metric 252 equivalent

little-else

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Does anyone run a progression scheme like the 252 scheme for metic distances? if so how do you go about it and do you differentiate between the different bow styles by altering the scratch score for example.
We are proposing to start a scheme in 2021 but are getting a little bogged down between simplicity of organisation and the complex maths that are actually needed to make the scoring properly comparable
 

Sinbad

Member
That looks like a good place to start. Gives everyone something to aim for when doing metric rounds. Will mention this idea to the club.
 

JonLockley

New member
Interesting idea. There's nothing as frustrating as scoring 9 for a perfect X, not that it's my biggest problem :)

So to get from 252 to 270, have you just assumed that half the 36 arrows will be rounded up a point? Because the area of the inner ring on any coloured zone is obviously smaller than the outer one. Maybe you could do a practical test and get a bunch of archers with a range of abilities to score with both an Imperial and Metric equivalent system at the same time to see how the difference comes out in practice?
 

tabashir

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KC do you have a link to handicap tables that include 252 rounds please? I can't find any from an, albeit quick, search.

Would only see it as of interest though, for the purposes of the 252 scheme, to Jon's point, not sure that anything other than a simple rounding of half the arrows is really needed. Different clubs do the 252 slightly differently anyway, some require 3 qualifiers, some just 2. Some only allow an end of sighters, others don't specify.

The point being that the 252, I believe, was only intended to be a guide for the archer that they may be ready for going to the next distance and can likely do so without expecting to spend the session constantly hunting for arrows. Please correct me if I'm mistaken here.
 

JonLockley

New member
I agree, I don't think the 252 was ever intended to be as rigorous a round, but more of a performance tracking aid. But *if* you did want the rigour, I'm just saying I'm not sure a simple rounding works, but happy to be corrected if I'm wrong.
 

little-else

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This is why I asked the question, to see what other do as it isnt as simple in reality as to assign half the arrows to the higher score in a colour. For example, the 10 is only 25% of the area of the gold, the 8 is only 41% of the red and so forth. also you have an increased distance so do you knock off a couple of points for that? However, it is easy to relate to and makes it a little more challenging than the imperial 252.

To get a true comparator score you need to chuck some decent statistics at it and bring this up at committee and people go to sleep or tell you to do whatever you want. Now this last advice might be OK unless the person charged with doing so has just applied the handicap tables at one diastance that isnt representative and you end up with a skewed scratch score.
this goes back to my observations on the classification scheme where you can get a world record score at 60yds and still only be a second class archer with a handicap of 11 rather than zero.
the 252 is easy to understand, you stick all of the arrows in the red or at least on average so a group around the size of the blue at each distance is par. group size then dictates rather than true score and a real flyer is not punished too severely (unless you use a higher par for compound which would make a comeback very hard but there you go, you choose the equipment) Adjustment for bow style at different distances very understandable and h/c tables tend to work better for this the further away you are from target.
 

KidCurry

Well-known member
KC do you have a link to handicap tables that include 252 rounds please? I can't find any from an, albeit quick, search.
Yes, and no :) The site I use is Crystal Palace Bowman, Handicap section. Archery Handicap Tables
Go to the bottom of the list of rounds and click on the non-standard round. Add the correct data for arrows/distance/face size etc
Hope this helps
 

tabashir

Supporter
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You are totally right Jon, as LE shows with some of the figures, simple rounding does not work to make a true equivalent round since as you move out from the centre, the difference in area of the colours becomes less.

Would love to see the calcs you have so far LE. It would be very interesting.

KC - Awesome thanks. The CPB site is one that I have bookmarked as I use it a fair bit. Had never noticed the non-standard round option before. That will be a great help in future.
 

JonLockley

New member
This is why I asked the question, to see what other do as it isnt as simple in reality as to assign half the arrows to the higher score in a colour. For example, the 10 is only 25% of the area of the gold, the 8 is only 41% of the red and so forth. also you have an increased distance so do you knock off a couple of points for that? However, it is easy to relate to and makes it a little more challenging than the imperial 252. To get a true comparator score you need to chuck some decent statistics at it and bring this up at committee and people go to sleep or tell you to do whatever you want.
Yep. But also, it would only scale as the area if you're evenly spreading arrows over the target. Now it might look like that's what I'm doing half the time(!) but obviously, the archer is trying to focus the shots into a tight group and bias them towards the higher score. How successful they are depends on their ability with respect to the chosen distance. So you're right, some good stats are needed to answer this rigourously. Seeing as it looks as though we're due for another lockdown soon, maybe I'll write a few simulations to keep myself busy...

Personally, I like the 252 round as a training exercise for pressure shots. When you're at your next distance, you don't have many arrows to make up for a couple of bad shots.
 

little-else

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You are totally right Jon, as LE shows with some of the figures, simple rounding does not work to make a true equivalent round since as you move out from the centre, the difference in area of the colours becomes less.

You also get a bigger problem with working out the stats of where an arrow will land and still be in the group.
The idea behind the handicap tables ect is that arrows will travel within a cone that is related to the archers ability to hold the bow still in the centre of the target. now once a group gets bigger than the size of the target this is no longer true and the deviation at longer distances can also be caused by other factors.
with rifle shooting you can say that shooter A with a centred group will score at least 45 ex 50 if their wobble is say 2 minutes of angle as the bullseye is that size. now what you cant predict with that limited information is how many the shooter will score, it could be 50 ex 50 with them evenly spread around the bull or it could be 45 with a group of about 1/4 of a minute of angle based in the edge of the bullseye or it could be 40 with a dispersed group that is centred but large as each shot was fired at the extreme of the wobble.
repeating the shooting under the same conditions will provide you with an average and collecting a mass of data will tell you quite a bit about whether your par score is about right
unfortunately things can then fall down if for example you have a batch of ammunition that cant hold a 1 minute of angle group as then you start to get holes in the group, even with a better shooter than shooter A and our shooter would be more likely to score around 40 than a score near 50.
The NRA and military used to collect such data as it was useful for the defence of the realm and to kick the ammo manufacturers if need be but AGB cant do so as no-one seems to record plots of their shooting arrow by arrow unless they are asked to by their coach and I dont see that too often.
 

JonLockley

New member
The idea behind the handicap tables ect is that arrows will travel within a cone that is related to the archers ability to hold the bow still in the centre of the target.
Yeah, I think I'll write a little sim that "shoots" a few thousand arrows with a Normal/Gaussian probability function to represent archers of different ability - just to keep my hand in with a bit of coding.
 

little-else

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Yep. But also, it would only scale as the area if you're evenly spreading arrows over the target. Now it might look like that's what I'm doing half the time(!) but obviously, the archer is trying to focus the shots into a tight group and bias them towards the higher score. How successful they are depends on their ability with respect to the chosen distance. So you're right, some good stats are needed to answer this rigourously. Seeing as it looks as though we're due for another lockdown soon, maybe I'll write a few simulations to keep myself busy...

Personally, I like the 252 round as a training exercise for pressure shots. When you're at your next distance, you don't have many arrows to make up for a couple of bad shots.
Now I agree and can give a simple example. To get 252 you have to keep 70% of the arrows within the red ( and that assumes an even balance between gold and flyers so if you create a plot for say 36 arrows with this in mind and place them as a square grid on your target you will end up with a metric equivalent of around 268, which to all intents and purposes si the same as allocating the arrows to their scoring zones by area. If you then try and add a calculation for the metric being at a slightly longer distance you dont get a score drop of anywhere near 10% because those arows going straight still go straight and the corresponding drop in score is only a couple of points. It is when you trya nd model a smaller group that is hollow so more 7's than 9's that you start to see differences.
I shot at 40 yds compound on a still day last week and scored 316/324 11 of those were 10's so if it was metric scoring the increase in score wouldnt be 18 as the simple conversion method would suggest giving a score of 334. The range of possible scores if converted to metric scoring would be between 316 and 356, I actually got 329 so increase is 32.5% of available possible increase rather than supposed 50% and this fits in to what you would expect on a target that has different areas for the scoring zones
 

little-else

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Yeah, I think I'll write a little sim that "shoots" a few thousand arrows with a Normal/Gaussian probability function to represent archers of different ability - just to keep my hand in with a bit of coding.
I agree that the flight and impact of a group of arrows will best be served by using a natural log to decide where the arrows in the group go rather than straight lines/cone. i have described the change in group size at changing distances to a trumpet mouth rather than an ice cream cone. that has raised more questions as to how the arrow flies around corners rather than been seen as an analogy
 

tabashir

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Yeah, I think I'll write a little sim that "shoots" a few thousand arrows with a Normal/Gaussian probability function to represent archers of different ability - just to keep my hand in with a bit of coding.
Would love to see the code when you have it. Can maybe even help with it depending on the language you decide on.
 

ArcheryFox

Active member
This is totally my jam, but I'm late to the party!
Guess that's what you get for slacking from AI over the holidays...

I made a spreadsheet to do this stuff if anyone wants a play :)


Would love to see the code when you have it. Can maybe even help with it depending on the language you decide on.
The spreadsheet 'code' above is also available in python and I would be happy to share parts of it or ideas if you are interested.
It does AGB handicaps, the archery Australia system, and a couple of custom handicap schemes.
I hard coded common rounds, including IFAA ones - because someone needs to answer which GMB is harder ;) , and has the possibility to create your own.
I really should put it online at some point though it's still WIP...


I agree that the flight and impact of a group of arrows will best be served by using a natural log to decide where the arrows in the group go rather than straight lines/cone. i have described the change in group size at changing distances to a trumpet mouth rather than an ice cream cone.
When you say flight do you mean the effect on the size of the group due to the distance travelled?
This is sort of factored in to David Lane's handicap system though he pursues it is more from the accounting for poundage and junior ratings perspective. Perhaps more explicit is the way Australia deal with it using a d^2 factor (d is distance). This still isn't perfect, however, and it's one of my side projects to try and come up with a better relation but the d^2 works remarkably well at the elite end of the sport.
I'd be interested in your ideas for using the natural log as an alternative.
(Though it occurs to me you may be talking about the distribution of the group at a fixed distance (i.e. that it follows a Gaussian...)?)


This is why I asked the question, to see what other do as it isn't as simple in reality as to assign half the arrows to the higher score in a colour. For example, the 10 is only 25% of the area of the gold, the 8 is only 41% of the red and so forth.
This is correct, but it gets a bit more subtle when we assume the archer is trying to hit the middle.
If they shot arrows randomly without aiming we might expect them to get a 10 only 25% of the time and a 9 the other 75%, but if they follow a Gaussian distribution then arrows will cluster about the centre and the probability of a 10 will actually be a bit higher.
(This is further complicated by the fact the target is a circle, not a line, so the final distribution across 1-D score values (1-10) is a Weibull/Rayleigh type.)


In an effort to try and claim that I am staying on topic - you can use the spreadsheet above (like the Crystal Palace site) to compare your imperial and metric 252s.
I'd be interested to see how well the 'add one to half the arrows' approach compares to the real values - even as a back of the envelope calculation I'd expected it to be reasonable, but perhaps not based on your experiment LE.

An issue you will have in making a similar metric scheme is that you will never be able to match the handicaps at all distances if you want to also keep the same score for all distances - I came across a similar issue when trying to do 252 awards for different bowstyles at my club.
My suggestion would perhaps be to match the handicaps at 50yds and 50m to choose your metric score for 'best fit'.
Alternatively perhaps match them at 90m and 100yds to ensure the 'end point' of both schemes are the same.

As others have said - the 252 is all about encouraging progression, especially at the lower levels, and isn't an official award.
Overall I'd say don't overthink it and get your members shooting (well... when they can safely...), progressing, and hooked on collecting shinies.
I do understand the desire to get it 'correct' however. ;)

I wrote all this on a coffee break, so it may not all be super clear, but I'd be happy to clarify anything or discuss further.
I really enjoy this stuff (sad, I know) and it's hard enough to find people to chat to about either archery or statistics, never mind both at once!
 

tabashir

Supporter
Supporter
Archery and bashing out a bit of code, add in a little game (ie achieving 252), what's not to like!

That's an amazing job on the spreadsheet there AF. I haven't had chance to study in detail yet.

I really struggled with stats on my maths A level though, scraped it by doing well in the applied maths instead so may have to rely on your more knowledgeable folks in that area.

I did wonder if there may be a bias based on the fact that the archer is intending to hit the centre not spread the arrows out.
 

JonLockley

New member
Hi guys,

So I knocked together a bit of not so production Python - this is just for fun during the lockdown and not intended to be serious. I used a random number generator following a Gaussian distribution of probability to simulate the archer aiming. A good archer (or one shooting well within their range) has a small standard deviation, a less able archer (or one shooting well beyond their 252 range) has a larger one. Surprisingly the difference between the metric and imperial scores is actually reasonably constant until you get to an archer who is nailing the yellows a lot of the time.

That's perhaps not so surprising, because if you take the extreme case, where someone scores 36 10s, the Imperial round will knock you down a whole 36 points. I guess the same is true if you hit 36 8s and are scored 36 7s, but I'd have to ask...why? :)

Anyway, here are a few outputs, just to pass the time..,
 

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