BPS vs. law of diminishing returns

[Scircal]

Let me preface this by saying it's not so much a physics question as it is an efficiency question (basically, economic), so I'm not sure if it belongs on this board, but here goes....

Been thinking about this ever since I watched the DM4 video over in paintball talk. One of the selling points of markers these days is cycle rate, or how many paintballs per second a marker could spit out. But I was thinking, how much better is it to shoot 20 bps vs., say, 19 bps? What's the marginal rate of return to your probability of hitting your target for firing that next ball? At some point, it seems certain that the probability enhancement of hitting target X would be greatly reduced to the point of not really being worth the opportunity cost of saving that paintball and shooting it at target Y (i.e. being able to shoot one ball at target Y clearly has a large rate of return vs. being able to shoot zero balls at Y). Anyway, the whole opportunity cost question is really something else beyond my initial thought. Have paintball guns reached that point? Is it possible for them to? Or are have they already passed that point and shooting 15 bps is all you really need to get the job done efficiently.

I recognize that there are a TON of variables to consider, but it seems you could do some basic testing that would yield results needed to make some formulation on bps vs. diminishing returns. I've thought of a few testing ideas. Like to get some other opinions first. Or perhaps it's a futile exercise. It's and it's getting hard to think.

What are your thoughts?

The slogan may be "accuracy by volume;" My question is, what volume?

[bleachit]

I think that it would vary from individual, basically because each person would have a different reaction time. Some one would be able to pick up a target faster, someone else may be able to get the first shot out faster, where as some one else may be able to lead the target better, assuming it is a moving target. I would guess that someone who can do these things well would require fewer bps and someone who couldn't would need a higher bps to get the job done.

edit: when I wrote this I was thinking about this with respect to the distance between balls being shorter at higher rof.

[Scircal]

I see your point, but...

I was thinking past the point of acquiring a target and firing in the path of the person. For example, if someone was running tangentially from the shooter within the range of the gun, and the shooter was firing a constant stream of paint. At some bps, it will be nearly impossible for the runner to make it through without getting hit. But at, say, 2 bps, it may be very possible for the person to get through. I think the fastest a human has been clocked at is 22 mph, or 32 fps. Given that maximum speed, there must be some rate of fire (call it "X" bps)where you'd have a 95 percent probability of hitting that person in the above scenario. If you fire at X+1 bps, you might have a 96 percent probability. And if firing at X-1 bps gave you only a 90 percent probability of success, then you're clearly seeing a diminishing marginal rate of return for volume of fire.

If you establish the absolute human maximums, and the corresponding bps is 22, you can be sure, in most cases, you won't have to fire that fast. And you can adjust you're rate of fire down to optimize paint usage. It also then becomes basically moot whether a gun can fire 30 or 31 bps because you've far surpassed the necessary bps.

But then I'm assuming there that 22 bps reaches optimimality. I don't know if its more or less than that. I realize there are plenty of scenarios, but it seems like you could, using average figures for some variables, develop some rules of thumb about effective bps which could be useful.

[athomas]

Allowing:

- A fast player running 30 ft/s (most will never run this fast with gear and from a dead stop). Lets alow 20ft/s.
- allowing a paintball speed is 250ft/sec at a sweetspot distance.
- lets say an average player is 2 ft thick (front to back with gear)
- Lets say an average player is 2 ft wide

A player takes 100ms to cross the sweetspot running at 20ft/s. It takes a paintball 8ms to travel the width of his body. This is time he can't occupy the sweetspot. the next ball must hit the sweetspot in 100ms after the 1st has left. The total time is 108ms. At that time between balls, a marker has to fire at a rate of only 9.3 bps.

Any increase from this number increases the chances of a break and a hit due to errant balls and other inaccuracies.

[Miscue]

Higher numbers provide a psychological advantage.

[Lord_Whoopass]

lol this reminds me of college economics...

Anyways, I think that you are correct in the fact of it not being worth shooting 30bps... when sweetspotting the gap between the balls is what really makes the difference. if your not firing a fast enough BPS the opponent has a better chance of "running the gap"... Higher BPS leaves the gap smaller and gives you a higher percentage of hitting the opponent... I actually sat down and ran the numbers about 6 months ago after a teammate told me that its so much better to shoot 25bps... I used 1ft as my moving target (width of a person), which I thought would be about average... I used 15fps for the average speed at which the target was moving(because you never really hit top speed and acceleration variables)... I think the number I came out with for the optimal number of BPS was 17 point something...

[rdb123]

We'd be better off using statistics to figure this out. We'd need a Mu (average) and a Rho (standard deviation) however. If someone could find me values for those, I could try to work something out.

[trains are bad]

I've long thought that 10bps was a good seat of the pants 'enough' figure.

[phyregod]

Simplified

Well, sometimes you have to over simplify.

We'll say the balls travel at 280FPS
Fired at 10BPS they would be 28 feet apart.
Said paintballs moves 28 feet in 1/10th of a second.
An object 18 inches wide traveling at 15fps (180 inches/sec) takes 1/10 second to cross a set point.

So if it takes the object 1/10th of a second to cross the point, and the point is open for 1/10th of a second, A 1bps increase would close the gap just enough.

Re-worked for a 9 inch target (head w/ mask or thin torso sideways) you would need to fire at least 21bps


So, I would say that anything over 21BPS is over kill.

[Aleis]

Too fast?

Actualy the extra speed is important, even if the human possible max BPS is around 20 if that was the max the gun could shoot you'd have to be pulling the trigger in perfect rythm with the cycle of the marker, even more impossible. But having a marker with a higher BPS rate allows for imperfactions in the rythm of the person pulling the trigger.