensive dataset, we cannot draw a strong conclusion because of a lack of information on conditions.

All I feel comfortable saying is that with paint of unknown roundness and size, a barrel of unknown quality and dimension, an unknown paint to bore relationship, and velocity fluctuations with a standard deviation of +-5 around 280 fps, there is no correlation between accuracy and consistency.

I'm not one to believe there is a correlation that won't be washed out by other effects, but unfortunately that's all we can say with the data provided. There's no doubt you would begin to see a correlation if you increased the standard deviation to +-50. Who knows, maybe if you were to use highly round paint and a properly under-bored barrel you might see an effect show through, even at +- 5.

Is there any chance you have a pair of calipers you could throw about 20 balls at, get a measure of seam and pole diameters? Measure your bore? Either way it would help just knowing the make and model of the paint and make and model of the barrel.


why would bore size or barrel make matter? we already have bounded that in terms of there non-effects on accuracy (and thus Y position).

the issue with using a normal regulator and adjusting it on the fly, is that you don't know what distribution of velocities you are are getting from that. there could be local averages, instead of a nice relatively normal distribution of velocities.
The ultimate truth in paintball is that the interaction between the gun and the player is far and away the largest factor in accuracy, consistency, and reliability.

And yes, Gordon is the sexiest manifestation of "to the front."


#14 Egomaniacal

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Posted 14 May 2012 - 12:20 PM

why would bore size or barrel make matter? we already have bounded that in terms of there non-effects on accuracy (and thus Y position).


Barrel make doesn't, I was just more or less looking for more information about the barrel.

The reason the bore is important is depending on how out of round the paintballs are, the amount of under-bore might play a role in how much spin is imparted to the ball. It's why I asked for paint measurements along with the bore measurement. I'll admit I'm making a bit of an assumption about spin imparted being a function of roundness and relative bore/paint diameter, but we have seen that accuracy deteriorates when the size of the paintball is close to the bore of the barrel.

Unless you guys have done tests that show accuracy is independent of paint quality (I actually believe you've found the opposite to be true), I suspect there is a dependence there, and it is dependent on relative bore size (in a way I'm not 100% sure about). I will admit I haven't been through every test in the experiment vault.

tl;dr - If quality paint were used in conjunction with a bore that attenuates spin and other effects that accuracy is dependent upon, a consistency dependence might show through. It's hard to say what we're dealing with in the data provided, for all we know these could be 5 year old dimpled monsterballs going through a bore matched barrel, which would likely wash out any correlation between consistency and accuracy.

Edited by Egomaniacal, 14 May 2012 - 12:33 PM.

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#15 cockerpunk

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Posted 14 May 2012 - 03:17 PM


why would bore size or barrel make matter? we already have bounded that in terms of there non-effects on accuracy (and thus Y position).


Barrel make doesn't, I was just more or less looking for more information about the barrel.

The reason the bore is important is depending on how out of round the paintballs are, the amount of under-bore might play a role in how much spin is imparted to the ball. It's why I asked for paint measurements along with the bore measurement. I'll admit I'm making a bit of an assumption about spin imparted being a function of roundness and relative bore/paint diameter, but we have seen that accuracy deteriorates when the size of the paintball is close to the bore of the barrel.

Unless you guys have done tests that show accuracy is independent of paint quality (I actually believe you've found the opposite to be true), I suspect there is a dependence there, and it is dependent on relative bore size (in a way I'm not 100% sure about). I will admit I haven't been through every test in the experiment vault.

tl;dr - If quality paint were used in conjunction with a bore that attenuates spin and other effects that accuracy is dependent upon, a consistency dependence might show through. It's hard to say what we're dealing with in the data provided, for all we know these could be 5 year old dimpled monsterballs going through a bore matched barrel, which would likely wash out any correlation between consistency and accuracy.


im not saying more info is a bad thing, im just saying there is enough here to draw real conclusions from (esp given the other data sets we have on the topic).
The ultimate truth in paintball is that the interaction between the gun and the player is far and away the largest factor in accuracy, consistency, and reliability.

And yes, Gordon is the sexiest manifestation of "to the front."


#16 Egomaniacal

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Posted 14 May 2012 - 03:30 PM

im not saying more info is a bad thing, im just saying there is enough here to draw real conclusions from (esp given the other data sets we have on the topic).


Right, which is why I'm just saying based on the information available, we need to exercise caution about how far we generalize these results. There is certainly a conclusion to be drawn here, but every conclusion has caveats.

Just going to point out, the consistency at least seems a little poor for a well-matched barrel with quality paint. Not that I'm implying that's why the accuracy is what it is, just pointing out that if it's bad paint that'll wash out any accuracy variation due to inconsistent velocities. There's little doubt in my mind that both inconsistency and inaccuracy are caused by bad paint, and what we're trying to determine is if the inaccuracy is caused by velocity fluctuation or by some other effects, like spin due to bad paint.

Which introduces an interesting point, the more energy you put into spinning a paintball, the less energy you have for translational motion. So while you're simultaneously lowering the muzzle velocity, you're also introducing drag effects that will put the projectile off-course. I'm going to check to see if this shows up in the data.

In my mind, consistency and accuracy are both dependent on bad paint. If you want to see if inaccuracy has any direct dependence on inconsistency, you need to reduce the variables they're both dependent upon as much as possible.

Edit#100: Hmm, nothing there.

Edited by Egomaniacal, 14 May 2012 - 04:36 PM.

eiπ = − 1

#17 cockerpunk

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Posted 14 May 2012 - 05:25 PM


im not saying more info is a bad thing, im just saying there is enough here to draw real conclusions from (esp given the other data sets we have on the topic).


Right, which is why I'm just saying based on the information available, we need to exercise caution about how far we generalize these results. There is certainly a conclusion to be drawn here, but every conclusion has caveats.

Just going to point out, the consistency at least seems a little poor for a well-matched barrel with quality paint. Not that I'm implying that's why the accuracy is what it is, just pointing out that if it's bad paint that'll wash out any accuracy variation due to inconsistent velocities. There's little doubt in my mind that both inconsistency and inaccuracy are caused by bad paint, and what we're trying to determine is if the inaccuracy is caused by velocity fluctuation or by some other effects, like spin due to bad paint.

Which introduces an interesting point, the more energy you put into spinning a paintball, the less energy you have for translational motion. So while you're simultaneously lowering the muzzle velocity, you're also introducing drag effects that will put the projectile off-course. I'm going to check to see if this shows up in the data.

In my mind, consistency and accuracy are both dependent on bad paint. If you want to see if inaccuracy has any direct dependence on inconsistency, you need to reduce the variables they're both dependent upon as much as possible.

Edit#100: Hmm, nothing there.


eh, combined with the other mountain of evidence we have for consistency and accuracy being linked below +/-15 fps ... i see no reason to be apprehensive about concluding the same thing.
The ultimate truth in paintball is that the interaction between the gun and the player is far and away the largest factor in accuracy, consistency, and reliability.

And yes, Gordon is the sexiest manifestation of "to the front."


#18 Egomaniacal

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Posted 14 May 2012 - 05:26 PM

So I did a little more digging, and decided that even with 100 shots the statistics were still not good enough to make a solid conclusion. Here's a graph of the distance from the average center vs. velocity:

Posted Image

It looked to me like the shots that were at a higher velocity tended to be more accurate, so I broke things down into velocity groups to get a better picture of what was going on.

Posted Image

If we ignore the first and last columns (the first has only 5 datapoints and the last 6, not enough to get a good picture) we can see that as the velocity increases, the average distance to the average center decreases. Also, as velocity increases, the spread (less strongly) seems to decrease.

Since we've already seen that the increase in distance from center is not a result of velocity fluctuations causing the ball to fall short, this data seems to support my hypothesis that more energy used to spin the ball results in lower translational velocity, and also causes a larger spread (in any direction)

It also makes me wonder about his bore, paint size and paint quality.

Edited by Egomaniacal, 14 May 2012 - 06:03 PM.

eiπ = − 1

#19 cockerpunk

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Posted 14 May 2012 - 07:03 PM

you'd have to know how much energy was imparted on each ball to make that conclusion. all we know is how much translational energy was imparted (velocity)
The ultimate truth in paintball is that the interaction between the gun and the player is far and away the largest factor in accuracy, consistency, and reliability.

And yes, Gordon is the sexiest manifestation of "to the front."


#20 Egomaniacal

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Posted 14 May 2012 - 08:17 PM

you'd have to know how much energy was imparted on each ball to make that conclusion. all we know is how much translational energy was imparted (velocity)


If you make the moderate assumption that the energy imparted on the ball is roughly equal from shot to shot, then no, you don't. And even if it weren't equal and you used that to explain the spread in velocity, that wouldn't explain the spread in position at lower velocities. It's still a hypothesis, I'm just saying the data we have to work with seems to support it.

Edited by Egomaniacal, 14 May 2012 - 08:20 PM.

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#21 Troy

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Posted 15 May 2012 - 06:20 AM

Egomaniacal, with all due respect, the coefficient of determination on that data set is crap. You can't draw any relevant conclusions with a value of .08.
\m/

#22 Egomaniacal

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Posted 20 May 2012 - 06:59 PM

Alright, time to squash this coefficient of determination thing once and for all.

Egomaniacal, with all due respect, the coefficient of determination on that data set is crap. You can't draw any relevant conclusions with a value of .08.


Troy,

This is why I threw the linear regression out. There's more than one way to analyze a set of data, and frankly just looking at r^2 tells us bupkis about whether or not there is a relationship between measured quantities. It is one of the many massively misleading things people are taught in K-12 math/science classes.

Frankly, for ANYTHING on this site, in my opinion you guys should almost never use r^2 as a determining factor of whether two things depend on each other. You guys do a thousand times better than anyone else out there, but there is just too much noise in the systems you're trying to measure and your sample sizes are too small to throw things out for not having r^2 >= 0.9.

Goodness of fit (R-squared) and trend
The least-squares fitting process produces a value – r-squared (r2) – which is the square of the residuals of the data after the fit. It says what fraction of the variance of the data is explained by the fitted trend line. It does not relate to the statistical significance of the trend line (see graph); statistical significance of the trend is determined by its t-statistic. A noisy series can have a very low r2 value but a very high significance in a test for the presence of trend. Often, filtering a series increases r2 while making little difference to the fitted trend or significance. In a method for identifying a statistically meaningful trend, only filtered or unfiltered series with r2 values exceeding 0.65 are counted as positive test results.


Again I would like to say that this is a fantastic data set. Thank you rntlee for taking it, the work must have been painstaking. That said, I would have loved for it to be 10,000 shots. :P

At any rate, instead of having 103 distinct data points to work with, I grouped them into 5 or so points each with an associated spread in the measurement - a perfectly legitimate step to take. By doing so, we can see that there is a very strongly suggested negatively correlated trend in the data. Note that I have not accounted for experimental uncertainties here, the SD is due to the randomness of events alone. This averaging is a form of discrete filter, and if we eliminate the first datapoint due to its low sample size for the filter the trend on this graph has an r^2 = 0.86.


Posted Image

So I decided this would be a good time to brush off the old statistics courses I thought I was wasting time in. Going back to the original data with n=103, (I did not want to exclude data due to the incompetence of my filter), we have:

Posted Image

Null hypothesis: There is no correlation between distance from the center and velocity, meaning the slope of the regression is not statistically significantly different from 0.

Doing this, I calculated a standard deviation in the slope of this regression of 0.044, and a t-score of -3.074 (the negative sign indicating the negative slope). Combining that with 101 degrees of freedom (as you would for a simple linear regression), I get a p-value of p=0.0014 (makes sense, slope was -.13 and error was .004). This is statistically significant by any standard, so using a slope from the regression of -0.13, we reject the null hypothesis and therefore can say without doubt there is a correlation between the average distance from center and velocity.

Next, I figured I'd check to see if there was a statistically significant correlation between velocity and height.

Posted Image

Null hypothesis: There is no correlation between height and velocity, meaning the slope of the regression is not statistically different from 0.

I calculated a standard error in the slope of this regression at .0076, and a t-score of 1.305. Again with 101 degrees of freedom our p-value is p=.19, so it is not statistically significant and we cannot reject the null hypothesis with this dataset (again this makes sense, slope was .009 and error was .007). We see that any range effects due to velocity over this velocity range are wiped out completely by other causes of inaccuracy.

If you want to follow what I've done I used the method straight off of Wikipedia, but it agrees with what I've previously learned (and the notes I was looking through).
http://en.wikipedia....near_regressionhttp://en.wikipedia....near_regression

I suppose the correct thing to do would have been to re-do the filter to be more rigorous, then done the t-test on the fit from that. That way from the same set of data we would have both r^2>=.65 and statistical significance, but I'm done, and looking at these results I don't feel it necessary to go back and do that. To point out why,
I just re-did the filter with a commonly used discrete filter, taking an average of every 10 shots (threw out the first two and the last one). With this, I still get r^2 = .687 and a slope of b = -0.135.

Ah fuck it, might as well do it.

n = 10
Standard error in slope: 0.03366
t-value: -4.00
p-value: .0039
So doing it completely rigorously we have r^2 = .687 and strong statistical significance.

Troy, I want to thank you for giving me a reason to review this material. It was a great afternoon.

Edited by Egomaniacal, 20 May 2012 - 07:14 PM.

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#23 Troy

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Posted 20 May 2012 - 09:39 PM

Ego, i love you :wub:... , but I think you are relying too heavily on data that doesn't have enough data points.

The most that a single shot velocity got was 12 shots (280fps and 278fps). I will grant you that your r^2 value of .86 would be convincing... if there was more data.

We need to figure out a way to standardize this test and deal for differences in paint etc. Now that I have a chrono, I'd like to throw in some results of my own. If we normalize shot spread to a percentage of the farthest vector recorded, would that work?
\m/

#24 Egomaniacal

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Posted 20 May 2012 - 10:11 PM

Ego, i love you :wub:... , but I think you are relying too heavily on data that doesn't have enough data points.

The most that a single shot velocity got was 12 shots (280fps and 278fps). I will grant you that your r^2 value of .86 would be convincing... if there was more data.

We need to figure out a way to standardize this test and deal for differences in paint etc. Now that I have a chrono, I'd like to throw in some results of my own. If we normalize shot spread to a percentage of the farthest vector recorded, would that work?


haha Posted Image it's nice to chat with someone who reads posts like that.

Anyway, with a t test/p value test the number of data points is accounted for. I may have been confusing by focusing on the number of balls at individual velocities for the graph with the averages, but when we use a t-test for the data set it is based on the full 103 points. The independent variable (as I treated velocity in this case) should actually be a continuous variable - so it doesn't really make sense to talk about the # of shots at a specific velocity. That is only an artifact of the limits of our precision, if the chrono read out to 0.01 I doubt we'd have more than a couple repeats, but the same statistics would apply. If there is a statistical significance, it means there are enough data points to reject the null hypothesis period. As the # of data points increases, if there is a correlation then the p value will decrease correspondingly. In this case we have over 99% certainty that there is a correlation between deviation from mean position and velocity, so there is clearly plenty of data.

But I agree about the standardization. As I was sifting through the data this afternoon I became convinced that there was something funky about the paint/barrel/paint-to-barrel. There's really no reason most markers would be this inconsistent unless something's up.

As far as taking measurements, I rather like the way he's done it already. It separates horizontal and vertical components, which lets us see whether or not the variation in distance is simply due to range considerations. It would be interesting to see what conditions are necessary for inconsistency to show up in the y-component. The only things I'd like to see added are information about the experimental setup - paint measurements, bore measurements, information about the marker etc. It could be interesting to do a run of say 40 shots where you measure the roundness of the paintball before firing - perhaps a measurement along the seam and another perpendicular to the plane of the seam? Once underbored by 0.03" and once overbored by 0.03"? With some rubber gloves so you don't get moisture on the ball before firing?

Anyone else have any suggestions?

Edited by Egomaniacal, 21 May 2012 - 09:28 AM.

eiπ = − 1

#25 bball

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Posted 20 May 2012 - 11:46 PM

Use first strike rounds? They should help to contrast the rotation.

edit: I always thought that the statistics course I took would be a waste... Now I see it has real-life value.

Edited by bball, 20 May 2012 - 11:48 PM.


#26 Troy

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Posted 22 May 2012 - 10:20 AM

So ego, after some time, and thinking... and talking with people that actually interpret this kind of data for a living (I didn't want to say anything stupid again), here are some conclusions I've come to:

Graph 2: I've now become convinced that graph 2 is legit. You're right, you have enough data to prove your point. I would point out that I only think you are confident between 270 and 285fps, what happens outside of those ranges is still up for grabs. I would expect any accuracy increases to be decaying exponentially as we approach 0.

Graph 3: You've shown there isn't any significant correlation between shot height and velocity (which echoed my interpretation earlier in this thread)... so this leads me to wonder, where the hell the accuracy increase is coming from. I would like to see you give the x values the same treatment.

June 9th, I am going to repeat this test ( I will also weigh each shot though, and have at least one more person helping me... who is much smarter than I am). I would still like to hear ideas on how we can normalize the data set. Keep in mind that when I say "normalize" I don't mean "standardize." There will always be factors beyond our control, marker accuracy chrono resolution/accuracy, paint batches, etc. So I would like to figure out a way to combine two or more data sets, so we can start plotting bigger trends. As I mentioned before, finding the either the max vector or standard deviation of all the vectors, and then graphing individual data points as percentages of that value may work... I would still like to get some more input on that though.

As a side bar, I am wondering if vector shedding isn't directly correlated with shot velocity. If the amount of time a shot takes to get from the barrel to the target decreases, and if the random frequency of the occurance of vorticies doesn't increase proportionally to the speed of the ball... then this result set might make sense.
\m/

#27 cockerpunk

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Posted 22 May 2012 - 01:00 PM

Graph 3: You've shown there isn't any significant correlation between shot height and velocity (which echoed my interpretation earlier in this thread)... so this leads me to wonder, where the hell the accuracy increase is coming from. I would like to see you give the x values the same treatment.


this is an interesting question ....

now, i would hardly say the link between distance from center and velocity is a strong trend (a trend maybe, but not a very strong one) but it still does beg the question.
The ultimate truth in paintball is that the interaction between the gun and the player is far and away the largest factor in accuracy, consistency, and reliability.

And yes, Gordon is the sexiest manifestation of "to the front."


#28 Egomaniacal

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Posted 22 May 2012 - 01:22 PM

Graph 2: I've now become convinced that graph 2 is legit. You're right, you have enough data to prove your point. I would point out that I only think you are confident between 270 and 285fps, what happens outside of those ranges is still up for grabs. I would expect any accuracy increases to be decaying exponentially as we approach 0.

I absolutely agree with you about the range, and in addition to that I would be careful to extrapolate outside of the data range - especially all the way down to an extreme value like zero. I believe it is important to consider the source of the velocity fluctuation in this spread. In my mind it can be attributed to one of a few things - inconsistency in the valve of the marker, inconsistency in the paint sizing, and inconsistency in other random effects acting on the paint. Without changing the valve setup (adjusting velocity), this data really has no implications for shooting close to zero fps, because it seems unlikely that the source of the inconsistency would extend that low.

Graph 3: You've shown there isn't any significant correlation between shot height and velocity (which echoed my interpretation earlier in this thread)... so this leads me to wonder, where the hell the accuracy increase is coming from. I would like to see you give the x values the same treatment.

Yup, just figured I'd confirm your suspicion. I believe the better way to look at it would be an accuracy decrease - if a side of the ball catches for example the side of the barrel, or experiences a particularly strong vortex shedding event at some point early in flight, then some of its translational energy will be lost and put into rotational energy. This would cause the velocity to be lower, and depending on the direction of the added spin to the ball (or other trajectory deflection) would cause the ball to travel off course in a way that dominates over range effects. I would imagine that if good paint and a barrel that mitigated these effects were used, the grouping would change in a way that range vs. velo would become a statistically significant phenomenon - because inconsistencies from variations in the energy imparted to the ball would be predominantly in fluctuations in the energy released from the valve, not from the dynamics of the ball travelling down the barrel and ultimately downrange.

As a side bar, I am wondering if vector shedding isn't directly correlated with shot velocity. If the amount of time a shot takes to get from the barrel to the target decreases, and if the random frequency of the occurance of vorticies doesn't increase proportionally to the speed of the ball... then this result set might make sense.


I don't think I'm going to comment on this because of ... things that are going on behind the scenes. I will say I don't think this is quite correct, because the velo measurement is taken almost immediately after the ball leaves the marker - so the energy is being lost before the ball begins the majority of its travel downrange, not as it travels.
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#29 UV Halo

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Posted 22 May 2012 - 01:28 PM

I admit that a lot of this statistics discussion is flying over my head but, it looks good.

Just some related points for consideration:

Has any thought been given to how much the drop should vary based on differing firing velocities?

Using dual Chrono data, we can determine the mean drag of the projectiles (forward hemisphere resistance, and the negative rear pressure caused by vortex shedding), and given a starting velocity, the weight of the rounds, and, a couple environmental factors, we can predict how much they should drop.

Under indoor, less than 1mph winds, the only vertical variation from the expected drop would come from random factors (seam orientation, vortex shedding, oblong orientation) outside of the mean.

#30 bball

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Posted 22 May 2012 - 01:55 PM

I'm curious has anyone done the calculations for the ideal flight of the paintball?

would it be useful to calculate the rotational coefficient for a paintball

Edited by bball, 22 May 2012 - 02:00 PM.


#31 Troy

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Posted 22 May 2012 - 02:04 PM

I believe the better way to look at it would be an accuracy decrease - if a side of the ball catches for example the side of the barrel, or experiences a particularly strong vortex shedding event at some point early in flight, then some of its translational energy will be lost and put into rotational energy. This would cause the velocity to be lower, and depending on the direction of the added spin to the ball (or other trajectory deflection) would cause the ball to travel off course in a way that dominates over range effects.


I like that idea. If it's true, then it sounds like an ideal candidate for a dual crono test. Test the velocity right out of an underbored barrel, then downrange slightly, and see if the shots with the greatest delta are the most inaccurate. Hmmm... maybe I can rope someone else into a test that has another crono.

Edited by Troy, 22 May 2012 - 02:05 PM.

\m/

#32 Egomaniacal

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Posted 22 May 2012 - 02:55 PM

now, i would hardly say the link between distance from center and velocity is a strong trend (a trend maybe, but not a very strong one)


Now I won't argue that the signal isn't muddy (clearly there are confounding factors), but the correlation here is really undeniable. It is extremely strong, with p < 0.01. Whether or not addressing this issue translates to an increase in accuracy on the field is certainly up for debate - but you can't claim the trend isn't strong.

I like that idea. If it's true, then it sounds like an ideal candidate for a dual crono test. Test the velocity right out of an underbored barrel, then downrange slightly, and see if the shots with the greatest delta are the most inaccurate. Hmmm... maybe I can rope someone else into a test that has another crono.



Really you'd want to test the velo before it left the barrel... I'm not sure that's feasible.

Also, as I went back to re-do the data for the x position, I realized I missed a ^2 term in the y position (but not distance - don't worry, I checked). Doesn't change the graph, but it increased the standard error in the fitted slope significantly and therefore the p-value went up.

Re-doing the data, I get:

Distance vs. Velocity:
Slope of fit: -0.1357680499
Standard Error in Slope: 0.0442434247
t= -3.0739030954
p=0.0027
Filtered Distance vs. Velocity:
Slope of fit: -0.1346926127
SE in slope: 0.0336635037
t= -4.0010689732
p= 0.0039
Y-position vs. Velocity
Slope of fit: 0.009957346
Standard Error in Slope: 0.0624854301
t= 0.1593546846
p= 0.8737
X-position vs. Velocity
Slope of fit: -0.0757000813
SE in slope: 0.4750982509
t= -0.1593354635
p= 0.8737

As you can see, with the revised calculation the fit in the y-direction is even worse than before. What was stunning to me was that the t-score for the fit in both the x and y directions are identical to the 10,000ths place - telling us the lack of correlation is nearly identical in both directions over the entire dataset. Interesting implications there for range. Don't worry, I double checked them and encourage you to do the same - it's a two tailed t-test, and you can get the t-value by dividing the slope of the fit by the standard error - remarkable that such different slopes give nearly identical t-test numbers due to the uncertainty calculation.

At any rate, here's the graph for the x-position

Posted Image

Next I'm going to see if I can come up with a way to quantify an increase in the spread of data, instead of looking at the increase in mean distance from center.

Edited by Egomaniacal, 22 May 2012 - 02:58 PM.

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#33 cockerpunk

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Posted 22 May 2012 - 03:13 PM


now, i would hardly say the link between distance from center and velocity is a strong trend (a trend maybe, but not a very strong one)


Now I won't argue that the signal isn't muddy (clearly there are confounding factors), but the correlation here is really undeniable. It is extremely strong, with p < 0.01. Whether or not addressing this issue translates to an increase in accuracy on the field is certainly up for debate - but you can't claim the trend isn't strong.


what im saying is the trend is not a very large one. a major increase in one does not have a very large effect on the other. im not denying a trend, im saying its a small trend.
The ultimate truth in paintball is that the interaction between the gun and the player is far and away the largest factor in accuracy, consistency, and reliability.

And yes, Gordon is the sexiest manifestation of "to the front."


#34 bball

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Posted 22 May 2012 - 03:16 PM

to test velocity before it leaves the barrel-

It may be possible with a ported barrel especially one that has ports on opposite sides of the barrel. Velocity could be measured by seeing when the paintball passes these points

Edit: could someone give me a quick abstract of what exactly is being tested- thanks

Edited by bball, 22 May 2012 - 03:17 PM.


#35 UV Halo

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Posted 22 May 2012 - 03:24 PM

to test velocity before it leaves the barrel-

It may be possible with a ported barrel especially one that has ports on opposite sides of the barrel. Velocity could be measured by seeing when the paintball passes these points

Edit: could someone give me a quick abstract of what exactly is being tested- thanks


In short, this thread is about whether or not velocity consistency impacts accuracy (and how much). It has since evolved into a statistical analysis of the data collected to date.

#36 Egomaniacal

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Posted 22 May 2012 - 04:09 PM

what im saying is the trend is not a very large one. a major increase in one does not have a very large effect on the other. im not denying a trend, im saying its a small trend.


Ah, right. As it stands the trend says the mean distance from center increases by 0.13" per fps lost, which doesn't seem trivial to me. But keep in mind as well that's the change in mean distance from the center - so it's in the radial direction only. So if you were to look across your shot pattern it's a quarter inch per fps, and suddenly it's not so trivial - and again this is just the average distance from the center, so we're loosing a lot of information about how much the distribution smears out as velocity drops. Still working on figuring out a rigorous way to examine that.

Edited by Egomaniacal, 22 May 2012 - 04:16 PM.

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#37 bball

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Posted 23 May 2012 - 09:25 AM

just to ask - could the inconsistency arising from a difference of mass in each paintball have some effect

#38 brycelarson

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Posted 23 May 2012 - 09:27 AM

just to ask - could the inconsistency arising from a difference of mass in each paintball have some effect


certainly.

#39 bball

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Posted 23 May 2012 - 09:33 AM

Has there been any evidence to show that this has had an effect?


Though it would seem reasonable - especially if there is variance in both force supplied and the mass of the paintball, I would not want to come to a premature conclusion if there is not any solid evidence to to support that conclusion.


(I now realize that I shouldn't have asked my question in such a vague manner).

Edited by bball, 23 May 2012 - 09:33 AM.


#40 cockerpunk

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Posted 23 May 2012 - 09:36 AM


what im saying is the trend is not a very large one. a major increase in one does not have a very large effect on the other. im not denying a trend, im saying its a small trend.


Ah, right. As it stands the trend says the mean distance from center increases by 0.13" per fps lost, which doesn't seem trivial to me. But keep in mind as well that's the change in mean distance from the center - so it's in the radial direction only. So if you were to look across your shot pattern it's a quarter inch per fps, and suddenly it's not so trivial - and again this is just the average distance from the center, so we're loosing a lot of information about how much the distribution smears out as velocity drops. Still working on figuring out a rigorous way to examine that.


no, its still .13" per FPS ... how are you getting a quarter inch?
The ultimate truth in paintball is that the interaction between the gun and the player is far and away the largest factor in accuracy, consistency, and reliability.

And yes, Gordon is the sexiest manifestation of "to the front."


#41 Snipez4664

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Posted 23 May 2012 - 10:30 AM

d=2r
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#42 Troy

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Posted 23 May 2012 - 10:33 AM



what im saying is the trend is not a very large one. a major increase in one does not have a very large effect on the other. im not denying a trend, im saying its a small trend.


Ah, right. As it stands the trend says the mean distance from center increases by 0.13" per fps lost, which doesn't seem trivial to me. But keep in mind as well that's the change in mean distance from the center - so it's in the radial direction only. So if you were to look across your shot pattern it's a quarter inch per fps, and suddenly it's not so trivial - and again this is just the average distance from the center, so we're loosing a lot of information about how much the distribution smears out as velocity drops. Still working on figuring out a rigorous way to examine that.


no, its still .13" per FPS ... how are you getting a quarter inch?


I believe what he's saying is that since the vector length is a radius, a vector of .13" would cause a shot spread of .26" in diameter.

EDIT: Damn, Snipez beat me to it!

Though it would seem reasonable - especially if there is variance in both force supplied and the mass of the paintball, I would not want to come to a premature conclusion if there is not any solid evidence to to support that conclusion.



I think that a paintball's weight would effect how much a random vortex would effect the ball's trajectory. It would take a higher magnitude of force to change the flight path of a heavier object than it would a lighter projectile.

Edited by Troy, 23 May 2012 - 10:34 AM.

\m/

#43 Egomaniacal

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Posted 23 May 2012 - 11:14 AM

Gordon -
Here's a plot of what the velocity correlation gives us. At 270 fps, r=2.75 inches and at 285 fps r = 4.8 inches. Again, remember this is a trend of the average distance to the center of the grouping.


Posted Image

That doesn't seem like a small change to me.

Edited by Egomaniacal, 23 May 2012 - 11:26 AM.

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#44 bball

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Posted 23 May 2012 - 12:51 PM

Would it be necessary to parse what is causing the inconsistency in order to better interpret the data? (e.g. a higher mass ball will be moving slightly slower but have greater inertia; a lower mass ball will move slightly faster and have lower inertia)

#45 Troy

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Posted 23 May 2012 - 01:09 PM

Would it be necessary to parse what is causing the inconsistency in order to better interpret the data? (e.g. a higher mass ball will be moving slightly slower but have greater inertia; a lower mass ball will move slightly faster and have lower inertia)


The more data, the better. We can't parse out weight data from the current data set, because it wasn't recorded.
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#46 bball

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Posted 23 May 2012 - 01:18 PM

This sound like a good test:
shoot paintballs at padded surface. Record the FPS of each ball, then recover and weigh each ball, and then look to see if there is any correlation with the inconsistency in FPS.

Edited by bball, 23 May 2012 - 01:19 PM.


#47 UV Halo

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Posted 23 May 2012 - 01:55 PM

Important Question- I've gone and reviewed the entire thread, and the PDFs but, was this test conducted indoors or outdoors?

If it was outdoors, we can assume that there was likely at least 1-3mph winds (3mph winds drift smoke but leave a weather vane still). In these conditions, a higher velocity shot will deviate less due to wind. Alernatively, a higher mass ball will better resist the wind.

Also in regards to velocity fluctuation due to mass- this will be hard to puzzle out with paintballs. Ball dimensions and orientations also contribute to variations in velocity. What I don't know is that with quality paint, what varies more, the mass of the balls or, the sizing (in three dimensions).

#48 Snipez4664

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Posted 23 May 2012 - 02:27 PM

Mass makes no sense as a confounding factor, the lower FPS number (suggesting higher mass) is actually LESS accurate (you'd expect mass to dampen spin/vortex shedding effects).

I lean towards Egomaniacal's "energy lost" explanation in that perhaps the same factor (grabbiness of a seam on the barrel, say) that is lowering fps is also increasing spread. It's odd because RNTLEE's testing with LARGE overbores produced smaller spreads, and so I tend to think that mere ball SIZE in terms of the specific over/under bore per shot is not the culprit either. That leaves us pretty much with friction and aerodynamics (muzzle effect) concerns.

I have a feeling we'll know a lot more shortly
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#49 UV Halo

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Posted 23 May 2012 - 02:37 PM

Mass makes no sense as a confounding factor, the lower FPS number (suggesting higher mass) is actually LESS accurate (you'd expect mass to dampen spin/vortex shedding effects).

I lean towards Egomaniacal's "energy lost" explanation in that perhaps the same factor (grabbiness of a seam on the barrel, say) that is lowering fps is also increasing spread. It's odd because RNTLEE's testing with LARGE overbores produced smaller spreads, and so I tend to think that mere ball SIZE in terms of the specific over/under bore per shot is not the culprit either. That leaves us pretty much with friction and aerodynamics (muzzle effect) concerns.

I have a feeling we'll know a lot more shortly


So, you're suggesting that the lower FPS shots must've had a higher mass, and that barrel fit, marker fluctuation, etc, were not more significant influences on FPS?

Overbore/'matched'/underbore conditions influence friction, friction influences final velocity and, final velocity influences spread in outdoor conditions.

Just to be clear, a faster round is less effected by wind due to the round having a lower duration of wind exposure. A heavier round is less effected by wind due to a higher inertia.

#50 bball

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Posted 23 May 2012 - 02:50 PM

I would also point out that there can be different combinations of factor (Mass and Force) here would be some examples

Heavy Ball 300 FPS
Heavy Ball 290 FPS
Light Ball 300 FPS
Light Ball 290 FPS

and any weight or speed in between. It would seem that the first and the last should be the most and least accurate - however there may be other factors at play and these factors may not have any significant affect. Additionally, unless there is some measured data ranking any particular combination of factors would be difficult.
(BTW UV I just was looking at the External Ballistics Primer :wub: It answered alot of things I wanted to know)




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