now the thing about missing the boss, esp with
longbow is that there isnt usually an even distribution, the individual's errors or the spining of the arrows or any other cause makes the arrows all go off to the left or the right rather than evenly spread around the target
Yes.
However...
In my handicap adventures I have considered trying to factor in what happens from having an off-centre group or an oval rather than circular group (i.e. enhanced L/R spread etc). I was also interested in seeing how much incorrect distance estimation could impact field archery scores*.
However, all algorithms rely heavily on the fact that everything is circular, and these circles lie exactly on top of one another. This allows us to reduce the problem from 2 to 1 dimensions**, eventually getting a nice simple equation that can be easily applied to many target sizes/distances/faces.
If we break from this symmetry then you'd need to do the calculations numerically using a computer - either like JohnLockley did in post #20, or with a numerical integration code - instead of having one direct equation. This is far less general as you would need to generate a different set of numerical tables for different combinations of face size, distance and handicap. As you allude to, this would take a lot of time and effort and likely be too daunting to users to be practically useful***.
My general approach to get around this is to acknowledge that archery does not reward tight groups in the wrong place.
At a competition you are rewarded on score - if you could have scored more by moving your group, well that's your fault!
As such, if we remove ourselves from their origin relating to group size (angular deviation) then the handicap scores can still provide a benchmark of your overall ability. You just have to acknowledge that your improvements in handicap can come from more than just a shrinking of groups.
As I allude to in footnote ***, there is a balance between a functional system that most archers/records officers can use, rather than a complicated system tuned to an individual archer. For a nationwide AGB scheme the former is the priority.
there are small changes in the scores achieved on say a 90m proportional target shot at 20m and one shot at 30m suitably scaled.
Aha!
Don't forget that if you were to be scaling everything correctly here you would also need to scale your arrow diameter (a key number in any handicap algorithm) not just the target size!!
If you wanted to compare properly you would need to be shooting arrows that were just 22% (= 20m/90m) of the diameter of your normal ones. Alternatively, if you were to take your scores from a scaled target at 20m you would need to be shooting arrows 4.5 times as thick at 90m to compare!
In fact - this is one of the reasons (
compound especially) archers tend to shoot a noticeably higher handicap indoors when they use maximum diameter arrows on small targets****. If you want a better comparison across seasons I recommend experimenting with the 'arrow diameter' parameter in the spreadsheet above.
in rifle shooting you sometimes have problems getting good groups at short range because the bullet hasnt "gone to sleep" [...] Not a problem we suffer from but vibration is.
I have a little more to add here.
In archery if you have issues with contact with a rest/riser/etc. it will show up in poor groups at short range. The effect will disappear at longer ranges as the arrow stabilises, just like a bullet.
At the other end if your poundage is too low/arrows too heavy/distance too far, you will see the groups opening up excessively at long range as the arrows begin to parachute.
Comparing handicaps at a range of distances can help highlight any potential issues if there is a trend or large discrepancy.
*Fun fact I discovered - it is actually harder in terms of handicaps to get MB and GMB field (even if you shot all the targets on the flat) than it is to get MB and GMB target! (for gent
compound at least, but also a few other bowstyles I expect)
**Happy to elaborate on this.
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.
***One of the biggest issues I feel with this topic is that it is often poorly explained and the average archer finds it too daunting to even bother with. I try and point people to the slightly simplified explanation
here so that they can hopefully get a broader idea of what the handicap means and why it can be useful.
****Again, if you use the spreadsheet and run the numbers you find that the only place max diameter arrows really make a difference is for compound archers on the indoor rounds where the size of the x ring becomes comparable to the size of the arrow. Anywhere else and you will generally pick up just one or two points across the entire competition. Given the difficulties of tuning thick arrows and changing setup this is why I usually recommend (non-compound) archers stick with one setup indoors and out.