Making Major At The Chrono

[kevin c]

While I recognize that the cushion most people use to make sure that they make their power factor is a matter of personal comfort, I'd like to know if there is some statistical validity to, say, having a five point cushion vs. ten, etc. Set aside the standard chrono voodoo that is outside of our control (altitude, humidity, temp, crabby electronics and the like) and assume that the chrono is the one we use on our own home range, under the same conditions you tested the ammo under.

I know that there will be a difference if your ammo has a higher SD, but for the sake of argument, let's just say that the SD is 10, and that half your rounds will be over the floor, and half will be under. Let's further assume that they will average out right at the desired PF, and that the wt of the bulllets pulled will all be the same (my Zero's and MG's are, within a couple of tenths, at least).

At the club level, any round that makes your PF is definitive. At the tournament level, the average of any three at/over the PF makes it, and you may shoot six, so that taking the best three's average will help you even if some of the fired rounds are under. This seems to me to say that, at the club level, you just need to be fairly sure that one in six of your rounds will meet PF, and at the tournament level, three of six, or may be just two of six if your SD/AD is really small.

I'm no statistician though. Any bright science types there willing to tackle this?

[sincityshooter]

Too much time on your hands. The difference between shooting a 168 PF load and a 165PF load is very little. So, why bother?

[GlocknSchpiel]

but for the sake of argument, let's just say that the SD is 10, and that half your rounds will be over the floor, and half will be under.

Kevin, using your chriteria, I'd go with the safety factor of 10. You said half above and half below.

Which of those 300 rounds you have loaded will go High?

The odds may be in your favor, but they are just as likely to be against.

The SO/RO grabs (randomly) 6 test rounds from your box, loads and tests. OOOoooppss, all 6 were under. They're nice there and allow you to shoot 6 more with YOUR gun. They get to choose the rounds..... Oh SH&*! Luck is against you again and all 6 were below. DQ, Pack up and GO HOME!

Better make sure that your SLOWEST round will at least make PF.

As far as the local matches? I'd still shoot the same "AbovePF" load that would be used in National level matches. Why get used to one load for local just to have to learn a different one for the Nats?

Take care,

Bert

[B.J. Norris]

Under powered ammo is not a DQ. If Major, you go minor. If minor, you shoot for no score.

[Nik Habicht]

Kevin,

I've been shooting the same load in my production/idpa guns since the beginning of the year --- and suffered anxiety at the chrono at every big match. My ammo was chrono'ed at the the IDPA Winter Championships in Springfield MA, after spending the night in the car in maybe 20 degree temps, at the Summer Blast, the Mid-Atlantic Section Championship, the FGN (in maybe 100 degree heat), and at the Area 8 match. There is a 1 power factor difference in chrono reading from lowest to highest, except for the IDPA match, where they don't give you results, they just score you pass/fail. That consistency tells me that that ammo is good to go anywhere, and that's what I'm looking for more than anything else, in respect to chrono. My power factor is around 133.... for the 125 requirement of minor production....

[EricW]

To *guarantee* that approximately 99% of all your loads are above 165, you need your average velocity to be 3 standard deviations above the velocity you need to make major. For example:

Your load makes major at 1000 fps.

The standard deviation of your load (output from chrono) is 15 fps. In order to guarantee that none of your rounds will go below 1000 fps, your average velocity needs to be 1045 fps.

As an equation:

Vavg = PF_MinVelocity + 3*SD

Make sense? In statistics, this is known as the "3 sigma" or "6 sigma" (+/- 3 sigma) rule. All you really need to know is that multiplying your standard deviation by 3 will give you the proper statistical cushion. This does NOT account for altitude/temperature/humidity variations, so you may want an extra standard deviation's cushion for that. i.e. Multiply by 4.

Vavg = PF_MinVelocity + 4*SD

Where did I come up with this mumbo jumbo? From the Gaussian Distribution. It's a mathematical description of how measurements of randomly distributed events (eg. shot velocities) distribute around an average value.

This picture is of "the bell curve" which decribes how repetitive measurements of a quantity distribute around an average value. It doesn't make it really obvious what's going on, but the decimal numbers indicate the fraction of data that is covered by the standard deviations.

e.g.

At 1 standard deviation, 2*(.3413)*100 = 68% of the data is included

At 2 standard deviations 2*(.3413+.1359) = 95.4% of the data is included

At 3 standard deviations, 2*(.3413+.1359+.0214) = 99.72% of the data is included.

At 4 standard deviations, 2*(.3413+.1359+.0214+.00135) = 99.99% of the data is included.

This is why 3 standard deviations is generally used as the statistical cushion to describe the operating range of a process. Using 4 SD's only adds .3% of the data, but expands the range by 33%. Not a practical tradeoff.

Aside from knowing/estimating your loads variation due to ambient conditions (which need to added to the above calculations), this is really the only "scientific/statistical" way to come up with a proper velocity cushion.

Great question by the way. I haven't had to grind through this stuff in years. Great refresher...

[eric nielsen]

I load 6-7PF above the minimum. For Open now that is 171-172.

My M.A.D. is always less than 15. Mean avg deviation.

PACT says right in their papers that SD is pretty meaningless for sample sizes of less than 100 shots. I hate math too much to prove or disprove that statement.

[Rufus The Bum]

My major match ammo is loaded to 170pf using MG and Titegroup, it has never varied outside of between 169-173 at ANY major match. I use the same load at sea level and as high as 3000asl, so I just stick with what has proven to work. I honestly notice NO DIFFERENCE between 165 and 173pf, so I load it to where I know it will make major.

[GlocknSchpiel]

Hey BJ, I should've said "in IDPA", Sorry, You may very well be right for IPSC or USPSA.

In IDPA, the PF is there for a purpose and there's not a Major/Minor in the same division.

Y'all take care,

Bert

[EricW]

PACT says right in their papers that SD is pretty meaningless for sample sizes of less than 100 shots. I hate math too much to prove or disprove that statement. 

The question was for a "scientific" method. Using statistics is the only scientific method I know of to answer the question. The technique I listed above is pretty much the primary method used among scientists, engineers, and manufacturers to describe variations in data. There are others, but they are much less common.

I don't have my PACT book handy, so I can't verify the statement. Like everything in statistics, one's results improve with the number of samples. However, a blanket statement that a SD using less than 100 samples is "meaningless" is not accurate. If that were so, then your mean velocity figures are also "meaningless," at which point you might as well throw your chrono in the trash as it's not giving you any meaningful information. Right?

Wrong.

You're getting meaningful information, but just a less than complete picture. Statistical data sets of less than 100 samples are used in science and industry all the time - as GUIDELINES. If someone puts 10, 20, or 30 shots over their chrono and uses that data knowledgeably as a GUIDELINE for how to proceed, they will generally make good decisions.

[DogmaDog]

The real short answer is 5. Load to 170 PF.

Eric is pointing us in the right direction with the normal distribution, and standard deviations, but there are a couple of things we can expand upon.

First off, your standard deviation describes how far individual rounds will stray from the average, but the chronographing procedure has us average the measured velocity of 3 rounds, not just one. It turns out that the variance (which is standard deviation squared) for groups of 3 rounds will be one third the variance seen in single shots...the larger the sample, the smaller the departure from the true mean velocity.

There's a pretty simple function in Microsoft Excel you can use to calculate the probability that you won't make major with your load, called "NORMDIST"

The format is =NORMDIST(X, Mean, Standard Deviation, Cumulative)

X is a value you select. NORMDIST will spit out the probability that you'll get a value lower than X, so X should be the velocity you need to make major, or minor.

Mean is the average velocity of your load

Standard deviation is the Standard Deviation of your load.

Cumulative should be set to "TRUE" you want the cumulative probability that your rounds will be any value less than or equal to X.

So if you need 1000 fps to make major, and your measured average velocity is exactly 1000 fps, there's 50% chance any single round won't make it. Say Std. D = 10. NORMDIST (1000, 1000, 10, TRUE) = 0.5

If you load to 1010 fps (measured), you've got a 1 standard deviation margin for error. NORMDIST (1000, 1010, 10, True) = 0.1586..., or about 16% chance that any one round will fail to make major.

Now for the club procedures it's pretty simple. One in six rounds has to make major, so you just figure out the probability that they all won't make major and subtract it from 100% to figure out the chance that one or some will make major. In the first example, the chance that all 6 won't make it is 0.5 ^6 = 1/64 = =0.015, or less than 2% chance that you'll be shooting minor, even if your ammo is right at the power factor floor (on average).

For the second example, the chance that any one round fails is about 16%. The chance all will fail is 0.16 ^6 = 0.0000159. Really, really small.

I'll leave it to you to figure the chance that a 3 round group will fail to make major, and I don't know how to treat the best 3 out of 6 statistically.

There are a couple of other caveats.

1) You really should be using the "T" distribution as opposed to the Normal distribution. The "T" distribution looks like a bell curve, but it's a little wider and not as peaked in the middle. The difference reflects results we should expect when dealing with small sample sizes, like more variability, and less certainty. Microsoft Excel doesn't have easy functions using the "T" distribution like it does for the Normal distribution, or else I'd use them.

2) You probably aren't shooting a whole lot of rounds over your chrony. 10? 20? So you don't REALLY know what the average velocity is for your load (which includes all the rounds you made and will make with the recipe...that's what you're trying to get information about, right?). But you can calculate CONFIDENCE INTERVALS for your measurements...figure out the degree of statistical uncertainty in your calculations.

Mathematically, the question you'll anser is, "If the mean velocity for this load really were X, and the std. D really were Y, what is the likelihood that I'd measure a mean velocity this much slower/faster?" This is not quite the question you really want to answer, but it's as close as one graduate statistics class will get you.

In Excel, the CONFIDENCE function will do this.

CONFIDENCE(alpha, std_dev, size)

alpha is a number between 0 and 1. Usually statisticians set alpha at 0.05. 1-alpha is the "confidence level"...95%

std_dev is the standard deviation of the POPULATION (not your sample, but that's all you have, so use it)

size is the size of your sampled population (10 rounds, or 20, or whatever)

So if I plug in CONFIDENCE(0.05, 10, 10) (I want the 95% confidence interval where the standard deviation is 10fps, and I shoot 10 shot strings), I get the answer "6.197..." That means that if I took numerous samples of 10 rounds from a population that really did have a mean velocity of 1000 fps, and really did have a standard deviation of 10 fps, then 95% of my samples would have a mean velocity within +/-6.197 fps of 1000fps.

Pick a level for alpha you feel comfortable with, and then assume the actual mean velocity of your load is at the low end of the confidence interval (by chance, you just happened to chrono faster than average rounds, and the real average may be as low as 994 fps).

Finally, my real answer. From playing around with the stats, it became apparent really quickly that the probability that you'll fail to make major through random chance, even with only 1 standard deviation as your cushion, is extremely minute, and therefore negligible compared to sources of systematic error (the weather, differences in chronographs, the loose chamber of the test gun, etc. etc. etc.) I therefore decided to go with the recommendations based on personal shooting experience many years longer than my own, from this site...load about 5 pf higher than the minimum you need.

Anyway, I hope you actually have excel, and can play around with some of those functions. I'd still like to figure out how to deal with the best 3 out of 6 statistically. I'll think about it some more.

Good luck,

DogmaDog

[kevin c]

Thanks to you all, especially EricW and DogmaDog (though I must confess to having the worst headache trying to follow you folks ).

[davecutts]

You know I did take a statistics class a year ago, and most of what Eric and DogmaDog said made some sense, or at least they've cloaked a bunch of BS in enough pesudo- sientific/stats lingo to make it passable to an undereducated goof ball like me.

[MoNsTeR]

I'm glad someone else hashed out the statistical details so I didn't have to, I have enough homework as it is

It's also worth pointing out the "rule of 30", that a sample size of 30 is usually all you need for the measurements of the basic statistics like mean and SD to closely approximate their true values. Trying only 10 rounds may be risky, but trying 100 is wasted effort.

Though if someone were really ambitious, they could chrono 100 or 200 rounds and give the raw data, the velociy of each round, and one of us mathematical types could analyze it and see how closely it hews to a Normal distribution.

[Patrick Sweeney]

To follow up on EricW and the idea that the SD of any test group less than 100 rounds is "menaingless":

The only meaningful test sample of any group is to test them all. Period. Not exactly useful for our purposes. The test sample group has a statistical confidence when compared to its larger group size. If you test the velocity of ten rounds out of a 500 round batch, you have tested to a higher degree of validity (statistically) than a factory that has tested 100 out of a ten million production batch. However, testing of ever larger amounts gets you running full-speed into the Law of Diminishing Returns. If you want a quick glimpse of the LDM, look at ErcW's bell curve. Notice how each SD from the mean is smaller than the previous one. And each will be smaller, to inifinity. So, at a certian point, your efforts to determine "exactly" what you want to know will return so little data for the effort expended as to be useless.

While the mathematics of testing, sampling, and predictions is fun (I knew guys who could practically get a woody, back in college, just walking into classes for higher math) what we need is useful advice.

Here it is: If you don't want to get nicked at a match, load your ammo to at least 5PF over the threshold. Do not use a load with an SD greater than 20-30 if you can. If you find your load is a tack-driving load, but the SD is up there, 50-60, bump your load to a 173PF (for Major).

Nice curve, by the way.

[DogmaDog]

Hmmm,

Looking at the short answer (5), and looking at Eric's answer (load to 3 SD's above 165 PF, it looks like they're about the same. For a 200 grain bullet, 10FPS (1 SD) = 2 PF, so 3 SDs would put those rounds at 171 PF. Hmmmm.

Also, I think the Pact manual was discussing Extreme Spread as a statistic, saying it is useless with a sample size less than 100, and that Standard Deviation is much more reliable. This makes sense, since my Extreme Spreads with 15 round chrony samples extends only to about 1.5 SDs from the mean, and we've already seen that data as far out as 3 SDs is to be expected (only about 1 in 100, but if you load thousands, then you'll see them).

Anyway, I'm currently working on a model to predict the velocity vs. charge weight I'll get with different weight bullets in .45. Maybe I'll nerd off on that in a later post.

DogmaDog