Chronograph & PF

[shred]

I sent this one over to the IPSC list, but my posts there regularly don't make it so I'm posting it here too.

The basic question is: Should we round off calculated Power Factors to whole digits? (I say yes)

Rule 5.2.2 (and I'm working from the USPSA 14th ed-- somebody let me know if this is already addressed) says only PF = Weight * Velocity / 1000, and then give the target numbers in whole numbers like 125, 165, etc. Note the lack of decimal places. Note also that the rulebook uses decimal places other places where greater precision seems to be required-- see the Rifle Standard compensator rules, for example).

Any 4th grader can tell you that 164.9 rounded to the nearest whole digit is 165.

Yet we see with regularity the "oops list" at the chronograph listing the poor souls that didn't make Major with a 164.943 or whatever PF.

The rulebook rounds PF numbers to whole numbers, the chronograph rounds velocities to whole numbers and the scale rounds weights to the nearest tenth.

A little Excel work tells me that the sum of worst-case chrono and scale round off could be 0.15 PF points or more. So somebody could chrono 164.86 and still actually be shooting over 165 PF. What's wrong with this picture?

So, I propose to explicitly round calculated PF's to the nearest whole digit. It would be consistent with the rules, would eliminate scale and chrono roundoff errors and considerably reduce the 'I got hosed' factor at the chrono.

Even if we don't do that, this grey area ought to make it onto somebody's 'to be addressed' list.

[Skywalker]

Shred,

I think you have a valid point in this.

At least, since the rulebook says the stage and match results shall be calculated up to the 4th decimal place, it should equally state the decimals (if any) to be used to calculate PF from bullet velocity and weight, or the digits to be used for each and every calculation to be made.

If Vince and other Rulebook writers are listening, they might want to add this issue to their personal list of addenda to the next rulebook.

Probably, we should all agree on the rounding method first.

From a mathematical point of view, rounding a number to the nearest integer gives the following: a number with the first decimal ranging from .1 to .4 leads to a rounding to the lowest nearest integer (e.g. PF 173.4 -> 173), which is actually a truncation rather than a rounding, while a number with the first decimal ranging from .5 to .9 leads to a rounding to the highest nearest integer (e.g. PF 173.7 -> 174).

But, from your proposal, it looks like you are proposing to always round the figures to the highest nearest integer.

Then, once agreed the rounding method, we should define the number of decimals to be used in calculations, and the digit to be rounded (you proposed to round the numbers to integers, but it could be done to the first decimal or whatever else).

Anybody else's thoughts?

[Garfield]

I vaguely seem to remember that Vince (or was it somebody else) had already said that the rules state a minimum PF. And although 124,9 gets rounded to 125, it actually still is below 125. And that therefore rounding was not an option.

Personally I don't care much as to what number of decimals is used, as long as it is clearly stated in the rules and it might not be a bad idea to state how the rounding (if any) should be done, as not everyone might know how it should be done from a mathematical point of view. (It could be defended that rounding should be done to the nearest LOWER intereger).

[Skywalker]

(It could be defended that rounding should be done to the nearest LOWER intereger).

I too don't care for the method, provided it is stated and written.

BTW, that's a truncation, not a rounding...

[Vince Pinto]

Hi guys,

Firstly, due to some necessary rule renumbering, the chrono rules are now covered by Section 5.6 in the new rulebook. However Shred raises an interesting and valid point about decimal places in respect of chrono, and I regret that we didn't address the issue in our last review. Having said that, we can issue a temporary "fix" at any time, by way of a rule interpretation under Section 11.8.

However as I'm not familiar will all brands of chrono and bullet scales, I'd welcome your further input. The primary questions which immediately come to mind in respect of chronos and bullet scales are:

1. Do all makes/models have a user-selectable number of decimal places option?

2. Do all makes/models have a user-selectable round-up or truncate option?

The other issue is I understand that only newer chronos calculate power factor (i.e. you can enter the bullet weight), while older models require the use of a separate calculator. If so, the calculator adds another dimension to the problem, because it's possible that some clubs use a very basic calculator with neither a round-up or truncate option.

And now, as Frasier Crane would say: "I'm listening"

[Skywalker]

Vince,

the chrono I have experience with (Chrony, CED, Oehler) all display the measured velocity the same way: if the velocity is below 1000 fps, they'll display the first decimal digit too (e.g. 945.7 fps), otherwise, if velocity is equal or above 1000 fps they'll display integer numbers only (e.g. 1025 fps).

The CED Millennium chrono will calculate PF based on the average of the measured velocities for a single string (thus it will be an integer or decimal figure depending on the average format according to the above) and bullet measured weight, including the first decimal digit.

I guess we could solve lots of problems by saying that all velocities used to calculate PF shall be rounded to the higher nearest integer (e.g. 942.3 fps -> 943), and all bullet weights shall be rounded to the higher nearest first decimal digit (e.g. 180.34 grains -> 180.4), then with these figures, PF shall be calculated by rounding the result to the higher nearest first decimal digit:

943 x 180.4 = 170.1172 -> 170.2

If the chrono is able to calculate the PF starting from its measured average velocity, the bullet weight shall be entered according to the chrono facility (but where possible to the first decimal digit rounded as described above), and the result shall be handled as above.

Your thoughts guys?

[Neil Beverley]

My main concern is that we mustn't fail someone because of the maths (I know you lot spell it math but I'm English and math just doesn't seem right ). I have checked shred's figures but then I have no reason to doubt him and if we do indeed create a possible anomaly because of the number of decimal places then we must fix it.

I'm not sure that I would like us to round to the nearest integer and would prefer to see PF calculated to 1 or 2 decimal places. On the other hand I'm not overly fired up by this either so will happily go with the flow.

[Vince Pinto]

I'm Australian, and we call it 'rithmetic, as in "readin', 'ritin and 'rithmetic"

[Yoda]

Hi guys,

let's throw in another variable - the PF of a particular load also varies because of differences in temperature, altitude, humidity. Although the chrono measures it to it's best ability I think it is useless to bicker around 0.xx difference in PF looking at the other variables. The other influences can make a difference of 5 PF points!

I raised this issue some time ago and was satisfied with the answer "124.x is below 125 and thus does not make minor and similar for Major". Just let's use some common sense People who load to the edge should not complain if they fall over.

[Garfield]

I raised this issue some time ago and was satisfied with the answer "124.x is below 125 and thus does not make minor and similar for Major".

Ah, that's where I remember it from !

Just let's use some common sense  People who load to the edge should not complain if they fall over.

That's why I shoot PF 150 in PD !

[Vince Pinto]

I guess we could solve lots of problems by saying that all velocities used to calculate PF shall be rounded to the higher nearest integer (e.g. 942.3 fps -> 943), and all bullet weights shall be rounded to the higher nearest first decimal digit (e.g. 180.34 grains -> 180.4), then with these figures, PF shall be calculated by rounding the result to the higher nearest first decimal digit: 943 x 180.4 = 170.1172 -> 170.2

Thanks for your feedback but I have a question, and I know I'm gonna regret asking an Engineer

Firstly my assumption: Different bullet scales, different chronos and different calculators probably have different ways to treat decimals (e.g. floating, sinking, dog-paddling), and some calculators may not have a round-up and/or truncate option.

My question is: In view of the above variables, would it be satisfactory to determine the power factor on a "pre-decimal" WYSIWYG basis?

In other words, a result of 169.0001 and a result of 169.9999) are both treated as being "less than 170" (we ignore the decimal places, and we neither round nor truncate the result)?

[JFD]

The shooter either makes power factor or they don't. 164.9999 is still minor.

The solution is to show up with loads that make the PF, not fiddle with the rules to allow minor loads to make major.

[Skywalker]

JFD,

you missed Shred's original post:

A little Excel work tells me that the sum of worst-case chrono and scale round off could be 0.15 PF points or more. So somebody could chrono 164.86 and still actually be shooting over 165 PF. What's wrong with this picture?

The problem is that if you're close to the edge, you might or might not meet declared PF depending on how the calculation is performed: you might make PF in Italy and not in Germany, with the same measured values, because of the (possible) different calculation accuracy.

Would you like to get a lower classification in a match, because the stats guy won't work with figures up to 4 decimals, but only with 2?

The problem is that the actual rulebook doesn't specify the accuracy level to be used to calculate PF, as it indeed does with stage and match results.

[Skywalker]

Vince,

we need to draw the line somewhere.

I guess we'll have no control over the instruments used to perform PF calculations, unless IPSC doesn't want to deal with the pain of declaring a list of recognized chronos, scales and calculators, as it does with scoring programs.

Thus, the only solution I can come up with is how the output of those instruments have to be treated.

- Velocities: all velocities used for PF calculations below 1000 fps will be rounded to the first decimal digit, equal or above 1000 fps will be rounded to integers. This might not be the easiest solution, but it's how all chronos I know of work and display measured velocities.

- Weights: all weights used for PF calculations will be rounded to the first decimal digit, since this is the most common incremental step I have seen on most of the normal and electronic scales available for reloading.

- P.F.: I don't really care if this figure will be rounded to the first decimal digit or to integers. My guess was that integers were easier to handle and to understand, but I can live with decimals in PF.

- Rounding method: higher nearest integer or higher nearest first decimal digit (as in the example I made in my previous post), according to the defined accuracy for that particular quantity.

Hope I kept this at a minimum level of "engineering"...

[.40AET]

So should a shooter bring his own calculator to a match? One that is capable of ritmetic to 9 decimal places. Then the only question left is, could you convince the chrono man that according to your scientific calculator, you have met the power factor requirement. I've been to chrono stations that use rather primative calculators because they are easy to use. It still seems easier to be 3-5 points over the floor for the given power factor.

[Neil Beverley]

I deleted a lot of text from my priginal post because I thought I was perhaps being too tough but I now see that others are of the same mind.

If you don't make factor, you don't make factor. If the PF being achieved is so tight that it needs to survive by being rounded up then the rounds are being built to too tight a margin.

Once we agree the procedures and measuring criteria I believe we should then truncate the final result to the integer so that 124.99 is regarded as 124.

We can't set a viable number of decimal places in the final result to avoid a PF that doesn't make it being rounded up so as to make it.

12.9, 124.99, 124.999, 124.9999 are all under PF but get rounded so as to make it. So does 124.5 for that matter. At some point, whether 1 decimal place, or 2 or 4, or 10, rounding can end up meaning someone who hasn't made it being treated as if they have. However, truncating the result leaves no ambiguity in the final result.

In the earlier stages there can be some variance but if the criteria is clearly stated then it will be fair for all and consistency is the main thing to strive for.

[Skywalker]

Neil,

I guess you too are starting to miss Shred's original meaning.

Let me try to make a summary.

Stage and Match scores: the rulebook says calculations have to be made with numbers up to (at least) the 4th decimal figure, to ensure the match is scored with due accuracy. Good. Everybody gets treated the same way in every part of the world.

PF calculations: the rulebook doesn't say anything about accuracy to be used to perform the PF calculation. Shred pointed out that, due to different accuracy employed (lacking an official guideline for this), it could happen someone shooting marginally inside the declared PF gets bumped in minor even if he/she's effectively shooting major. Bad. You might or might not make factor depending on the calculation method being used.

The latter is a situation that shall be avoided.

I can agree with all of you that instead of tempting the fate you'd better load up your rounds, and exceed the PF threshold by a healty margin (I shoot @ 178 PF to ensure a 5PF points cushion and still be scored IPSC Standard major...), but in principle I cannot accept the possibility of such an error because there is no unique calculation method specified.

The whole question of rounding figures, or defining a prescribed accuracy to be used, is not to help someone shooting @ 169.8 to be scored major, but to avoid someone effectively shooting @ 170.2 being scored minor because we don't use enough decimals.

Consider the following example.

Bullet weight as read on a Lyman electronic scale: 181.2 grains.

Bullet average velocity as displayed on a Chrony chronograph: 938.4 fps.

PF= 181.2 * 938.4 / 1000 = 170.03808 => Major.

But wait a moment, I'm a lazy chrono guy, and will only consider integer numbers (or I'm a scientific guy, and decide to work rounding to integers):

PF= 181 * 938 / 1000 = 169.778 => Minor

Does this make sense?

[Neil Beverley]

Sky

You misunderstand me if you think I mistunderstand shred.

I agree completely that there should be a definitive method of calculating and I'm not even against your proposals for weights and velocities.

The only point of my last post was that I don't support a final rounding on the PF, whether to an integer or to n decimal places. I think the PF result should be truncated to the integer at the final stage.

[Skywalker]

Neil,

I just re-read your post, and I have to say that the idea of truncating the final result to an integer value appeals to me, because (as you said) it totally eliminates any kind of ambiguity.

My last post (edited with a numeric example), was mainly meant to show that, lacking a precise definition on the number of figures and decimals to be used in PF calculation, we could get a different scoring even if we're (marginally) shooting at declared PF. And this is an unfairness we shall avoid.

[shred]

Truncating is wrong because by truncating you add additional error not in the shooter's favor to the calculation and may Minor even more people that in reality are shooting Major.

I had two points:

1 - There are no decimal places given in the rules for the PF limit.  There are decimal places given in the rules for other limits.  This implies that PF is to be reported in whole numbers (historically we have not done this).  Reporting in whole numbers requires rounding to be most mathematically correct.

2 - Rounding error in chronographs and scales can cause shooters that are actually shooting Major to be scored Minor PF. 

My suggested solution to both is to quit screwing around with reporting PF to three decimal places, which is mathematically garbage and round the chrono results to match the rulebook.

I am suggesting we round only the final result. All intervening results take place at whatever precision they were generated with.

By using standard rounding rules that everybody learned in grade school or doing their taxes (ending between .000000000 and .4999999999, round down. .500000000 and up round up), we not only simplify the math, reduce shooter contention, become consistant in a significant-figures way with the rulebook, and avoid the problem where equipment roundoff error may accidentally Minor somebody that in reality is shooting Major

Anybody remember "significant figures" from science class? There aren't any beyond what the measurements give you. And in this case (excepting maybe the PF-calculating-chronos), they aren't there. To anybody that lives on this stuff 164.9 is 165 if the decimal place isn't supported.

If you really don't like that, how about giving the shooter 1 extra fps on one of their 3 velocities?. The chrono-roundoff-fixing results are similar, although more hassle and less correct.

[Vince Pinto]

Guys,

My hair hurts.

Frankly, if we really need to do it, I don't care how we do it, but I'd like to use the simplest, most concise and least ambiguous language, because apart from obviating our native English speakers (and Australians!) from having problems, we must also consider about 10 foreign language rulebook translations.

For consistency, would the language used in Rule 9.7.1 "recorded to 2 decimal places" be sufficient? Since this rule does not specifically mention rounding up or truncating, the first two decimal places must be taken at face value (e.g. 12.3456789 is recorded as 12.34).

Obviously, "recorded" means "written down", but the determinaton of PF is by the book (e.g. any number below 125 fails to make Minor).

Are we there yet or have I lost the plot?

[shred]

Not really. Rounding is the default way to shorten/report decimals in most cases, and this still doesn't fix the measurement error problem, although it does fix the rulebook ambiguity.

I still prefer 'rounded to the nearest whole number', but the people that enjoy seeing shooters miss PF by 0.1 point could go with "rounded to the nearest tenth". This would eliminate most equipment error from the calculations. I don't believe that the current variety of measurement equipment justifies any further decimal places.

'Rounded to the nearest x' should translate well-- everybody does it and I believe the rounding rules are consistent world-wide.

[Skywalker]

For consistency, would the language used in Rule 9.7.1 "recorded to 2 decimal places" be sufficient?

Sorry Vince,

no, it won't.

Please take another look at the numerical example I made. Your proposed solution, to write down the PF with 2 decimals, won't help in the second case. A shooter actually shooting Major is scored minor even using two decimals for the final result.

Let's make a comparison with match results: it's not only the final result that's specified in format (4 decimals), it's also the stage results (4 decimals again) used to calculate final results, it's the time (recorded at cents of second) used to calculate stage results; no mention is made about scored points on targets only because they are integers not subject to any kind of different accuracy reading...

At the same level, we not only need to specify the format for the PF final result, but we need also to specify the format for the various data (weight and velocity) to be used as input for the calculations.

Does this make sense?

[shred]

Here's another example:

We do a poll. 50% of shooters say they love Vince, with a possible error of plus or minus 5%. The question is: Do half the shooters love Vince? Answer, who knows. With that error, it could be 45%, it could be 55%, it could be anywhere in between.

This is what's happening with the equipment roundoff. By my estimates (and somebody please check them), the shooter's PF is plus-or-minus 0.15, and we don't know any more than that. A "169.99" coming out of the chrono-calculator only means the shooter's actual PF is somewhere between 169.84 and 170.14.

[Skywalker]

Let's recap briefly (or start it all over again).

FACTS:

Bullet weight reading on a Lyman electronic scale: 181.2 grains.

Bullet average velocity reading on a Chrony chronograph: 938.4 fps.

PROBLEM: arising from lack of directions in the rulebook; two different chrono guys performing PF calculations:

1st guy: PF= 181.2 * 938.4 / 1000 = 170.03808 => Major.

2nd guy: PF= 181 * 938 / 1000 = 169.778 => Minor!

There is nothing in the rulebook preventing the second guy doing it, and, yes, before you ask, I've seen the above done in different places (not the minor scoring, but the truncation of readings). This practice could lead to the above error.

Now, solutions welcome.