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
Handicap Calculator Handicap Table,NOTE: THESE VALUES ARE FOR THE NEW ArcheryGB HANDICAP SCHEME ACTIVE FROM 1 JANUARY 2023. FOR THE OLD SCHEME PLEASE SEE THE 'Old Handicap Calculator' SHEET. Spreadsheet,For specific rounds and classifications please use <a href="https://www.archerycalculator.co....
docs.google.com
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!